Sample records for pattern applying fourier

1. Fourier convergence analysis applied to neutron diffusion Eigenvalue problem

International Nuclear Information System (INIS)

Lee, Hyun Chul; Noh, Jae Man; Joo, Hyung Kook

2004-01-01

Fourier error analysis has been a standard technique for the stability and convergence analysis of linear and nonlinear iterative methods. Though the methods can be applied to Eigenvalue problems too, all the Fourier convergence analyses have been performed only for fixed source problems and a Fourier convergence analysis for Eigenvalue problem has never been reported. Lee et al proposed new 2-D/1-D coupling methods and they showed that the new ones are unconditionally stable while one of the two existing ones is unstable at a small mesh size and that the new ones are better than the existing ones in terms of the convergence rate. In this paper the convergence of method A in reference 4 for the diffusion Eigenvalue problem was analyzed by the Fourier analysis. The Fourier convergence analysis presented in this paper is the first one applied to a neutronics eigenvalue problem to the best of our knowledge

2. Applied Fourier analysis from signal processing to medical imaging

CERN Document Server

Olson, Tim

2017-01-01

The first of its kind, this focused textbook serves as a self-contained resource for teaching from scratch the fundamental mathematics of Fourier analysis and illustrating some of its most current, interesting applications, including medical imaging and radar processing. Developed by the author from extensive classroom teaching experience, it provides a breadth of theory that allows students to appreciate the utility of the subject, but at as accessible a depth as possible. With myriad applications included, this book can be adapted to a one or two semester course in Fourier Analysis or serve as the basis for independent study. Applied Fourier Analysis assumes no prior knowledge of analysis from its readers, and begins by making the transition from linear algebra to functional analysis. It goes on to cover basic Fourier series and Fourier transforms before delving into applications in sampling and interpolation theory, digital communications, radar processing, medical i maging, and heat and wave equations. Fo...

3. Selection of unstable patterns and control of optical turbulence by Fourier plane filtering

DEFF Research Database (Denmark)

Mamaev, A.V.; Saffman, M.

1998-01-01

We report on selection and stabilization of transverse optical patterns in a feedback mirror experiment. Amplitude filtering in the Fourier plane is used to select otherwise unstable spatial patterns. Optical turbulence observed for nonlinearities far above the pattern formation threshold...

4. Two dimensional Fourier transform methods for fringe pattern analysis

Science.gov (United States)

Sciammarella, C. A.; Bhat, G.

An overview of the use of FFTs for fringe pattern analysis is presented, with emphasis on fringe patterns containing displacement information. The techniques are illustrated via analysis of the displacement and strain distributions in the direction perpendicular to the loading, in a disk under diametral compression. The experimental strain distribution is compared to the theoretical, and the agreement is found to be excellent in regions where the elasticity solution models well the actual problem.

5. Fourier Transform Infrared Radiation Spectroscopy Applied for Wood Rot Decay and Mould Fungi Growth Detection

OpenAIRE

Jelle, Bjørn Petter; Hovde, Per Jostein

2012-01-01

Material characterization may be carried out by the attenuated total reflectance (ATR) Fourier transform infrared (FTIR) radiation spectroscopical technique, which represents a powerful experimental tool. The ATR technique may be applied on both solid state materials, liquids, and gases with none or only minor sample preparations, also including materials which are nontransparent to IR radiation. This facilitation is made possible by pressing the sample directly onto various crystals, for exa...

6. Optimization of sampling pattern and the design of Fourier ptychographic illuminator.

Science.gov (United States)

Guo, Kaikai; Dong, Siyuan; Nanda, Pariksheet; Zheng, Guoan

2015-03-09

Fourier ptychography (FP) is a recently developed imaging approach that facilitates high-resolution imaging beyond the cutoff frequency of the employed optics. In the original FP approach, a periodic LED array is used for sample illumination, and therefore, the scanning pattern is a uniform grid in the Fourier space. Such a uniform sampling scheme leads to 3 major problems for FP, namely: 1) it requires a large number of raw images, 2) it introduces the raster grid artefacts in the reconstruction process, and 3) it requires a high-dynamic-range detector. Here, we investigate scanning sequences and sampling patterns to optimize the FP approach. For most biological samples, signal energy is concentrated at low-frequency region, and as such, we can perform non-uniform Fourier sampling in FP by considering the signal structure. In contrast, conventional ptychography perform uniform sampling over the entire real space. To implement the non-uniform Fourier sampling scheme in FP, we have designed and built an illuminator using LEDs mounted on a 3D-printed plastic case. The advantages of this illuminator are threefold in that: 1) it reduces the number of image acquisitions by at least 50% (68 raw images versus 137 in the original FP setup), 2) it departs from the translational symmetry of sampling to solve the raster grid artifact problem, and 3) it reduces the dynamic range of the captured images 6 fold. The results reported in this paper significantly shortened acquisition time and improved quality of FP reconstructions. It may provide new insights for developing Fourier ptychographic imaging platforms and find important applications in digital pathology.

7. Relative-coordinate determination for visual double stars by applying Fourier transforms

Directory of Open Access Journals (Sweden)

2013-01-01

Full Text Available We discuss the software developed for the purpose of determining the relative coordinates (position angle θ and separation ρ for visual double or multiple stars. It is based on application of Fourier transforms in treating CCD frames of these systems. The objective was to determine the relative coordinates automatically to an extent as large as possible. In this way the time needed for the reduction of many CCD frames becomes shorter. The capabilities and limitations of the software are examined. Besides, the possibility of improving is also considered. The software has been tested and checked on a sample consisting of CCD frames of 165 double or multiple stars obtained with the 2m telescope at NAO Rozhen in Bulgaria in October 2011. The results have been compared with the corresponding results obtained by applying different software and the agreement is found to be very good.

8. Fourier Transform Infrared Radiation Spectroscopy Applied for Wood Rot Decay and Mould Fungi Growth Detection

Directory of Open Access Journals (Sweden)

Bjørn Petter Jelle

2012-01-01

Full Text Available Material characterization may be carried out by the attenuated total reflectance (ATR Fourier transform infrared (FTIR radiation spectroscopical technique, which represents a powerful experimental tool. The ATR technique may be applied on both solid state materials, liquids, and gases with none or only minor sample preparations, also including materials which are nontransparent to IR radiation. This facilitation is made possible by pressing the sample directly onto various crystals, for example, diamond, with high refractive indices, in a special reflectance setup. Thus ATR saves time and enables the study of materials in a pristine condition, that is, the comprehensive sample preparation by pressing thin KBr pellets in traditional FTIR transmittance spectroscopy is hence avoided. Materials and their ageing processes, both ageing by natural and accelerated climate exposure, decomposition and formation of chemical bonds and products, may be studied in an ATR-FTIR analysis. In this work, the ATR-FTIR technique is utilized to detect wood rot decay and mould fungi growth on various building material substrates. An experimental challenge and aim is to be able to detect the wood rot decay and mould fungi growth at early stages when it is barely visible to the naked eye. Another goal is to be able to distinguish between various species of fungi and wood rot.

9. Optimal defocus selection based on normed Fourier transform for digital fringe pattern profilometry.

Science.gov (United States)

Kamagara, Abel; Wang, Xiangzhao; Li, Sikun

2017-10-01

Owing to gamma-effect robustness and high-speed imaging capabilities, projector defocusing of binary-coded fringe patterns is by far the most widely used and effective technique in generating sinusoidal fringe patterns for three-dimensional optical topography measurement with digital fringe projection techniques. However, this technique is not trouble-free. It is borne with uncertainty and challenges mainly because it remains somewhat difficult to quantify and ascertain the level of defocus required for desired fidelity in sinuousness of the projected fringe pattern. Too much or too little defocusing will affect the sinuosity accuracy of fringe patterns and consequently jeopardize the quality of the measurement results. In this paper, by combining intrinsic phase spectral sensitivities and normed Fourier transform, a method to quantify the amount of defocus and subsequently select the optimal degree of sinuosity for generating digital sinusoidal fringe patterns with projector defocusing for fringe pattern optical three-dimensional profilometry is proposed. Numerical simulations plus experiments give evidence of the feasibility and validity of the proposed method in enabling an improved digital binary defocusing technique for optical phase-shift profilometry using the digital fringe projection technique.

10. Characterization of Campylobacter jejuni applying flaA short variable region sequencing, multilocus sequencing and Fourier transform infrared spectroscopy

DEFF Research Database (Denmark)

Josefsen, Mathilde Hartmann; Bonnichsen, Lise; Larsson, Jonas

flaA short variable region sequencing and phenetic Fourier transform infrared (FTIR) spectroscopy was applied on a collection of 102 Campylobacter jejuni isolated from continuous sampling of organic, free range geese and chickens. FTIR has been shown to serve as a valuable tool in typing...

11. Applying and Developing Patterns in Teaching

DEFF Research Database (Denmark)

Bennedsen, Jens; Eriksen, Ole

2003-01-01

A community of teachers and researchers within computer science has adopted the idea of patterns and developed a set of pedagogical patterns. These patterns capture best practices in teaching. From our research and teaching practice we have observed that pedagogical patterns are useful...... enriches the notion of pedagogical patterns. Inspired by conditions for learning we identify three values in teaching in the field of engineering-related educations. Further we present a value-based template for guidelines in teaching, causing a better understanding of the patterns and help teachers...

12. Gastric cancer differentiation using Fourier transform near-infrared spectroscopy with unsupervised pattern recognition

Science.gov (United States)

Yi, Wei-song; Cui, Dian-sheng; Li, Zhi; Wu, Lan-lan; Shen, Ai-guo; Hu, Ji-ming

2013-01-01

The manuscript has investigated the application of near-infrared (NIR) spectroscopy for differentiation gastric cancer. The 90 spectra from cancerous and normal tissues were collected from a total of 30 surgical specimens using Fourier transform near-infrared spectroscopy (FT-NIR) equipped with a fiber-optic probe. Major spectral differences were observed in the CH-stretching second overtone (9000-7000 cm-1), CH-stretching first overtone (6000-5200 cm-1), and CH-stretching combination (4500-4000 cm-1) regions. By use of unsupervised pattern recognition, such as principal component analysis (PCA) and cluster analysis (CA), all spectra were classified into cancerous and normal tissue groups with accuracy up to 81.1%. The sensitivity and specificity was 100% and 68.2%, respectively. These present results indicate that CH-stretching first, combination band and second overtone regions can serve as diagnostic markers for gastric cancer.

13. Reference Beam Pattern Design for Frequency Invariant Beamforming Based on Fast Fourier Transform

Directory of Open Access Journals (Sweden)

Wang Zhang

2016-09-01

Full Text Available In the field of fast Fourier transform (FFT-based frequency invariant beamforming (FIB, there is still an unsolved problem. That is the selection of the reference beam to make the designed wideband pattern frequency invariant (FI over a given frequency range. This problem is studied in this paper. The research shows that for a given array, the selection of the reference beam pattern is determined by the number of sensors and the ratio of the highest frequency to the lowest frequency of the signal (RHL. The length of the weight vector corresponding to a given reference beam pattern depends on the reference frequency. In addition, the upper bound of the weight length to ensure the FI property over the whole frequency band of interest is also given. When the constraints are added to the reference beam, it does not affect the FI property of the designed wideband beam as long as the symmetry of the reference beam is ensured. Based on this conclusion, a scheme for reference beam design is proposed.

14. Preconditioners based on windowed Fourier frames applied to elliptic partial differential equations

NARCIS (Netherlands)

Bhowmik, S.K.; Stolk, C.C.

2011-01-01

We investigate the application of windowed Fourier frames to the numerical solution of partial differential equations, focussing on elliptic equations. The action of a partial differential operator (PDO) on a windowed plane wave is close to a multiplication, where the multiplication factor is given

15. Pattern recognition applied to uranium prospecting

Energy Technology Data Exchange (ETDEWEB)

Briggs, P L; Press, F [Massachusetts Inst. of Tech., Cambridge (USA). Dept. of Earth and Planetary Sciences

1977-07-14

It is stated that pattern recognition techniques provide one way of combining quantitative and descriptive geological data for mineral prospecting. A quantified decision process using computer-selected patterns of geological data has the potential for selecting areas with undiscovered deposits of uranium or other minerals. When a natural resource is mined more rapidly than it is discovered, its continued production becomes increasingly difficult, and it has been noted that, although a considerable uranium reserve may remain in the U.S.A., the discovery rate for uranium is decreasing exponentially with cumulative exploration footage drilled. Pattern recognition methods of organising geological information for prospecting may provide new predictive power, as well as insight into the occurrence of uranium ore deposits. Often the task of prospecting consists of three stages of information processing: (1) collection of data on known ore deposits; (2) noting any regularities common to the known examples of an ore; (3) selection of new exploration targets based on the results of the second stage. A logical pattern recognition algorithm is here described that implements this geological procedure to demonstrate the possibility of building a quantified uranium prospecting guide from diverse geologic data.

16. Gradient pattern analysis applied to galaxy morphology

Science.gov (United States)

Rosa, R. R.; de Carvalho, R. R.; Sautter, R. A.; Barchi, P. H.; Stalder, D. H.; Moura, T. C.; Rembold, S. B.; Morell, D. R. F.; Ferreira, N. C.

2018-06-01

Gradient pattern analysis (GPA) is a well-established technique for measuring gradient bilateral asymmetries of a square numerical lattice. This paper introduces an improved version of GPA designed for galaxy morphometry. We show the performance of the new method on a selected sample of 54 896 objects from the SDSS-DR7 in common with Galaxy Zoo 1 catalogue. The results suggest that the second gradient moment, G2, has the potential to dramatically improve over more conventional morphometric parameters. It separates early- from late-type galaxies better (˜ 90 per cent) than the CAS system (C˜ 79 per cent, A˜ 50 per cent, S˜ 43 per cent) and a benchmark test shows that it is applicable to hundreds of thousands of galaxies using typical processing systems.

17. Applying Fourier Transform Mid Infrared Spectroscopy to Detect the Adulteration of Salmo salar with Oncorhynchus mykiss

Science.gov (United States)

Moreira, Maria João

2018-01-01

The aim of this study was to evaluate the potential of Fourier transform infrared (FTIR) spectroscopy coupled with chemometric methods to detect fish adulteration. Muscles of Atlantic salmon (Salmo salar) (SS) and Salmon trout (Onconrhynchus mykiss) (OM) muscles were mixed in different percentages and transformed into mini-burgers. These were stored at 3 °C, then examined at 0, 72, 160, and 240 h for deteriorative microorganisms. Mini-burgers was submitted to Soxhlet extraction, following which lipid extracts were analyzed by FTIR. The principal component analysis (PCA) described the studied adulteration using four principal components with an explained variance of 95.60%. PCA showed that the absorbance in the spectral region from 721, 1097, 1370, 1464, 1655, 2805, to 2935, 3009 cm−1 may be attributed to biochemical fingerprints related to differences between SS and OM. The partial least squares regression (PLS-R) predicted the presence/absence of adulteration in fish samples of an external set with high accuracy. The proposed methods have the advantage of allowing quick measurements, despite the storage time of the adulterated fish. FTIR combined with chemometrics showed that a methodology to identify the adulteration of SS with OM can be established, even when stored for different periods of time. PMID:29621135

18. Fast Fourier and discrete wavelet transforms applied to sensorless vector control induction motor for rotor bar faults diagnosis.

Science.gov (United States)

Talhaoui, Hicham; Menacer, Arezki; Kessal, Abdelhalim; Kechida, Ridha

2014-09-01

This paper presents new techniques to evaluate faults in case of broken rotor bars of induction motors. Procedures are applied with closed-loop control. Electrical and mechanical variables are treated using fast Fourier transform (FFT), and discrete wavelet transform (DWT) at start-up and steady state. The wavelet transform has proven to be an excellent mathematical tool for the detection of the faults particularly broken rotor bars type. As a performance, DWT can provide a local representation of the non-stationary current signals for the healthy machine and with fault. For sensorless control, a Luenberger observer is applied; the estimation rotor speed is analyzed; the effect of the faults in the speed pulsation is compensated; a quadratic current appears and used for fault detection. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

19. Factorization of products of discontinuous functions applied to Fourier-Bessel basis.

Science.gov (United States)

Popov, Evgeny; Nevière, Michel; Bonod, Nicolas

2004-01-01

The factorization rules of Li [J. Opt. Soc. Am. A 13, 1870 (1996)] are generalized to a cylindrical geometry requiring the use of a Bessel function basis. A theoretical study confirms the validity of the Laurent rule when a product of two continuous functions or of one continuous and one discontinuous function is factorized. The necessity of applying the so-called inverse rule in factorizing a continuous product of two discontinuous functions in a truncated basis is demonstrated theoretically and numerically.

20. Microstructure imaging of the YBCO thin film/MgO substrate interface: HRTEM and Fourier analysis of the Moire fringe pattern

International Nuclear Information System (INIS)

Auzary, S.; Pailloux, F.; Denanot, M.F.; Gaboriaud, R.J.

1998-01-01

Detailed microstructural aspects of the interface between YBaCuO thin films and MgO substrate are studied by means of a Fourier analysis of Moire fringe pattern obtained from HRTEM investigations of plan view samples. The main features of the observations are large, well oriented crystallographic domains surrounded by wide boundaries. HRTEM investigations together with the Fourier analysis show evidence of both orthorhombic and pseudo-tetragonal structure in the YBaCuO film. An accommodation mechanism is suggested from the Fourier analysis of the Moire fringe pattern. (orig.)

1. Quantitative EEG Applying the Statistical Recognition Pattern Method

DEFF Research Database (Denmark)

Engedal, Knut; Snaedal, Jon; Hoegh, Peter

2015-01-01

BACKGROUND/AIM: The aim of this study was to examine the discriminatory power of quantitative EEG (qEEG) applying the statistical pattern recognition (SPR) method to separate Alzheimer's disease (AD) patients from elderly individuals without dementia and from other dementia patients. METHODS...

2. Nycterohemeral eating and ruminating patterns in heifers fed grass or corn silage: analysis by finite Fourier transform.

Science.gov (United States)

Deswysen, A G; Dutilleul, P; Godfrin, J P; Ellis, W C

1993-10-01

Average daily and within-day nycterohemeral patterns of eating and ruminating behavior were determined in six Holstein-Friesian heifers (average BW = 427 kg) given ad libitum access to either corn or grass silage in a two-period crossover design. Rhythm components (number of cycles/24 h) were characterized by finite Fourier transform of the 24-h mastication activities as measured during 4 d by continuous jaw movement recordings. Average daily voluntary intake of corn silage was 8.2% greater (P = .05) than that for grass silage and was associated (P finite Fourier transform was reparameterized to express the amplitude (as periodograms) and phase of each rhythm component. Rhythm Components 1, 3, and 4 contributed primarily to explaining the total dispersion of the 24-h series of time spent eating and ruminating, for both silage types and individual heifers. Relative importance of Rhythm Component 1 of time spent eating, indicative of a main circadian pattern, was related positively to pedigree value for milk production (P = .01) and negatively to milk protein concentration (P = .09).(ABSTRACT TRUNCATED AT 250 WORDS)

3. Estimation of fringe orientation for optical fringe patterns with poor quality based on Fourier transform.

Science.gov (United States)

Tang, Chen; Wang, Zhifang; Wang, Linlin; Wu, Jian; Gao, Tao; Yan, Si

2010-02-01

Fringe orientation represents an important property of fringes. The estimation of orientation from a poor quality fringe image is still a challenging problem faced in this area. This paper introduces a new approach for estimating optical fringe orientation with a poor quality image. This approach is based on the power spectrum analysis of the Fourier transform. We evaluate the performance of this algorithm via application to a variety of test cases and comparison with the widely used gradient-based method and accumulate-differences method. The experimental results show that our method is capable of calculating fringe orientation robustly even when the quality of fringe images is considerably low because of high or low density, high noise, and low contrast. Under the same conditions, our accuracy is even better than that obtained with the gradient-based and accumulate-differences methods, especially for fringe images with poor quality.

4. The Fourier analysis applied to the relationship between (7)Be activity in the Serbian atmosphere and meteorological parameters.

Science.gov (United States)

Rajačić, M M; Todorović, D J; Krneta Nikolić, J D; Janković, M M; Djurdjević, V S

2016-09-01

Air sample monitoring in Serbia, Belgrade started in the 1960s, while (7)Be activity in air and total (dry and wet) deposition has been monitored for the last 22 years by the Environment and Radiation Protection Department of the Institute for Nuclear Sciences, Vinca. Using this data collection, the changes of the (7)Be activity in the air and the total (wet and dry) deposition samples, as well as their correlation with meteorological parameters (temperature, pressure, cloudiness, sunshine duration, precipitation and humidity) that affect (7)Be concentration in the atmosphere, were mathematically described using the Fourier analysis. Fourier analysis confirmed the expected; the frequency with the largest intensity in the harmonic spectra of the (7)Be activity corresponds to a period of 1 year, the same as the largest intensity frequency in Fourier series of meteorological parameters. To analyze the quality of the results produced by the Fourier analysis, we compared the measured values of the parameters with the values calculated according to the Fourier series. Absolute deviations between measured and predicted mean monthly values are in range from 0.02 mBq/m(3) to 0.7 mBq/m(3) for (7)Be activity in air, and 0.01 Bq/m(2) and 0.6 Bq/m(2) for (7)Be activity in deposition samples. Relatively good agreement of measured and predicted results offers the possibility of prediction of the (7)Be activity. Copyright © 2016 Elsevier Ltd. All rights reserved.

5. Continuous firefly algorithm applied to PWR core pattern enhancement

Energy Technology Data Exchange (ETDEWEB)

Poursalehi, N., E-mail: npsalehi@yahoo.com [Engineering Department, Shahid Beheshti University, G.C., P.O. Box 1983963113, Tehran (Iran, Islamic Republic of); Zolfaghari, A.; Minuchehr, A.; Moghaddam, H.K. [Engineering Department, Shahid Beheshti University, G.C., P.O. Box 1983963113, Tehran (Iran, Islamic Republic of)

2013-05-15

Highlights: ► Numerical results indicate the reliability of CFA for the nuclear reactor LPO. ► The major advantages of CFA are its light computational cost and fast convergence. ► Our experiments demonstrate the ability of CFA to obtain the near optimal loading pattern. -- Abstract: In this research, the new meta-heuristic optimization strategy, firefly algorithm, is developed for the nuclear reactor loading pattern optimization problem. Two main goals in reactor core fuel management optimization are maximizing the core multiplication factor (K{sub eff}) in order to extract the maximum cycle energy and minimizing the power peaking factor due to safety constraints. In this work, we define a multi-objective fitness function according to above goals for the core fuel arrangement enhancement. In order to evaluate and demonstrate the ability of continuous firefly algorithm (CFA) to find the near optimal loading pattern, we developed CFA nodal expansion code (CFANEC) for the fuel management operation. This code consists of two main modules including CFA optimization program and a developed core analysis code implementing nodal expansion method to calculate with coarse meshes by dimensions of fuel assemblies. At first, CFA is applied for the Foxholes test case with continuous variables in order to validate CFA and then for KWU PWR using a decoding strategy for discrete variables. Results indicate the efficiency and relatively fast convergence of CFA in obtaining near optimal loading pattern with respect to considered fitness function. At last, our experience with the CFA confirms that the CFA is easy to implement and reliable.

6. Continuous firefly algorithm applied to PWR core pattern enhancement

International Nuclear Information System (INIS)

Poursalehi, N.; Zolfaghari, A.; Minuchehr, A.; Moghaddam, H.K.

2013-01-01

Highlights: ► Numerical results indicate the reliability of CFA for the nuclear reactor LPO. ► The major advantages of CFA are its light computational cost and fast convergence. ► Our experiments demonstrate the ability of CFA to obtain the near optimal loading pattern. -- Abstract: In this research, the new meta-heuristic optimization strategy, firefly algorithm, is developed for the nuclear reactor loading pattern optimization problem. Two main goals in reactor core fuel management optimization are maximizing the core multiplication factor (K eff ) in order to extract the maximum cycle energy and minimizing the power peaking factor due to safety constraints. In this work, we define a multi-objective fitness function according to above goals for the core fuel arrangement enhancement. In order to evaluate and demonstrate the ability of continuous firefly algorithm (CFA) to find the near optimal loading pattern, we developed CFA nodal expansion code (CFANEC) for the fuel management operation. This code consists of two main modules including CFA optimization program and a developed core analysis code implementing nodal expansion method to calculate with coarse meshes by dimensions of fuel assemblies. At first, CFA is applied for the Foxholes test case with continuous variables in order to validate CFA and then for KWU PWR using a decoding strategy for discrete variables. Results indicate the efficiency and relatively fast convergence of CFA in obtaining near optimal loading pattern with respect to considered fitness function. At last, our experience with the CFA confirms that the CFA is easy to implement and reliable

7. Principles of Fourier analysis

CERN Document Server

Howell, Kenneth B

2001-01-01

Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas.Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author''s development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based ...

8. Reducing aberration effect of Fourier transform lens by modifying Fourier spectrum of diffractive optical element in beam shaping optical system.

Science.gov (United States)

Zhang, Fang; Zhu, Jing; Song, Qiang; Yue, Weirui; Liu, Jingdan; Wang, Jian; Situ, Guohai; Huang, Huijie

2015-10-20

In general, Fourier transform lenses are considered as ideal in the design algorithms of diffractive optical elements (DOEs). However, the inherent aberrations of a real Fourier transform lens disturb the far field pattern. The difference between the generated pattern and the expected design will impact the system performance. Therefore, a method for modifying the Fourier spectrum of DOEs without introducing other optical elements to reduce the aberration effect of the Fourier transform lens is proposed. By applying this method, beam shaping performance is improved markedly for the optical system with a real Fourier transform lens. The experiments carried out with a commercial Fourier transform lens give evidence for this method. The method is capable of reducing the system complexity as well as improving its performance.

9. Applying Moving Objects Patterns towards Estimating Future Stocks Direction

Directory of Open Access Journals (Sweden)

Galal Dahab

2016-01-01

Full Text Available Stock is gaining vast popularity as a strategic investment tool not just by investor bankers, but also by the average worker. Large capitals are being traded within the stock market all around the world, making its impact not only macro economically focused, but also greatly valued taking into consideration its direct social impact. As a result, almost 66% of all American citizens are striving in their respective fields every day, trying to come up with better ways to predict and find patterns in stocks that could enhance their estimation and visualization so as to have the opportunity to take better investment decisions. Given the amount of effort that has been put into enhancing stock prediction techniques, there is still a factor that is almost completely neglected when handling stocks. The factor that has been obsolete for so long is in fact the effect of a correlation existing between stocks of the same index or parent company. This paper proposes a distinct approach for studying the correlation between stocks that belong to the same index by modelling stocks as moving objects to be able to track their movements while considering their relationships. Furthermore, it studies one of the movement techniques applied to moving objects to predict stock movement. The results yielded that both the movement technique and correlation coefficient technique are consistent in directions, with minor variations in values. The variations are attributed to the fact that the movement technique takes into consideration the sibling relationship

10. Fourier series

CERN Document Server

Tolstov, Georgi P

1962-01-01

Richard A. Silverman's series of translations of outstanding Russian textbooks and monographs is well-known to people in the fields of mathematics, physics, and engineering. The present book is another excellent text from this series, a valuable addition to the English-language literature on Fourier series.This edition is organized into nine well-defined chapters: Trigonometric Fourier Series, Orthogonal Systems, Convergence of Trigonometric Fourier Series, Trigonometric Series with Decreasing Coefficients, Operations on Fourier Series, Summation of Trigonometric Fourier Series, Double Fourie

11. Grip-pattern recognition: Applied to a smart gun

NARCIS (Netherlands)

Shang, X.

2008-01-01

In our work the verification performance of a biometric recognition system based on grip patterns, as part of a smart gun for use by the police ocers, has been investigated. The biometric features are extracted from a two-dimensional pattern of the pressure, exerted on the grip of a gun by the hand

12. Beyond Fourier

Science.gov (United States)

Hoch, Jeffrey C.

2017-10-01

Non-Fourier methods of spectrum analysis are gaining traction in NMR spectroscopy, driven by their utility for processing nonuniformly sampled data. These methods afford new opportunities for optimizing experiment time, resolution, and sensitivity of multidimensional NMR experiments, but they also pose significant challenges not encountered with the discrete Fourier transform. A brief history of non-Fourier methods in NMR serves to place different approaches in context. Non-Fourier methods reflect broader trends in the growing importance of computation in NMR, and offer insights for future software development.

13. Beyond Fourier.

Science.gov (United States)

Hoch, Jeffrey C

2017-10-01

Non-Fourier methods of spectrum analysis are gaining traction in NMR spectroscopy, driven by their utility for processing nonuniformly sampled data. These methods afford new opportunities for optimizing experiment time, resolution, and sensitivity of multidimensional NMR experiments, but they also pose significant challenges not encountered with the discrete Fourier transform. A brief history of non-Fourier methods in NMR serves to place different approaches in context. Non-Fourier methods reflect broader trends in the growing importance of computation in NMR, and offer insights for future software development. Copyright © 2017 Elsevier Inc. All rights reserved.

14. PABRE-Proj: applying patterns in requirements elicitation

OpenAIRE

Palomares Bonache, Cristina; Quer Bosor, Maria Carme; Franch Gutiérrez, Javier

2013-01-01

Software requirement patterns have been proposed as a type of artifact for fostering requirements reuse. In this paper, we present PABRE-Proj, a tool aimed at supporting requirements elicitation and specification. Peer Reviewed

15. [Apply fourier transform infrared spectra coupled with two-dimensional correlation analysis to study the evolution of humic acids during composting].

Science.gov (United States)

Bu, Gui-jun; Yu, Jing; Di, Hui-hui; Luo, Shi-jia; Zhou, Da-zhai; Xiao, Qiang

2015-02-01

The composition and structure of humic acids formed during composting play an important influence on the quality and mature of compost. In order to explore the composition and evolution mechanism, municipal solid wastes were collected to compost and humic and fulvic acids were obtained from these composted municipal solid wastes. Furthermore, fourier transform infrared spectra and two-dimensional correlation analysis were applied to study the composition and transformation of humic and fulvic acids during composting. The results from fourier transform infrared spectra showed that, the composition of humic acids was complex, and several absorbance peaks were observed at 2917-2924, 2844-2852, 2549, 1662, 1622, 1566, 1454, 1398, 1351, 990-1063, 839 and 711 cm(-1). Compared to humic acids, the composition of fulvci acids was simple, and only three peaks were detected at 1725, 1637 and 990 cm(-1). The appearance of these peaks showed that both humic and fulvic acids comprised the benzene originated from lignin and the polysaccharide. In addition, humic acids comprised a large number of aliphatic and protein which were hardly detected in fulvic acids. Aliphatic, polysaccharide, protein and lignin all were degraded during composting, however, the order of degradation was different between humic and fulvci acids. The result from two-dimensional correlation analysis showed that, organic compounds in humic acids were degraded in the following sequence: aliphatic> protein> polysaccharide and lignin, while that in fulvic acids was as following: protein> polysaccharide and aliphatic. A large number of carboxyl, alcohols and ethers were formed during the degradation process, and the carboxyl was transformed into carbonates. It can be concluded that, fourier transform infrared spectra coupled with two-dimensional correlation analysis not only can analyze the function group composition of humic substances, but also can characterize effectively the degradation sequence of these

16. Conditional Random Fields for Pattern Recognition Applied to Structured Data

Directory of Open Access Journals (Sweden)

Tom Burr

2015-07-01

Full Text Available Pattern recognition uses measurements from an input domain, X, to predict their labels from an output domain, Y. Image analysis is one setting where one might want to infer whether a pixel patch contains an object that is “manmade” (such as a building or “natural” (such as a tree. Suppose the label for a pixel patch is “manmade”; if the label for a nearby pixel patch is then more likely to be “manmade” there is structure in the output domain that can be exploited to improve pattern recognition performance. Modeling P(X is difficult because features between parts of the model are often correlated. Therefore, conditional random fields (CRFs model structured data using the conditional distribution P(Y|X = x, without specifying a model for P(X, and are well suited for applications with dependent features. This paper has two parts. First, we overview CRFs and their application to pattern recognition in structured problems. Our primary examples are image analysis applications in which there is dependence among samples (pixel patches in the output domain. Second, we identify research topics and present numerical examples.

17. Applying local binary patterns in image clustering problems

Science.gov (United States)

Skorokhod, Nikolai N.; Elizarov, Alexey I.

2017-11-01

Due to the fact that the cloudiness plays a critical role in the Earth radiative balance, the study of the distribution of different types of clouds and their movements is relevant. The main sources of such information are artificial satellites that provide data in the form of images. The most commonly used method of solving tasks of processing and classification of images of clouds is based on the description of texture features. The use of a set of local binary patterns is proposed to describe the texture image.

18. Fourier Series

polynomials are dense in the class of continuous functions! The body of literature dealing with Fourier series has reached epic proportions over the last two centuries. We have only given the readers an outline of the topic in this article. For the full length episode we refer the reader to the monumental treatise of. A Zygmund.

19. Fourier Series

The theory of Fourier series deals with periodic functions. By a periodic ..... including Dirichlet, Riemann and Cantor occupied themselves with the problem of ... to converge only on a set which is negligible in a certain sense (Le. of measure ...

20. Clifford Fourier transform on vector fields.

Science.gov (United States)

Ebling, Julia; Scheuermann, Gerik

2005-01-01

Image processing and computer vision have robust methods for feature extraction and the computation of derivatives of scalar fields. Furthermore, interpolation and the effects of applying a filter can be analyzed in detail and can be advantages when applying these methods to vector fields to obtain a solid theoretical basis for feature extraction. We recently introduced the Clifford convolution, which is an extension of the classical convolution on scalar fields and provides a unified notation for the convolution of scalar and vector fields. It has attractive geometric properties that allow pattern matching on vector fields. In image processing, the convolution and the Fourier transform operators are closely related by the convolution theorem and, in this paper, we extend the Fourier transform to include general elements of Clifford Algebra, called multivectors, including scalars and vectors. The resulting convolution and derivative theorems are extensions of those for convolution and the Fourier transform on scalar fields. The Clifford Fourier transform allows a frequency analysis of vector fields and the behavior of vector-valued filters. In frequency space, vectors are transformed into general multivectors of the Clifford Algebra. Many basic vector-valued patterns, such as source, sink, saddle points, and potential vortices, can be described by a few multivectors in frequency space.

1. App. 1. Fourier series and Fourier transform

International Nuclear Information System (INIS)

Anon.

1977-01-01

Definitions, formulas and practical properties in quantum mechanics are presented: Fourier series (development of periodic function, Bessel-Parseval equality); Fourier transform (Parseval-Plancherel formula, Fourier transform in three-dimensional space) [fr

2. Median Hetero-Associative Memories Applied to the Categorization of True-Color Patterns

Science.gov (United States)

Vázquez, Roberto A.; Sossa, Humberto

Median associative memories (MED-AMs) are a special type of associative memory based on the median operator. This type of associative model has been applied to the restoration of gray scale images and provides better performance than other models, such as morphological associative memories, when the patterns are altered with mixed noise. Despite of his power, MED-AMs have not been applied in problems involving true-color patterns. In this paper we describe how a median hetero-associative memory (MED-HAM) could be applied in problems that involve true-color patterns. A complete study of the behavior of this associative model in the restoration of true-color images is performed using a benchmark of 14400 images altered by different type of noises. Furthermore, we describe how this model can be applied to an image categorization problem.

3. A Dynamic Interval-Valued Intuitionistic Fuzzy Sets Applied to Pattern Recognition

Directory of Open Access Journals (Sweden)

Zhenhua Zhang

2013-01-01

Full Text Available We present dynamic interval-valued intuitionistic fuzzy sets (DIVIFS, which can improve the recognition accuracy when they are applied to pattern recognition. By analyzing the degree of hesitancy, we propose some DIVIFS models from intuitionistic fuzzy sets (IFS and interval-valued IFS (IVIFS. And then we present a novel ranking condition on the distance of IFS and IVIFS and introduce some distance measures of DIVIFS satisfying the ranking condition. Finally, a pattern recognition example applied to medical diagnosis decision making is given to demonstrate the application of DIVIFS and its distances. The simulation results show that the DIVIFS method is more comprehensive and flexible than the IFS method and the IVIFS method.

4. Fourier-muunnoksesta

OpenAIRE

NIEMELÄ, EERO

2008-01-01

Tutkielman aiheena on Fourier-muunnoksen esittely. Tarkoituksena on erityisesti johdatella lukija Fourier-sarjan ja -muunnoksen käsitteisiin. Fourier-muunnosten teoria kuuluu yleisempään Fourier-analyysin aihepiiriin. Fourier-analyysin keskiössä on tulos, jonka mukaan tietyt ehdot täyttävää funktiota voidaan approksimoida mielivaltaisen tarkasti niin sanotun Fourier-sarjan avulla. Osoitamme, että 2\\pi-jaksollisen funktion Lebesgue-neliöintegroituvuus takaa suppenevan Fourier-sarjakehitelm...

5. Contribution made by multivariate curve resolution applied to gel permeation chromatography-Fourier transform infrared data for an in-depth characterization of styrene-butadiene rubber blends.

Science.gov (United States)

Ruckebusch, C; Vilmin, F; Coste, N; Huvenne, J P

2008-07-01

We evaluate the contribution made by multivariate curve resolution-alternating least squares (MCR-ALS) for resolving gel permeation chromatography-Fourier transform infrared (GPC-FT-IR) data collected on butadiene rubber (BR) and styrene butadiene rubber (SBR) blends in order to access in-depth knowledge of polymers along the molecular weight distribution (MWD). In the BR-SBR case, individual polymers differ in chemical composition but share almost the same MWD. Principal component analysis (PCA) gives a general overview of the data structure and attests to the feasibility of modeling blends as a binary system. MCR-ALS is then performed. It allows resolving the chromatographic coelution and validates the chosen methodology. For SBR-SBR blends, the problem is more challenging since the individual elastomers present the same chemical composition. Rank deficiency is detected from the PCA data structure analysis. MCR-ALS is thus performed on column-wise augmented matrices. It brings very useful insight into the composition of the analyzed blends. In particular, a weak change in the composition of individual SBR in the MWD's lowest mass region is revealed.

6. Teaching pattern diversification for optics course: motivate interest, open minds and apply flexibly

Science.gov (United States)

Wang, Yunxin; Wang, Dayong; Rong, Lu; Zhao, Jie

2015-10-01

Optics is one of the most important basic courses for college students majoring in Applied Physics in university, which can supply the essential theoretical foundation for the subsequent courses such as Information Optics and Electrodynamics etc.. So Optics course plays a supporting effect in the knowledge frame of the college students. Optics course has its own feature, for one thing, many optical contents cannot be understood directly and easily, for another the optical phenomenon or experiments are interesting and can be displayed intuitively. Considering the above feature, the diversiform teaching patterns are developed to improve the teaching effect. To motivate their interest, students have the chance to visit optical laboratory for both teaching demonstration and science research, and voluntary demonstration of teaching apparatus in class are another approach. Furthermore, digital simulation and experimental design according to the classical knowledge are introduced to the optics course, so students can comprehend and verify the optical principle. Students are encouraged to propose new ideas, and these ideas can be achieved with the help of teachers and the funds support from our university. Besides, some talent students will be invited to join a research group composing by graduate students and teachers. In this group, the students have the chance to touch frontier topics in optics. The diversification of teaching patterns can supply a developing space with the rising gradient for students, which can inspire the interest, open their minds and make them apply flexibly by the participatory and inquiry.

7. Pattern recognition applied to infrared images for early alerts in fog

Science.gov (United States)

Boucher, Vincent; Marchetti, Mario; Dumoulin, Jean; Cord, Aurélien

2014-09-01

Fog conditions are the cause of severe car accidents in western countries because of the poor induced visibility. Its forecast and intensity are still very difficult to predict by weather services. Infrared cameras allow to detect and to identify objects in fog while visibility is too low for eye detection. Over the past years, the implementation of cost effective infrared cameras on some vehicles has enabled such detection. On the other hand pattern recognition algorithms based on Canny filters and Hough transformation are a common tool applied to images. Based on these facts, a joint research program between IFSTTAR and Cerema has been developed to study the benefit of infrared images obtained in a fog tunnel during its natural dissipation. Pattern recognition algorithms have been applied, specifically on road signs which shape is usually associated to a specific meaning (circular for a speed limit, triangle for an alert, …). It has been shown that road signs were detected early enough in images, with respect to images in the visible spectrum, to trigger useful alerts for Advanced Driver Assistance Systems.

8. Knowledge-Based Trajectory Error Pattern Method Applied to an Active Force Control Scheme

Directory of Open Access Journals (Sweden)

Endra Pitowarno, Musa Mailah, Hishamuddin Jamaluddin

2012-08-01

Full Text Available The active force control (AFC method is known as a robust control scheme that dramatically enhances the performance of a robot arm particularly in compensating the disturbance effects. The main task of the AFC method is to estimate the inertia matrix in the feedback loop to provide the correct (motor torque required to cancel out these disturbances. Several intelligent control schemes have already been introduced to enhance the estimation methods of acquiring the inertia matrix such as those using neural network, iterative learning and fuzzy logic. In this paper, we propose an alternative scheme called Knowledge-Based Trajectory Error Pattern Method (KBTEPM to suppress the trajectory track error of the AFC scheme. The knowledge is developed from the trajectory track error characteristic based on the previous experimental results of the crude approximation method. It produces a unique, new and desirable error pattern when a trajectory command is forced. An experimental study was performed using simulation work on the AFC scheme with KBTEPM applied to a two-planar manipulator in which a set of rule-based algorithm is derived. A number of previous AFC schemes are also reviewed as benchmark. The simulation results show that the AFC-KBTEPM scheme successfully reduces the trajectory track error significantly even in the presence of the introduced disturbances.Key Words:  Active force control, estimated inertia matrix, robot arm, trajectory error pattern, knowledge-based.

9. Arrangement and Applying of Movement Patterns in the Cerebellum Based on Semi-supervised Learning.

Science.gov (United States)

2016-06-01

Biological control systems have long been studied as a possible inspiration for the construction of robotic controllers. The cerebellum is known to be involved in the production and learning of smooth, coordinated movements. Therefore, highly regular structure of the cerebellum has been in the core of attention in theoretical and computational modeling. However, most of these models reflect some special features of the cerebellum without regarding the whole motor command computational process. In this paper, we try to make a logical relation between the most significant models of the cerebellum and introduce a new learning strategy to arrange the movement patterns: cerebellar modular arrangement and applying of movement patterns based on semi-supervised learning (CMAPS). We assume here the cerebellum like a big archive of patterns that has an efficient organization to classify and recall them. The main idea is to achieve an optimal use of memory locations by more than just a supervised learning and classification algorithm. Surely, more experimental and physiological researches are needed to confirm our hypothesis.

10. Implementation of quantum and classical discrete fractional Fourier transforms

Science.gov (United States)

Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander

2016-01-01

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. PMID:27006089

11. Implementation of quantum and classical discrete fractional Fourier transforms.

Science.gov (United States)

Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander

2016-03-23

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.

12. Can Link Analysis Be Applied to Identify Behavioral Patterns in Train Recorder Data?

Science.gov (United States)

Strathie, Ailsa; Walker, Guy H

2016-03-01

13. Quantification of microplastic mass and removal rates at wastewater treatment plants applying Focal Plane Array (FPA)-based Fourier Transform Infrared (FT-IR) imaging

DEFF Research Database (Denmark)

Simon, Marta; van Alst, Nikki; Vollertsen, Jes

2018-01-01

in the environment. It concludes that MP mass should be included when quantifying MP pollution in the environment, supplementing the conventional approach of reporting particle numbers. Applying mass as the unit of MP measurement, the paper presents data showing that Danish wastewater treatment plants discharge...

14. Entropy criteria applied to pattern selection in systems with free boundaries

Science.gov (United States)

Kirkaldy, J. S.

1985-10-01

The steady state differential or integral equations which describe patterned dissipative structures, typically to be identified with first order phase transformation morphologies like isothermal pearlites, are invariably degenerate in one or more order parameters (the lamellar spacing in the pearlite case). It is often observed that a different pattern is attained at the steady state for each initial condition (the hysteresis or metastable case). Alternatively, boundary perturbations and internal fluctuations during transition up to, or at the steady state, destroy the path coherence. In this case a statistical ensemble of imperfect patterns often emerges which represents a fluctuating but recognizably patterned and unique average steady state. It is cases like cellular, lamellar pearlite, involving an assembly of individual cell patterns which are regularly perturbed by local fluctuation and growth processes, which concern us here. Such weakly fluctuating nonlinear steady state ensembles can be arranged in a thought experiment so as to evolve as subsystems linking two very large mass-energy reservoirs in isolation. Operating on this discontinuous thermodynamic ideal, Onsager’s principle of maximum path probability for isolated systems, which we interpret as a minimal time correlation function connecting subsystem and baths, identifies the stable steady state at a parametric minimum or maximum (or both) in the dissipation rate. This nonlinear principle is independent of the Principle of Minimum Dissipation which is applicable in the linear regime of irreversible thermodynamics. The statistical argument is equivalent to the weak requirement that the isolated system entropy as a function of time be differentiable to the second order despite the macroscopic pattern fluctuations which occur in the subsystem. This differentiability condition is taken for granted in classical stability theory based on the 2nd Law. The optimal principle as applied to isothermal and

15. Pattern recognition applied to mineral characterization of Brazilian coffees and sugar-cane spirits

International Nuclear Information System (INIS)

Fernandes, Andrea P.; Santos, Mirian C.; Lemos, Sherlan G.; Ferreira, Marcia M.C.; Nogueira, Ana Rita A.; Nobrega, Joaquim A.

2005-01-01

Aluminium, Ca, Cu, Fe, K, Mg, Mn, Na, Pb, S, Se, Si, Sn, Sr, and Zn were determined in coffee and sugar-cane spirit (cachaca) samples by axial viewing inductively coupled plasma optical emission spectrometry (ICP OES). Pattern recognition techniques such as principal component analysis and cluster analysis were applied to data sets in order to characterize samples with relation to their geographical origin and production mode (industrial or homemade and organically or conventionally produced). Attempts to correlate metal ion content with the geographical origin of coffee and the production mode (organic or conventional) of cachaca were not successful. Some differentiation was suggested for the geographical origin of cachaca of three regions (Northeast, Central, and South), and for coffee samples, related to the production mode. Clear separations were only obtained for differentiation between industrial and homemade cachacas, and between instant soluble and roasted coffees

16. National youth sedentary behavior and physical activity daily patterns using latent class analysis applied to accelerometry.

Science.gov (United States)

Evenson, Kelly R; Wen, Fang; Hales, Derek; Herring, Amy H

2016-05-03

Applying latent class analysis (LCA) to accelerometry can help elucidated underlying patterns. This study described the patterns of accelerometer-determined sedentary behavior and physical activity among youth by applying LCA to a nationally representative United States (US) sample. Using 2003-2006 National Health and Nutrition Examination Survey data, 3998 youths 6-17 years wore an ActiGraph 7164 accelerometer for one week, providing > =3 days of wear for > =8 h/day from 6:00 am-midnight. Cutpoints defined sedentary behavior ( = 2296 counts/minute), and vigorous activity (> = 4012 counts/minute). To account for wear time differences, outcomes were expressed as percent of day in a given intensity. LCA was used to classify daily (Monday through Sunday) patterns of average counts/minute, sedentary behavior, light activity, MVPA, and vigorous activity separately. The latent classes were explored overall and by age (6-11, 12-14, 15-17 years), gender, and whether or not youth attended school during measurement. Estimates were weighted to account for the sampling frame. For average counts/minute/day, four classes emerged from least to most active: 40.9% of population (mean 323.5 counts/minute/day), 40.3% (559.6 counts/minute/day), 16.5% (810.0 counts/minute/day), and 2.3% (1132.9 counts/minute/day). For percent of sedentary behavior, four classes emerged: 13.5% of population (mean 544.6 min/day), 30.1% (455.1 min/day), 38.5% (357.7 min/day), and 18.0% (259.2 min/day). For percent of light activity, four classes emerged: 12.3% of population (mean 222.6 min/day), 29.3% (301.7 min/day), 41.8% (384.0 min/day), and 16.6% (455.5 min/day). For percent of MVPA, four classes emerged: 59.9% of population (mean 25.0 min/day), 33.3% (60.9 min/day), 3.1% (89.0 min/day), and 3.6% (109.3 min/day). For percent of vigorous activity, three classes emerged: 76.8% of population (mean 7.1 min/day), 18.5% (23.9 min/day), and 4.7% (47.4 min/day). Classes were developed by age

17. Phase-Transition-Induced Pattern Formation Applied to Basic Research on Homeopathy: A Systematic Review.

Science.gov (United States)

Kokornaczyk, Maria Olga; Scherr, Claudia; Bodrova, Natalia Borisovna; Baumgartner, Stephan

2018-05-16

Methods based on phase-transition-induced pattern formation (PTPF) are increasingly used in medical research. Frequent application fields are medical diagnosis and basic research in homeopathy. Here, we present a systematic review of experimental studies concerning PTPF-based methods applied to homeopathy research. We also aimed at categorizing the PTPF methods included in this review.  Experimental studies were collected from scientific databases (PubMed, Web of Science, Russian eLibrary) and from experts in the research field in question, following the PRISMA guidelines. The studies were rated according to pre-defined scientific criteria.  The review included 15 experimental studies. We identified seven different PTPF methods applied in 12 experimental models. Among these methods, phase-transition was triggered through evaporation, freezing, or solution, and in most cases led to the formation of crystals. First experimental studies concerning the application of PTPF methods in homeopathic research were performed in the first half of the 20th century; however, they were not continued in the following years. Only in the last decade, different research groups re-launched the idea, introducing new experimental approaches and computerized pattern evaluation techniques. The here-identified PTPF methods are for the first time proposed to be classified as one group of methods based on the same basic physical phenomenon.  Although the number of experimental studies in the area is still rather limited, the long tradition in the application of PTPF methods and the dynamics of the present developments point out the high potential of these methods and indicate that they might meet the demand for scientific methods to study potentized preparations. The Faculty of Homeopathy.

18. Attractor structure discriminates sleep states: recurrence plot analysis applied to infant breathing patterns.

Science.gov (United States)

Terrill, Philip Ian; Wilson, Stephen James; Suresh, Sadasivam; Cooper, David M; Dakin, Carolyn

2010-05-01

Breathing patterns are characteristically different between infant active sleep (AS) and quiet sleep (QS), and statistical quantifications of interbreath interval (IBI) data have previously been used to discriminate between infant sleep states. It has also been identified that breathing patterns are governed by a nonlinear controller. This study aims to investigate whether nonlinear quantifications of infant IBI data are characteristically different between AS and QS, and whether they may be used to discriminate between these infant sleep states. Polysomnograms were obtained from 24 healthy infants at six months of age. Periods of AS and QS were identified, and IBI data extracted. Recurrence quantification analysis (RQA) was applied to each period, and recurrence calculated for a fixed radius in the range of 0-8 in steps of 0.02, and embedding dimensions of 4, 6, 8, and 16. When a threshold classifier was trained, the RQA variable recurrence was able to correctly classify 94.3% of periods in a test dataset. It was concluded that RQA of IBI data is able to accurately discriminate between infant sleep states. This is a promising step toward development of a minimal-channel automatic sleep state classification system.

19. Fourier optics treatment of classical relativistic electrodynamics

Energy Technology Data Exchange (ETDEWEB)

Geloni, G.; Saldin, E.; Schneidmiller, E.; Yurkov, M.

2006-08-15

In this paper we couple Synchrotron Radiation (SR) theory with a branch of physical optics, namely laser beam optics. We show that the theory of laser beams is successful in characterizing radiation fields associated with any SR source. Both radiation beam generated by an ultra-relativistic electron in a magnetic device and laser beam are solutions of the wave equation based on paraxial approximation. It follows that they are similar in all aspects. In the space-frequency domain SR beams appear as laser beams whose transverse extents are large compared with the wavelength. In practical solutions (e.g. undulator, bending magnet sources), radiation beams exhibit a virtual ''waist'' where the wavefront is often plane. Remarkably, the field distribution of a SR beam across the waist turns out to be strictly related with the inverse Fourier transform of the far-field angle distribution. Then, we take advantage of standard Fourier Optics techniques and apply the Fresnel propagation formula to characterize the SR beam. Altogether, we show that it is possible to reconstruct the near-field distribution of the SR beam outside the magnetic setup from the knowledge of the far-field pattern. The general theory of SR in the near-zone developed in this paper is illustrated for the special cases of undulator radiation, edge radiation and transition undulator radiation. Using known analytical formulas for the far-field pattern and its inverse Fourier transform we find analytical expressions for near-field distributions in terms of far-field distributions. Finally, we compare these expressions with incorrect or incomplete literature. (orig.)

20. Electronic speckle-pattern interferometry (ESPI) applied to the study of mechanical behavior of human jaws

Science.gov (United States)

Roman, Juan F.; Moreno de las Cuevas, Vincente; Salgueiro, Jose R.; Suarez, David; Fernandez, Paula; Gallas, Mercedes; Blanchard, Alain

1996-01-01

The study of the mechanical behavior of the human jaw during chewing is helpful in several specific medical fields that cover the maxillo-facial area. In this work, electronic speckle pattern interferometry has been applied to study dead jaw bones under external stress which simulates the deformations induced during chewing. Fringes obtained after subtraction of two images of the jaw, the image of the relaxed jaw and that of the jaw under stress, give us information about the most stressed zones. The interferometric analysis proposed here is attractive as it can be done in real time with the jaw under progressive stress. Image processing can be applied for improving the quality of fringes. This research can be of help in orthognathic surgery, for example in diagnosis and treatment of fractured jaws, in oral surgery, and in orthodontics because it would help us to know the stress dispersion when we insert an osseointegrated implant or place an orthodontic appliance, respectively. Studying fragments of human jaw some results about its elasticity and flexibility were obtained.

1. Fourier transform NMR

International Nuclear Information System (INIS)

Hallenga, K.

1991-01-01

This paper discusses the concept of Fourier transformation one of the many precious legacies of the French mathematician Jean Baptiste Joseph Fourier, essential for understanding the link between continuous-wave (CW) and Fourier transform (FT) NMR. Although in modern FT NMR the methods used to obtain a frequency spectrum from the time-domain signal may vary greatly, from the efficient Cooley-Tukey algorithm to very elaborate iterative least-square methods based other maximum entropy method or on linear prediction, the principles for Fourier transformation are unchanged and give invaluable insight into the interconnection of many pairs of physical entities called Fourier pairs

2. Applications of Fourier transforms to generalized functions

CERN Document Server

Rahman, M

2011-01-01

This book explains how Fourier transforms can be applied to generalized functions. The generalized function is one of the important branches of mathematics and is applicable in many practical fields. Its applications to the theory of distribution and signal processing are especially important. The Fourier transform is a mathematical procedure that can be thought of as transforming a function from its time domain to the frequency domain.The book contains six chapters and three appendices. Chapter 1 deals with preliminary remarks on Fourier series from a general point of view and also contains an introduction to the first generalized function. Chapter 2 is concerned with the generalized functions and their Fourier transforms. Chapter 3 contains the Fourier transforms of particular generalized functions. The author has stated and proved 18 formulas dealing with the Fourier transforms of generalized functions, and demonstrated some important problems of practical interest. Chapter 4 deals with the asymptotic esti...

3. Phase-only SLM Generating Variable Patterns Applied in Optical Connection

International Nuclear Information System (INIS)

Liu, B H; Wu, L Y; Zhang, J

2006-01-01

An adaptive optical communication system is proposed. The system sends spatial information by emitting multiple variable laser beams generated from a programmable diffractive optical element (DOE): phase-only liquid crystal Spatial Light Modulator (SLM). Laser beams carrying signals are programmable by an optimal algorithm based on an iterative Fourier transformation algorithm. The system has the advantage in redundancy of signal by the means of broadcast. It can adaptively seek position and transmit information in parallel

4. Applying machine learning to pattern analysis for automated in-design layout optimization

Science.gov (United States)

Cain, Jason P.; Fakhry, Moutaz; Pathak, Piyush; Sweis, Jason; Gennari, Frank; Lai, Ya-Chieh

2018-04-01

Building on previous work for cataloging unique topological patterns in an integrated circuit physical design, a new process is defined in which a risk scoring methodology is used to rank patterns based on manufacturing risk. Patterns with high risk are then mapped to functionally equivalent patterns with lower risk. The higher risk patterns are then replaced in the design with their lower risk equivalents. The pattern selection and replacement is fully automated and suitable for use for full-chip designs. Results from 14nm product designs show that the approach can identify and replace risk patterns with quantifiable positive impact on the risk score distribution after replacement.

5. Knowledge fusion: Time series modeling followed by pattern recognition applied to unusual sections of background data

International Nuclear Information System (INIS)

Burr, T.; Doak, J.; Howell, J.A.; Martinez, D.; Strittmatter, R.

1996-03-01

This report describes work performed during FY 95 for the Knowledge Fusion Project, which by the Department of Energy, Office of Nonproliferation and National Security. The project team selected satellite sensor data as the one main example to which its analysis algorithms would be applied. The specific sensor-fusion problem has many generic features that make it a worthwhile problem to attempt to solve in a general way. The generic problem is to recognize events of interest from multiple time series in a possibly noisy background. By implementing a suite of time series modeling and forecasting methods and using well-chosen alarm criteria, we reduce the number of false alarms. We then further reduce the number of false alarms by analyzing all suspicious sections of data, as judged by the alarm criteria, with pattern recognition methods. This report describes the implementation and application of this two-step process for separating events from unusual background. As a fortunate by-product of this activity, it is possible to gain a better understanding of the natural background

6. Knowledge fusion: Time series modeling followed by pattern recognition applied to unusual sections of background data

Energy Technology Data Exchange (ETDEWEB)

Burr, T.; Doak, J.; Howell, J.A.; Martinez, D.; Strittmatter, R.

1996-03-01

This report describes work performed during FY 95 for the Knowledge Fusion Project, which by the Department of Energy, Office of Nonproliferation and National Security. The project team selected satellite sensor data as the one main example to which its analysis algorithms would be applied. The specific sensor-fusion problem has many generic features that make it a worthwhile problem to attempt to solve in a general way. The generic problem is to recognize events of interest from multiple time series in a possibly noisy background. By implementing a suite of time series modeling and forecasting methods and using well-chosen alarm criteria, we reduce the number of false alarms. We then further reduce the number of false alarms by analyzing all suspicious sections of data, as judged by the alarm criteria, with pattern recognition methods. This report describes the implementation and application of this two-step process for separating events from unusual background. As a fortunate by-product of this activity, it is possible to gain a better understanding of the natural background.

7. A University Web Portal redesign applying accessibility patterns. Breaking Down Barriers for Visually Impaired Users

Directory of Open Access Journals (Sweden)

Hernán Sosa

2015-08-01

Full Text Available Definitely, the WWW and ICTs have become the preferred media for the interaction between society and its citizens, and public and private organizations have today the possibility of deploying their activities through the Web. In particular, university education is a domain where the benefits of these technological resources can strongly contribute in caring for students. However, most university Web portals are inaccessible to their user community (students, professors, and non-teaching staff, between others, since these portals do not take into account the needs of people with different capabilities. In this work, we propose an accessibility pattern driven process to the redesign of university Web portals, aiming to break down barriers for visually impaired users. The approach is implemented to a real case study: the Web portal of Universidad Nacional de la Patagonia Austral (UNPA. The results come from applying accessibility recommendations and evaluation tools (automatic and manual from internationally recognized organizations, to both versions of the Web portal: the original and the redesign one.

8. Metasurface Enabled Wide-Angle Fourier Lens.

Science.gov (United States)

Liu, Wenwei; Li, Zhancheng; Cheng, Hua; Tang, Chengchun; Li, Junjie; Zhang, Shuang; Chen, Shuqi; Tian, Jianguo

2018-06-01

Fourier optics, the principle of using Fourier transformation to understand the functionalities of optical elements, lies at the heart of modern optics, and it has been widely applied to optical information processing, imaging, holography, etc. While a simple thin lens is capable of resolving Fourier components of an arbitrary optical wavefront, its operation is limited to near normal light incidence, i.e., the paraxial approximation, which puts a severe constraint on the resolvable Fourier domain. As a result, high-order Fourier components are lost, resulting in extinction of high-resolution information of an image. Other high numerical aperture Fourier lenses usually suffer from the bulky size and costly designs. Here, a dielectric metasurface consisting of high-aspect-ratio silicon waveguide array is demonstrated experimentally, which is capable of performing 1D Fourier transform for a large incident angle range and a broad operating bandwidth. Thus, the device significantly expands the operational Fourier space, benefitting from the large numerical aperture and negligible angular dispersion at large incident angles. The Fourier metasurface will not only facilitate efficient manipulation of spatial spectrum of free-space optical wavefront, but also be readily integrated into micro-optical platforms due to its compact size. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

9. Fractional finite Fourier transform.

Science.gov (United States)

Khare, Kedar; George, Nicholas

2004-07-01

We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.

10. Fourier Series Optimization Opportunity

Science.gov (United States)

Winkel, Brian

2008-01-01

This note discusses the introduction of Fourier series as an immediate application of optimization of a function of more than one variable. Specifically, it is shown how the study of Fourier series can be motivated to enrich a multivariable calculus class. This is done through discovery learning and use of technology wherein students build the…

11. Jean Baptiste Joseph Fourier

Science.gov (United States)

Sterken, C.

2003-03-01

This paper gives a short account of some key elements in the life of Jean Baptiste Joseph Fourier (1768-1830), specifically his relation to Napoleon Bonaparte. The mathematical approach to Fourier series and the original scepticism by French mathematicians are briefly illustrated.

12. Generalized Fourier transforms classes

DEFF Research Database (Denmark)

Berntsen, Svend; Møller, Steen

2002-01-01

The Fourier class of integral transforms with kernels $B(\\omega r)$ has by definition inverse transforms with kernel $B(-\\omega r)$. The space of such transforms is explicitly constructed. A slightly more general class of generalized Fourier transforms are introduced. From the general theory...

13. Direct fourier method reconstruction based on unequally spaced fast fourier transform

International Nuclear Information System (INIS)

Wu Xiaofeng; Zhao Ming; Liu Li

2003-01-01

First, We give an Unequally Spaced Fast Fourier Transform (USFFT) method, which is more exact and theoretically more comprehensible than its former counterpart. Then, with an interesting interpolation scheme, we discusse how to apply USFFT to Direct Fourier Method (DFM) reconstruction of parallel projection data. At last, an emulation experiment result is given. (authors)

14. Computing exact Fourier series coefficients of IC rectilinear polygons from low-resolution fast Fourier coefficients

Science.gov (United States)

Scheibler, Robin; Hurley, Paul

2012-03-01

We present a novel, accurate and fast algorithm to obtain Fourier series coefficients from an IC layer whose description consists of rectilinear polygons on a plane, and how to implement it using off-the-shelf hardware components. Based on properties of Fourier calculus, we derive a relationship between the Discrete Fourier Transforms of the sampled mask transmission function and its continuous Fourier series coefficients. The relationship leads to a straightforward algorithm for computing the continuous Fourier series coefficients where one samples the mask transmission function, compute its discrete Fourier transform and applies a frequency-dependent multiplicative factor. The algorithm is guaranteed to yield the exact continuous Fourier series coefficients for any sampling representing the mask function exactly. Computationally, this leads to significant saving by allowing to choose the maximal such pixel size and reducing the fast Fourier transform size by as much, without compromising accuracy. In addition, the continuous Fourier series is free from aliasing and follows closely the physical model of Fourier optics. We show that in some cases this can make a significant difference, especially in modern very low pitch technology nodes.

15. Fourier spectral simulations for wake fields in conducting cavities

International Nuclear Information System (INIS)

Min, M.; Chin, Y.-H.; Fischer, P.F.; Chae, Y.-Chul; Kim, K.-J.

2007-01-01

We investigate Fourier spectral time-domain simulations applied to wake field calculations in two-dimensional cylindrical structures. The scheme involves second-order explicit leap-frogging in time and Fourier spectral approximation in space, which is obtained from simply replacing the spatial differentiation operator of the YEE scheme by the Fourier differentiation operator on nonstaggered grids. This is a first step toward investigating high-order computational techniques with the Fourier spectral method, which is relatively simple to implement.

16. Comparison of multivariate preprocessing techniques as applied to electronic tongue based pattern classification for black tea

International Nuclear Information System (INIS)

Palit, Mousumi; Tudu, Bipan; Bhattacharyya, Nabarun; Dutta, Ankur; Dutta, Pallab Kumar; Jana, Arun; Bandyopadhyay, Rajib; Chatterjee, Anutosh

2010-01-01

In an electronic tongue, preprocessing on raw data precedes pattern analysis and choice of the appropriate preprocessing technique is crucial for the performance of the pattern classifier. While attempting to classify different grades of black tea using a voltammetric electronic tongue, different preprocessing techniques have been explored and a comparison of their performances is presented in this paper. The preprocessing techniques are compared first by a quantitative measurement of separability followed by principle component analysis; and then two different supervised pattern recognition models based on neural networks are used to evaluate the performance of the preprocessing techniques.

17. Applying Learning Analytics to Explore the Effects of Motivation on Online Students' Reading Behavioral Patterns

Science.gov (United States)

Sun, Jerry Chih-Yuan; Lin, Che-Tsun; Chou, Chien

2018-01-01

This study aims to apply a sequential analysis to explore the effect of learning motivation on online reading behavioral patterns. The study's participants consisted of 160 graduate students who were classified into three group types: low reading duration with low motivation, low reading duration with high motivation, and high reading duration…

18. A feasibility study of low-order harmonics expansion applied to loading pattern search

Energy Technology Data Exchange (ETDEWEB)

Shaohong, Z.; Dong, L.; Tao, W. [Shanghai Jiao Tong Univ., 1954 Hua Shan Road, Shanghai, 200030 (China); Chao, Y. A. [Westinghouse Electric Company, P. O. Box 355, Pittsburgh, PA 15230-0355 (United States)

2006-07-01

Despite significant progress in core loading pattern search methods over years, there still remains the issue of large computing workload and the need for improving the speed of evaluating loading pattern candidates during the search process. This paper focuses on improving the computing speed for loading pattern evaluation, rather than the method of searching for the patterns. A low order harmonics expansion method for flux distribution representation is proposed for fast LP evaluation application. The novel feature of the method is the separation of the short range local perturbation effect from the long range global tilt effect. The latter effect can be captured by low order harmonics expansion. Demonstration examples are presented to show that even for extremely large perturbations induced by fuel shuffling the proposed method can accurately calculate the flux distribution for the LP with very minimal computation. (authors)

19. Fourier analysis an introduction

CERN Document Server

Stein, Elias M

2003-01-01

This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions.The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as th

20. A Short Biography of Joseph Fourier and Historical Development of Fourier Series and Fourier Transforms

Science.gov (United States)

Debnath, Lokenath

2012-01-01

This article deals with a brief biographical sketch of Joseph Fourier, his first celebrated work on analytical theory of heat, his first great discovery of Fourier series and Fourier transforms. Included is a historical development of Fourier series and Fourier transforms with their properties, importance and applications. Special emphasis is made…

1. Digital Fourier analysis fundamentals

CERN Document Server

Kido, Ken'iti

2015-01-01

This textbook is a thorough, accessible introduction to digital Fourier analysis for undergraduate students in the sciences. Beginning with the principles of sine/cosine decomposition, the reader walks through the principles of discrete Fourier analysis before reaching the cornerstone of signal processing: the Fast Fourier Transform. Saturated with clear, coherent illustrations, "Digital Fourier Analysis - Fundamentals" includes practice problems and thorough Appendices for the advanced reader. As a special feature, the book includes interactive applets (available online) that mirror the illustrations.  These user-friendly applets animate concepts interactively, allowing the user to experiment with the underlying mathematics. For example, a real sine signal can be treated as a sum of clockwise and counter-clockwise rotating vectors. The applet illustration included with the book animates the rotating vectors and the resulting sine signal. By changing parameters such as amplitude and frequency, the reader ca...

2. Fourier Transform Mass Spectrometry

Science.gov (United States)

Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander

2011-01-01

This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook. PMID:21742802

3. Generalized Fourier transforms classes

DEFF Research Database (Denmark)

Berntsen, Svend; Møller, Steen

2002-01-01

The Fourier class of integral transforms with kernels $B(\\omega r)$ has by definition inverse transforms with kernel $B(-\\omega r)$. The space of such transforms is explicitly constructed. A slightly more general class of generalized Fourier transforms are introduced. From the general theory foll...... follows that integral transform with kernels which are products of a Bessel and a Hankel function or which is of a certain general hypergeometric type have inverse transforms of the same structure....

4. Generalized fiber Fourier optics.

Science.gov (United States)

Cincotti, Gabriella

2011-06-15

A twofold generalization of the optical schemes that perform the discrete Fourier transform (DFT) is given: new passive planar architectures are presented where the 2 × 2 3 dB couplers are replaced by M × M hybrids, reducing the number of required connections and phase shifters. Furthermore, the planar implementation of the discrete fractional Fourier transform (DFrFT) is also described, with a waveguide grating router (WGR) configuration and a properly modified slab coupler.

5. Improved Fourier-transform profilometry

International Nuclear Information System (INIS)

Mao Xianfu; Chen Wenjing; Su Xianyu

2007-01-01

An improved optical geometry of the projected-fringe profilometry technique, in which the exit pupil of the projecting lens and the entrance pupil of the imaging lens are neither at the same height above the reference plane nor coplanar, is discussed and used in Fourier-transform profilometry. Furthermore, an improved fringe-pattern description and phase-height mapping formula based on the improved geometrical generalization is deduced. Employing the new optical geometry, it is easier for us to obtain the full-field fringe by moving either the projector or the imaging device. Therefore the new method offers a flexible way to obtain reliable height distribution of a measured object

6. Applying a Machine Learning Technique to Classification of Japanese Pressure Patterns

Directory of Open Access Journals (Sweden)

H Kimura

2009-04-01

Full Text Available In climate research, pressure patterns are often very important. When a climatologists need to know the days of a specific pressure pattern, for example "low pressure in Western areas of Japan and high pressure in Eastern areas of Japan (Japanese winter-type weather," they have to visually check a huge number of surface weather charts. To overcome this problem, we propose an automatic classification system using a support vector machine (SVM, which is a machine-learning method. We attempted to classify pressure patterns into two classes: "winter type" and "non-winter type". For both training datasets and test datasets, we used the JRA-25 dataset from 1981 to 2000. An experimental evaluation showed that our method obtained a greater than 0.8 F-measure. We noted that variations in results were based on differences in training datasets.

7. X-ray interferometric Fourier holography

International Nuclear Information System (INIS)

Balyan, M.K.

2016-01-01

The X-ray interferometric Fourier holography is proposed and theoretically investigated. Fourier The X-ray interferometric Young fringes and object image reconstruction are investigated. It is shown that the interference pattern of two slits formed on the exit surface of the crystal-analyzer (the third plate of the interferometer) is the X-ray interferometric Young fringes. An expression for X-ray interferometric Young fringes period is obtained. The subsequent reconstruction of the slit image as an object is performed by means of Fourier transform of the intensity distribution on the hologram. Three methods of reconstruction of the amplitude transmission complex function of the object are presented: analytical - approximate method, method of iteration and step by step method. As an example the X-ray Fourier interferometric hologram recording and the complex amplitude transmission function reconstruction for a beryllium circular wire are considered

8. Fourier transformation for engineering and natural science

International Nuclear Information System (INIS)

Klingen, B.

2001-01-01

The following topics are covered: functions, Dirac delta function, Fourier operators, Fourier integrals, Fourier transformation and periodic functions, discrete Fourier transformations and discrete filters, applications. (WL)

9. Pattern recognition and data mining software based on artificial neural networks applied to proton transfer in aqueous environments

International Nuclear Information System (INIS)

Tahat Amani; Marti Jordi; Khwaldeh Ali; Tahat Kaher

2014-01-01

In computational physics proton transfer phenomena could be viewed as pattern classification problems based on a set of input features allowing classification of the proton motion into two categories: transfer ‘occurred’ and transfer ‘not occurred’. The goal of this paper is to evaluate the use of artificial neural networks in the classification of proton transfer events, based on the feed-forward back propagation neural network, used as a classifier to distinguish between the two transfer cases. In this paper, we use a new developed data mining and pattern recognition tool for automating, controlling, and drawing charts of the output data of an Empirical Valence Bond existing code. The study analyzes the need for pattern recognition in aqueous proton transfer processes and how the learning approach in error back propagation (multilayer perceptron algorithms) could be satisfactorily employed in the present case. We present a tool for pattern recognition and validate the code including a real physical case study. The results of applying the artificial neural networks methodology to crowd patterns based upon selected physical properties (e.g., temperature, density) show the abilities of the network to learn proton transfer patterns corresponding to properties of the aqueous environments, which is in turn proved to be fully compatible with previous proton transfer studies. (condensed matter: structural, mechanical, and thermal properties)

10. An Approach for Pattern Recognition of EEG Applied in Prosthetic Hand Drive

Directory of Open Access Journals (Sweden)

Xiao-Dong Zhang

2011-12-01

Full Text Available For controlling the prosthetic hand by only electroencephalogram (EEG, it has become the hot spot in robotics research to set up a direct communication and control channel between human brain and prosthetic hand. In this paper, the EEG signal is analyzed based on multi-complicated hand activities. And then, two methods of EEG pattern recognition are investigated, a neural prosthesis hand system driven by BCI is set up, which can complete four kinds of actions (arm’s free state, arm movement, hand crawl, hand open. Through several times of off-line and on-line experiments, the result shows that the neural prosthesis hand system driven by BCI is reasonable and feasible, the C-support vector classifiers-based method is better than BP neural network on the EEG pattern recognition for multi-complicated hand activities.

11. Applying acoustic telemetry to understand contaminant exposure and bioaccumulation patterns in mobile fishes.

Science.gov (United States)

Taylor, Matthew D; van der Meulen, Dylan E; Brodie, Stephanie; Cadiou, Gwenaël; Knott, Nathan A

2018-06-01

Contamination in urbanised estuaries presents a risk to human health, and to the viability of populations of exploited species. Assessing animal movements in relation to contaminated areas may help to explain patterns in bioaccumulation, and assist in the effective management of health risks associated with consumption of exploited species. Using polychlorinated dibenzodioxin and polychlorinated dibenzofuran (PCDD/Fs) contamination in Sydney Harbour estuary as a case study, we present a study that links movement patterns resolved using acoustic telemetry to the accumulation of contaminants in mobile fish on a multi-species basis. Fifty-four individuals across six exploited species (Sea Mullet Mugil cephalus; Luderick Girella tricuspidata; Yellowfin Bream Acanthopagrus australis; Silver Trevally Pseudocaranx georgianus; Mulloway Argyrosomus japonicus; Yellowtail Kingfish Seriola lalandi) were tagged with acoustic transmitters, and their movements tracked for up to 3years. There was substantial inter-specific variation in fish distribution along the estuary. The proportion of distribution that overlapped with contaminated areas explained 84-98% of the inter-specific variation in lipid-standardised biota PCDD/F concentration. There was some seasonal variation in distribution along the estuary, but movement patterns indicated that Sea Mullet, Yellowfin Bream, Silver Trevally, and Mulloway were likely to be exposed to contaminated areas during the period of gonadal maturation. Acoustic telemetry allows examination of spatial and temporal patterns in exposure to contamination. When used alongside biota sampling and testing, this offers a powerful approach to assess exposure, bioaccumulation, and potential risks faced by different species, as well as human health risks associated with their consumption. Crown Copyright © 2017. Published by Elsevier B.V. All rights reserved.

12. User Activity Recognition in Smart Homes Using Pattern Clustering Applied to Temporal ANN Algorithm.

Science.gov (United States)

Bourobou, Serge Thomas Mickala; Yoo, Younghwan

2015-05-21

This paper discusses the possibility of recognizing and predicting user activities in the IoT (Internet of Things) based smart environment. The activity recognition is usually done through two steps: activity pattern clustering and activity type decision. Although many related works have been suggested, they had some limited performance because they focused only on one part between the two steps. This paper tries to find the best combination of a pattern clustering method and an activity decision algorithm among various existing works. For the first step, in order to classify so varied and complex user activities, we use a relevant and efficient unsupervised learning method called the K-pattern clustering algorithm. In the second step, the training of smart environment for recognizing and predicting user activities inside his/her personal space is done by utilizing the artificial neural network based on the Allen's temporal relations. The experimental results show that our combined method provides the higher recognition accuracy for various activities, as compared with other data mining classification algorithms. Furthermore, it is more appropriate for a dynamic environment like an IoT based smart home.

13. User Activity Recognition in Smart Homes Using Pattern Clustering Applied to Temporal ANN Algorithm

Directory of Open Access Journals (Sweden)

Serge Thomas Mickala Bourobou

2015-05-01

Full Text Available This paper discusses the possibility of recognizing and predicting user activities in the IoT (Internet of Things based smart environment. The activity recognition is usually done through two steps: activity pattern clustering and activity type decision. Although many related works have been suggested, they had some limited performance because they focused only on one part between the two steps. This paper tries to find the best combination of a pattern clustering method and an activity decision algorithm among various existing works. For the first step, in order to classify so varied and complex user activities, we use a relevant and efficient unsupervised learning method called the K-pattern clustering algorithm. In the second step, the training of smart environment for recognizing and predicting user activities inside his/her personal space is done by utilizing the artificial neural network based on the Allen’s temporal relations. The experimental results show that our combined method provides the higher recognition accuracy for various activities, as compared with other data mining classification algorithms. Furthermore, it is more appropriate for a dynamic environment like an IoT based smart home.

14. Optimization of the temporal pattern of applied dose for a single fraction of radiation: Implications for radiation therapy

Science.gov (United States)

Altman, Michael B.

15. Content adaptive illumination for Fourier ptychography.

Science.gov (United States)

Bian, Liheng; Suo, Jinli; Situ, Guohai; Zheng, Guoan; Chen, Feng; Dai, Qionghai

2014-12-01

Fourier ptychography (FP) is a recently reported technique, for large field-of-view and high-resolution imaging. Specifically, FP captures a set of low-resolution images, under angularly varying illuminations, and stitches them together in the Fourier domain. One of FP's main disadvantages is its long capturing process, due to the requisite large number of incident illumination angles. In this Letter, utilizing the sparsity of natural images in the Fourier domain, we propose a highly efficient method, termed adaptive Fourier ptychography (AFP), which applies content adaptive illumination for FP, to capture the most informative parts of the scene's spatial spectrum. We validate the effectiveness and efficiency of the reported framework, with both simulated and real experiments. Results show that the proposed AFP could shorten the acquisition time of conventional FP, by around 30%-60%.

16. On Fourier re-expansions

OpenAIRE

Liflyand, E.

2012-01-01

We study an extension to Fourier transforms of the old problem on absolute convergence of the re-expansion in the sine (cosine) Fourier series of an absolutely convergent cosine (sine) Fourier series. The results are obtained by revealing certain relations between the Fourier transforms and their Hilbert transforms.

17. Applying Evidence-Based Medicine in Telehealth: An Interactive Pattern Recognition Approximation

Directory of Open Access Journals (Sweden)

Carlos Fernández-Llatas

2013-10-01

Full Text Available Born in the early nineteen nineties, evidence-based medicine (EBM is a paradigm intended to promote the integration of biomedical evidence into the physicians daily practice. This paradigm requires the continuous study of diseases to provide the best scientific knowledge for supporting physicians in their diagnosis and treatments in a close way. Within this paradigm, usually, health experts create and publish clinical guidelines, which provide holistic guidance for the care for a certain disease. The creation of these clinical guidelines requires hard iterative processes in which each iteration supposes scientific progress in the knowledge of the disease. To perform this guidance through telehealth, the use of formal clinical guidelines will allow the building of care processes that can be interpreted and executed directly by computers. In addition, the formalization of clinical guidelines allows for the possibility to build automatic methods, using pattern recognition techniques, to estimate the proper models, as well as the mathematical models for optimizing the iterative cycle for the continuous improvement of the guidelines. However, to ensure the efficiency of the system, it is necessary to build a probabilistic model of the problem. In this paper, an interactive pattern recognition approach to support professionals in evidence-based medicine is formalized.

18. Fourier plane imaging microscopy

Energy Technology Data Exchange (ETDEWEB)

Dominguez, Daniel, E-mail: daniel.dominguez@ttu.edu; Peralta, Luis Grave de [Department of Physics, Texas Tech University, Lubbock, Texas 79409 (United States); Nano Tech Center, Texas Tech University, Lubbock, Texas 79409 (United States); Alharbi, Nouf; Alhusain, Mdhaoui [Department of Physics, Texas Tech University, Lubbock, Texas 79409 (United States); Bernussi, Ayrton A. [Nano Tech Center, Texas Tech University, Lubbock, Texas 79409 (United States); Department of Electrical and Computer Engineering, Texas Tech University, Lubbock, Texas 79409 (United States)

2014-09-14

We show how the image of an unresolved photonic crystal can be reconstructed using a single Fourier plane (FP) image obtained with a second camera that was added to a traditional compound microscope. We discuss how Fourier plane imaging microscopy is an application of a remarkable property of the obtained FP images: they contain more information about the photonic crystals than the images recorded by the camera commonly placed at the real plane of the microscope. We argue that the experimental results support the hypothesis that surface waves, contributing to enhanced resolution abilities, were optically excited in the studied photonic crystals.

19. Improving Spectral Results Using Row-by-Row Fourier Transform of Spatial Heterodyne Raman Spectrometer Interferogram.

Science.gov (United States)

Barnett, Patrick D; Strange, K Alicia; Angel, S Michael

2017-06-01

This work describes a method of applying the Fourier transform to the two-dimensional Fizeau fringe patterns generated by the spatial heterodyne Raman spectrometer (SHRS), a dispersive interferometer, to correct the effects of certain types of optical alignment errors. In the SHRS, certain types of optical misalignments result in wavelength-dependent and wavelength-independent rotations of the fringe pattern on the detector. We describe here a simple correction technique that can be used in post-processing, by applying the Fourier transform in a row-by-row manner. This allows the user to be more forgiving of fringe alignment and allows for a reduction in the mechanical complexity of the SHRS.

20. Fourier Transform Mass Spectrometry.

Science.gov (United States)

Gross, Michael L.; Rempel, Don L.

1984-01-01

Discusses the nature of Fourier transform mass spectrometry and its unique combination of high mass resolution, high upper mass limit, and multichannel advantage. Examines its operation, capabilities and limitations, applications (ion storage, ion manipulation, ion chemistry), and future applications and developments. (JN)

1. Connectivity strategies for higher-order neural networks applied to pattern recognition

Science.gov (United States)

Spirkovska, Lilly; Reid, Max B.

1990-01-01

Different strategies for non-fully connected HONNs (higher-order neural networks) are discussed, showing that by using such strategies an input field of 128 x 128 pixels can be attained while still achieving in-plane rotation and translation-invariant recognition. These techniques allow HONNs to be used with the larger input scenes required for practical pattern-recognition applications. The number of interconnections that must be stored has been reduced by a factor of approximately 200,000 in a T/C case and about 2000 in a Space Shuttle/F-18 case by using regional connectivity. Third-order networks have been simulated using several connection strategies. The method found to work best is regional connectivity. The main advantages of this strategy are the following: (1) it considers features of various scales within the image and thus gets a better sample of what the image looks like; (2) it is invariant to shape-preserving geometric transformations, such as translation and rotation; (3) the connections are predetermined so that no extra computations are necessary during run time; and (4) it does not require any extra storage for recording which connections were formed.

2. Applied Swarm-based medicine: collecting decision trees for patterns of algorithms analysis.

Science.gov (United States)

Panje, Cédric M; Glatzer, Markus; von Rappard, Joscha; Rothermundt, Christian; Hundsberger, Thomas; Zumstein, Valentin; Plasswilm, Ludwig; Putora, Paul Martin

2017-08-16

The objective consensus methodology has recently been applied in consensus finding in several studies on medical decision-making among clinical experts or guidelines. The main advantages of this method are an automated analysis and comparison of treatment algorithms of the participating centers which can be performed anonymously. Based on the experience from completed consensus analyses, the main steps for the successful implementation of the objective consensus methodology were identified and discussed among the main investigators. The following steps for the successful collection and conversion of decision trees were identified and defined in detail: problem definition, population selection, draft input collection, tree conversion, criteria adaptation, problem re-evaluation, results distribution and refinement, tree finalisation, and analysis. This manuscript provides information on the main steps for successful collection of decision trees and summarizes important aspects at each point of the analysis.

3. Approximating the Analytic Fourier Transform with the Discrete Fourier Transform

OpenAIRE

Axelrod, Jeremy

2015-01-01

The Fourier transform is approximated over a finite domain using a Riemann sum. This Riemann sum is then expressed in terms of the discrete Fourier transform, which allows the sum to be computed with a fast Fourier transform algorithm more rapidly than via a direct matrix multiplication. Advantages and limitations of using this method to approximate the Fourier transform are discussed, and prototypical MATLAB codes implementing the method are presented.

4. Fourier optical cryptosystem using complex spatial modulation

International Nuclear Information System (INIS)

2014-01-01

Our goal is to enhance the security level of a Fourier optical encryption system. Therefore we propose a Mach–Zehnder interferometer based encryption setup. The input data is organized in a binary array, and it is encoded in the two wave fronts propagated in the arms of the interferometer. Both input wave fronts are independently encrypted by Fourier systems, hence the proposed method has two encryption keys. During decryption, the encrypted wave fronts are propagated through the interferometer setup. The interference pattern of the output shows the reconstructed data in cases where the correct decryption Fourier keys are used. We propose a novel input image modulation method with a user defined phase parameter. We show that the security level of the proposed cryptosystem can be enhanced by an optimally chosen phase parameter. (paper)

5. Reduction and coding of synthetic aperture radar data with Fourier transforms

Science.gov (United States)

Tilley, David G.

1995-01-01

Recently, aboard the Space Radar Laboratory (SRL), the two roles of Fourier Transforms for ocean image synthesis and surface wave analysis have been implemented with a dedicated radar processor to significantly reduce Synthetic Aperture Radar (SAR) ocean data before transmission to the ground. The object was to archive the SAR image spectrum, rather than the SAR image itself, to reduce data volume and capture the essential descriptors of the surface wave field. SAR signal data are usually sampled and coded in the time domain for transmission to the ground where Fourier Transforms are applied both to individual radar pulses and to long sequences of radar pulses to form two-dimensional images. High resolution images of the ocean often contain no striking features and subtle image modulations by wind generated surface waves are only apparent when large ocean regions are studied, with Fourier transforms, to reveal periodic patterns created by wind stress over the surface wave field. Major ocean currents and atmospheric instability in coastal environments are apparent as large scale modulations of SAR imagery. This paper explores the possibility of computing complex Fourier spectrum codes representing SAR images, transmitting the coded spectra to Earth for data archives and creating scenes of surface wave signatures and air-sea interactions via inverse Fourier transformations with ground station processors.

6. Classical Fourier analysis

CERN Document Server

Grafakos, Loukas

2014-01-01

The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood–Paley theory. The primary readership is intended to be graduate students in mathematics with the prerequisite including satisfactory completion of courses in real and complex variables. The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study. This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on “Weighted Inequalities,” which has been moved from GTM 250, 2nd Edition. Appendices I and B.9 are also new to this edition.  Countless corrections and improvements have been made to the material from the second edition. Additions and improvements include: more examples and applications, new and more relevant hints for the existing exercises, new exercises, and...

7. Fourier techniques and applications

CERN Document Server

1985-01-01

The first systematic methods of Fourier analysis date from the early eighteenth century with the work of Joseph Fourier on the problem of the flow of heat. (A brief history is contained in the first paper.) Given the initial tempera­ ture at all points of a region, the problem was to determine the changes in the temperature distribution over time. Understanding and predicting these changes was important in such areas as the handling of metals and the determination of geological and atmospheric temperatures. Briefly, Fourier noticed that the solution of the heat diffusion problem was simple if the initial temperature dis­ tribution was sinusoidal. He then asserted that any distri­ bution can be decomposed into a sum of sinusoids, these being the harmonics of the original function. This meant that the general solution could now be obtained by summing the solu­ tions of the component sinusoidal problems. This remarkable ability of the series of sinusoids to describe all "reasonable" functions, the sine qua n...

8. Releasing Pattern of Applied Phosphorus and Distribution Change of Phosphorus Fractions in the Acid Upland Soils with Successive Resin Extraction

Directory of Open Access Journals (Sweden)

Arief Hartono

2008-05-01

Full Text Available The releasing pattern of applied P in the acid upland soils and the soil properties influencing the pattern were studied. Surface horizons of six acid upland soils from Sumatra, Java and Kalimantan were used in this study. The releasing pattern of applied P (300 mg P kg-1 of these soils were studied by successive resin extraction. P fractionation was conducted to evaluate which fractions released P to the soil solution after successive resin extraction. The cumulative of resin-Pinorganic (Pi release of soils was fitted to the first order kinetic. Regression analyses using factor scores obtained from the previous principal components analyses was applied to determine soil properties influencing P releasing pattern. The results suggested that the maximum P release was significantly (P < 0.05 increased by acidity plus 1.4 nm mineral-related factor (PC2 i.e. exchangeable Al and 1.4 nm minerals (smectite and vermiculite and decreased by oxide related factor (PC1 i.e. aluminum (Al plus 1/2 iron (Fe (by ammonium oxalate, crystalline Al and Fe oxides, cation exchange capacity, and clay content. P fractionation analysis after successive resin extraction showed that both labile and less labile in the form of NaHCO3-Pi and NaOH-Pi fractions, respectively, can be transformed into resin-Pi when in the most labile resin-Pi is depleted. Most of P released in high oxides soils were from NaOH-Pi fraction while in low oxides soils were from NaHCO3-Pi. P release from the former fraction resulted in the maximum P release lower than that of the latter one. When NaHCO3-Pi was high, NaOH-Pi was relatively more stable than NaHCO3-Pi despite resin-Pi removal. NaHCO3-Pi and NaOH-Pi are very important P fractions in replenishing resin-Pi in these acid upland soils.

9. Fourier Spectroscopy: A Bayesian Way

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Stefan Schmuck

2017-01-01

Full Text Available The concepts of standard analysis techniques applied in the field of Fourier spectroscopy treat fundamental aspects insufficiently. For example, the spectra to be inferred are influenced by the noise contribution to the interferometric data, by nonprobed spatial domains which are linked to Fourier coefficients above a certain order, by the spectral limits which are in general not given by the Nyquist assumptions, and by additional parameters of the problem at hand like the zero-path difference. To consider these fundamentals, a probabilistic approach based on Bayes’ theorem is introduced which exploits multivariate normal distributions. For the example application, we model the spectra by the Gaussian process of a Brownian bridge stated by a prior covariance. The spectra themselves are represented by a number of parameters which map linearly to the data domain. The posterior for these linear parameters is analytically obtained, and the marginalisation over these parameters is trivial. This allows the straightforward investigation of the posterior for the involved nonlinear parameters, like the zero-path difference location and the spectral limits, and hyperparameters, like the scaling of the Gaussian process. With respect to the linear problem, this can be interpreted as an implementation of Ockham’s razor principle.

10. Fourier transforms principles and applications

CERN Document Server

Hansen, Eric W

2014-01-01

Fourier Transforms: Principles and Applications explains transform methods and their applications to electrical systems from circuits, antennas, and signal processors-ably guiding readers from vector space concepts through the Discrete Fourier Transform (DFT), Fourier series, and Fourier transform to other related transform methods.  Featuring chapter end summaries of key results, over two hundred examples and four hundred homework problems, and a Solutions Manual this book is perfect for graduate students in signal processing and communications as well as practicing engineers.

11. On the Fourier integral theorem

NARCIS (Netherlands)

Koekoek, J.

1987-01-01

Introduction. In traditional proofs of convergence of Fourier series and of the Fourier integraI theorem basic tools are the theory of Dirichlet integraIs and the Riemann-Lebesgue lemma. Recently CHERNOFF [I) and REoIlEFFER (2) gave new proofs of convergenceof Fourier series which make no use of the

12. Fourier analysis in several complex variables

CERN Document Server

Ehrenpreis, Leon

2006-01-01

Suitable for advanced undergraduates and graduate students, this text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations.The three-part treatment begins by establishing the quotient structure theorem or fundamental principle of Fourier analysis. Topics include the geometric structure of ideals and modules, quantitative estimates, and examples in which the theory can be applied. The second part focuses on applications to partial differential equations and covers the solution of homogeneous and inh

13. Dynamic moire patterns for profilometry applications

Energy Technology Data Exchange (ETDEWEB)

De Oliveira, G N [Pos-graduacao em Engenharia Mecanica, TEM/PGMEC, Universidade Federal Fluminense, Rua Passos da Patria, 156, Niteroi, R.J., Cep.: 24.210-240 (Brazil); De Oliveira, M E; Dos Santos, P A M, E-mail: pams@if.uff.br [Instituto de Fisica, Laboratorio de Optica Nao-linear e Aplicada, Universidade Federal Fluminense, Av. Gal. Nilton Tavares de Souza, s/n, Gragoata, Niteroi, R.J., Cep.:24.210-346 (Brazil)

2011-01-01

In the present work is proposed that dynamic moire-like fringe patterns produced by photorefraction, with low spatial frequencies, could be used for profile determination of small objects. The Fourier transform profilometry technique is applied in the projected moire fringe pattern onto an object surface. Basically, the Fourier transform of the projected fringes is obtained. After that, a phase map is generated. Then, the optical profile of object is obtained using phase unwrapping. So, the entire process can be indicated to measure, with good accuracy degree, profile of small objects in sub-micrometer scale in optical mechanical systems.

14. Fourier Series Formalization in ACL2(r

Directory of Open Access Journals (Sweden)

Cuong K. Chau

2015-09-01

Full Text Available We formalize some basic properties of Fourier series in the logic of ACL2(r, which is a variant of ACL2 that supports reasoning about the real and complex numbers by way of non-standard analysis. More specifically, we extend a framework for formally evaluating definite integrals of real-valued, continuous functions using the Second Fundamental Theorem of Calculus. Our extended framework is also applied to functions containing free arguments. Using this framework, we are able to prove the orthogonality relationships between trigonometric functions, which are the essential properties in Fourier series analysis. The sum rule for definite integrals of indexed sums is also formalized by applying the extended framework along with the First Fundamental Theorem of Calculus and the sum rule for differentiation. The Fourier coefficient formulas of periodic functions are then formalized from the orthogonality relations and the sum rule for integration. Consequently, the uniqueness of Fourier sums is a straightforward corollary. We also present our formalization of the sum rule for definite integrals of infinite series in ACL2(r. Part of this task is to prove the Dini Uniform Convergence Theorem and the continuity of a limit function under certain conditions. A key technique in our proofs of these theorems is to apply the overspill principle from non-standard analysis.

15. Redis applied design patterns

CERN Document Server

Chinnachamy, Arun

2014-01-01

This book is for developers who are already proficient in programming and capable of designing systems using traditional databases, but are new to Redis. It is assumed that you understand the basics of Redis and are familiar with the various data structures. You are also expected to be proficient in one or more programming languages through which you want to use Redis.

16. The influence of applying additional weight to the affected leg on gait patterns during aquatic treadmill walking in people poststroke.

Science.gov (United States)

Jung, Taeyou; Lee, Dokyeong; Charalambous, Charalambos; Vrongistinos, Konstantinos

2010-01-01

Jung T, Lee D, Charalambous C, Vrongistinos K. The influence of applying additional weight to the affected leg on gait patterns during aquatic treadmill walking in people poststroke. To investigate how the application of additional weights to the affected leg influences gait patterns of people poststroke during aquatic treadmill walking. Comparative gait analysis. University-based aquatic therapy center. Community-dwelling volunteers (n=22) with chronic hemiparesis caused by stroke. Not applicable. Spatiotemporal and kinematic gait parameters. The use of an ankle weight showed an increase in the stance phase percentage of gait cycle (3%, P=.015) when compared with no weight. However, the difference was not significant after a Bonferroni adjustment was applied for a more stringent statistical analysis. No significant differences were found in cadence and stride length. The use of an ankle weight showed a significant decrease of the peak hip flexion (7.9%, P=.001) of the affected limb as compared with no weight condition. This decrease was marked as the reduction of unwanted limb flotation because people poststroke typically show excessive hip flexion of the paretic leg in the late swing phase followed by fluctuating hip movements during aquatic treadmill walking. The frontal and transverse plane hip motions did not show any significant differences but displayed a trend of a decrease in the peak hip abduction during the swing phase with additional weights. The use of additional weight did not alter sagittal plane kinematics of the knee and ankle joints. The use of applied weight on the affected limb can reduce unwanted limb flotation on the paretic side during aquatic treadmill walking. It can also assist the stance stability by increasing the stance phase percentage closer to 60% of gait cycle. Both findings can contribute to the development of more efficient motor patterns in gait training for people poststroke. The use of a cuff weight does not seem to reduce the

17. Fourier transforms in spectroscopy

CERN Document Server

Kauppinen, Jyrki

2000-01-01

This modern approach to the subject is clearly and logically structured, and gives readers an understanding of the essence of Fourier transforms and their applications. All important aspects are included with respect to their use with optical spectroscopic data. Based on popular lectures, the authors provide the mathematical fundamentals and numerical applications which are essential in practical use. The main part of the book is dedicated to applications of FT in signal processing and spectroscopy, with IR and NIR, NMR and mass spectrometry dealt with both from a theoretical and practical poi

18. Fourier Domain Sensing

Science.gov (United States)

Feldkhun, Daniel (Inventor); Wagner, Kelvin H. (Inventor)

2013-01-01

Methods and systems are disclosed of sensing an object. A first radiation is spatially modulated to generate a structured second radiation. The object is illuminated with the structured second radiation such that the object produces a third radiation in response. Apart from any spatially dependent delay, a time variation of the third radiation is spatially independent. With a single-element detector, a portion of the third radiation is detected from locations on the object simultaneously. At least one characteristic of a sinusoidal spatial Fourier-transform component of the object is estimated from a time-varying signal from the detected portion of the third radiation.

19. High-resolution electrical resistivity tomography applied to patterned ground, Wedel Jarlsberg Land, south-west Spitsbergen

Directory of Open Access Journals (Sweden)

Marek Kasprzak

2015-06-01

Full Text Available This article presents results of two-dimensional electrical resistivity tomography (ERT applied to three types of patterned ground in Wedel-Jarlsberg Land (Svalbard, carried out in late July 2012. The structures investigated include sorted circles, non-sorted polygons and a net with sorted coarser material. ERT was used to recognize the internal ground structure, the shape of permafrost table below the active layer and the geometric relationships between permafrost, ground layering and surface patterns. Results of inversion modelling indicate that the permafrost table occurs at a depth of 0.5–1 m in a mountain valley and 1–2.5 m on raised marine terraces. The permafrost table was nearly planar beneath non-sorted deposits and wavy beneath sorted materials. The mutual relationships between the permafrost table and the shape of a stone circle are different from those typically presented in literature. Ground structure beneath the net with sorted coarser materials is complex as implied in convective models. In non-sorted polygons, the imaging failed to reveal vertical structures between them.

20. Fast Fourier transform telescope

International Nuclear Information System (INIS)

Tegmark, Max; Zaldarriaga, Matias

2009-01-01

We propose an all-digital telescope for 21 cm tomography, which combines key advantages of both single dishes and interferometers. The electric field is digitized by antennas on a rectangular grid, after which a series of fast Fourier transforms recovers simultaneous multifrequency images of up to half the sky. Thanks to Moore's law, the bandwidth up to which this is feasible has now reached about 1 GHz, and will likely continue doubling every couple of years. The main advantages over a single dish telescope are cost and orders of magnitude larger field-of-view, translating into dramatically better sensitivity for large-area surveys. The key advantages over traditional interferometers are cost (the correlator computational cost for an N-element array scales as Nlog 2 N rather than N 2 ) and a compact synthesized beam. We argue that 21 cm tomography could be an ideal first application of a very large fast Fourier transform telescope, which would provide both massive sensitivity improvements per dollar and mitigate the off-beam point source foreground problem with its clean beam. Another potentially interesting application is cosmic microwave background polarization.

1. Fourier Transform Spectrometer System

Science.gov (United States)

Campbell, Joel F. (Inventor)

2014-01-01

A Fourier transform spectrometer (FTS) data acquisition system includes an FTS spectrometer that receives a spectral signal and a laser signal. The system further includes a wideband detector, which is in communication with the FTS spectrometer and receives the spectral signal and laser signal from the FTS spectrometer. The wideband detector produces a composite signal comprising the laser signal and the spectral signal. The system further comprises a converter in communication with the wideband detector to receive and digitize the composite signal. The system further includes a signal processing unit that receives the composite signal from the converter. The signal processing unit further filters the laser signal and the spectral signal from the composite signal and demodulates the laser signal, to produce velocity corrected spectral data.

2. Rainbow Fourier Transform

Science.gov (United States)

Alexandrov, Mikhail D.; Cairns, Brian; Mishchenko, Michael I.

2012-01-01

We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).

3. Quadrature formulas for Fourier coefficients

KAUST Repository

Bojanov, Borislav

2009-09-01

We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives. © 2009 Elsevier B.V. All rights reserved.

4. Interferogram conditioning for improved Fourier analysis and application to X-ray phase imaging by grating interferometry.

Science.gov (United States)

Montaux-Lambert, Antoine; Mercère, Pascal; Primot, Jérôme

2015-11-02

An interferogram conditioning procedure, for subsequent phase retrieval by Fourier demodulation, is presented here as a fast iterative approach aiming at fulfilling the classical boundary conditions imposed by Fourier transform techniques. Interference fringe patterns with typical edge discontinuities were simulated in order to reveal the edge artifacts that classically appear in traditional Fourier analysis, and were consecutively used to demonstrate the correction efficiency of the proposed conditioning technique. Optimization of the algorithm parameters is also presented and discussed. Finally, the procedure was applied to grating-based interferometric measurements performed in the hard X-ray regime. The proposed algorithm enables nearly edge-artifact-free retrieval of the phase derivatives. A similar enhancement of the retrieved absorption and fringe visibility images is also achieved.

5. Fourier-Hermite communications; where Fourier meets Hermite

NARCIS (Netherlands)

Korevaar, C.W.; Kokkeler, Andre B.J.; de Boer, Pieter-Tjerk; Smit, Gerardus Johannes Maria

A new signal set, based on the Fourier and Hermite signal bases, is introduced. It combines properties of the Fourier basis signals with the perfect time-frequency localization of the Hermite functions. The signal set is characterized by both a high spectral efficiency and good time-frequency

6. Fourier transform inequalities for phylogenetic trees.

Science.gov (United States)

Matsen, Frederick A

2009-01-01

Phylogenetic invariants are not the only constraints on site-pattern frequency vectors for phylogenetic trees. A mutation matrix, by its definition, is the exponential of a matrix with non-negative off-diagonal entries; this positivity requirement implies non-trivial constraints on the site-pattern frequency vectors. We call these additional constraints "edge-parameter inequalities". In this paper, we first motivate the edge-parameter inequalities by considering a pathological site-pattern frequency vector corresponding to a quartet tree with a negative internal edge. This site-pattern frequency vector nevertheless satisfies all of the constraints described up to now in the literature. We next describe two complete sets of edge-parameter inequalities for the group-based models; these constraints are square-free monomial inequalities in the Fourier transformed coordinates. These inequalities, along with the phylogenetic invariants, form a complete description of the set of site-pattern frequency vectors corresponding to bona fide trees. Said in mathematical language, this paper explicitly presents two finite lists of inequalities in Fourier coordinates of the form "monomial < or = 1", each list characterizing the phylogenetically relevant semialgebraic subsets of the phylogenetic varieties.

7. On fractional Fourier transform moments

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.

2000-01-01

Based on the relation between the ambiguity function represented in a quasi-polar coordinate system and the fractional power spectra, the fractional Fourier transform moments are introduced. Important equalities for the global second-order fractional Fourier transform moments are derived and their

8. Modern Fourier analysis

CERN Document Server

Grafakos, Loukas

2014-01-01

This text is addressed to graduate students in mathematics and to interested researchers who wish to acquire an in depth understanding of Euclidean Harmonic analysis. The text covers modern topics and techniques in function spaces, atomic decompositions, singular integrals of nonconvolution type, and the boundedness and convergence of Fourier series and integrals. The exposition and style are designed to stimulate further study and promote research. Historical information and references are included at the end of each chapter. This third edition includes a new chapter entitled "Multilinear Harmonic Analysis" which focuses on topics related to multilinear operators and their applications. Sections 1.1 and 1.2 are also new in this edition. Numerous corrections have been made to the text from the previous editions and several improvements have been incorporated, such as the adoption of clear and elegant statements. A few more exercises have been added with relevant hints when necessary. Reviews fr...

9. Mathematical principles of signal processing Fourier and wavelet analysis

CERN Document Server

Brémaud, Pierre

2002-01-01

Fourier analysis is one of the most useful tools in many applied sciences. The recent developments of wavelet analysis indicates that in spite of its long history and well-established applications, the field is still one of active research. This text bridges the gap between engineering and mathematics, providing a rigorously mathematical introduction of Fourier analysis, wavelet analysis and related mathematical methods, while emphasizing their uses in signal processing and other applications in communications engineering. The interplay between Fourier series and Fourier transforms is at the heart of signal processing, which is couched most naturally in terms of the Dirac delta function and Lebesgue integrals. The exposition is organized into four parts. The first is a discussion of one-dimensional Fourier theory, including the classical results on convergence and the Poisson sum formula. The second part is devoted to the mathematical foundations of signal processing - sampling, filtering, digital signal proc...

10. Solution of 3-dimensional diffusion equation by finite Fourier transformation

International Nuclear Information System (INIS)

Krishnani, P.D.

1978-01-01

Three dimensional diffusion equation in Cartesian co-ordinates is solved by using the finite Fourier transformation. This method is different from the usual Fourier transformation method in the sense that the solutions are obtained without performing the inverse Fourier transformation. The advantage has been taken of the fact that the flux is finite and integrable in the finite region. By applying this condition, a two-dimensional integral equation, involving flux and its normal derivative at the boundary, is obtained. By solving this equation with given boundary conditions, all of the boundary values are determined. In order to calculate the flux inside the region, flux is expanded into three-dimensional Fourier series. The Fourier coefficients of the flux in the region are calculated from the boundary values. The advantage of this method is that the integrated flux is obtained without knowing the fluxes inside the region as in the case of finite difference method. (author)

11. Fan beam image reconstruction with generalized Fourier slice theorem.

Science.gov (United States)

Zhao, Shuangren; Yang, Kang; Yang, Kevin

2014-01-01

For parallel beam geometry the Fourier reconstruction works via the Fourier slice theorem (or central slice theorem, projection slice theorem). For fan beam situation, Fourier slice can be extended to a generalized Fourier slice theorem (GFST) for fan-beam image reconstruction. We have briefly introduced this method in a conference. This paper reintroduces the GFST method for fan beam geometry in details. The GFST method can be described as following: the Fourier plane is filled by adding up the contributions from all fanbeam projections individually; thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the Fourier domain; inverse fast Fourier transform is applied to the image in Fourier plane and leads to a reconstructed image in spacial domain. The reconstructed image is compared between the result of the GFST method and the result from the filtered backprojection (FBP) method. The major differences of the GFST and the FBP methods are: (1) The interpolation process are at different data sets. The interpolation of the GFST method is at projection data. The interpolation of the FBP method is at filtered projection data. (2) The filtering process are done in different places. The filtering process of the GFST is at Fourier domain. The filtering process of the FBP method is the ramp filter which is done at projections. The resolution of ramp filter is variable with different location but the filter in the Fourier domain lead to resolution invariable with location. One advantage of the GFST method over the FBP method is in short scan situation, an exact solution can be obtained with the GFST method, but it can not be obtained with the FBP method. The calculation of both the GFST and the FBP methods are at O(N^3), where N is the number of pixel in one dimension.

12. Principal component analysis applied to Fourier transform infrared spectroscopy for the design of calibration sets for glycerol prediction models in wine and for the detection and classification of outlier samples.

Science.gov (United States)

Nieuwoudt, Helene H; Prior, Bernard A; Pretorius, Isak S; Manley, Marena; Bauer, Florian F

2004-06-16

Principal component analysis (PCA) was used to identify the main sources of variation in the Fourier transform infrared (FT-IR) spectra of 329 wines of various styles. The FT-IR spectra were gathered using a specialized WineScan instrument. The main sources of variation included the reducing sugar and alcohol content of the samples, as well as the stage of fermentation and the maturation period of the wines. The implications of the variation between the different wine styles for the design of calibration models with accurate predictive abilities were investigated using glycerol calibration in wine as a model system. PCA enabled the identification and interpretation of samples that were poorly predicted by the calibration models, as well as the detection of individual samples in the sample set that had atypical spectra (i.e., outlier samples). The Soft Independent Modeling of Class Analogy (SIMCA) approach was used to establish a model for the classification of the outlier samples. A glycerol calibration for wine was developed (reducing sugar content 8% v/v) with satisfactory predictive ability (SEP = 0.40 g/L). The RPD value (ratio of the standard deviation of the data to the standard error of prediction) was 5.6, indicating that the calibration is suitable for quantification purposes. A calibration for glycerol in special late harvest and noble late harvest wines (RS 31-147 g/L, alcohol > 11.6% v/v) with a prediction error SECV = 0.65 g/L, was also established. This study yielded an analytical strategy that combined the careful design of calibration sets with measures that facilitated the early detection and interpretation of poorly predicted samples and outlier samples in a sample set. The strategy provided a powerful means of quality control, which is necessary for the generation of accurate prediction data and therefore for the successful implementation of FT-IR in the routine analytical laboratory.

13. Wavelength modulation spectroscopy--digital detection of gas absorption harmonics based on Fourier analysis.

Science.gov (United States)

Mei, Liang; Svanberg, Sune

2015-03-20

This work presents a detailed study of the theoretical aspects of the Fourier analysis method, which has been utilized for gas absorption harmonic detection in wavelength modulation spectroscopy (WMS). The lock-in detection of the harmonic signal is accomplished by studying the phase term of the inverse Fourier transform of the Fourier spectrum that corresponds to the harmonic signal. The mathematics and the corresponding simulation results are given for each procedure when applying the Fourier analysis method. The present work provides a detailed view of the WMS technique when applying the Fourier analysis method.

14. Residual Stress Studies Using the Cairo Fourier Diffractometer Facility

International Nuclear Information System (INIS)

Maayouf, R.M.A.; El-Shaer, Y.H.

2002-01-01

The present paper deals with residual stress studies using the Cairo Fourier diffractometer facility CFDF. The CFDF is a reverse - time of -flight (RTOF) diffractometer; applies a Fourier chopper. The measurements were performed for copper samples in order to study the residual stress after welding. The maximum modulation of the Fourier chopper during the measurements was 136 khz; leading to a time resolution half-width of about 7 μ s. It has been found from the present measurements that, the resulting diffraction spectra could be successfully used for studying the residual stress; in the wavelength range between 0.7-2.9 A degree at ∼ 0.45 % relative resolution

15. Fourier phase in Fourier-domain optical coherence tomography

Science.gov (United States)

Uttam, Shikhar; Liu, Yang

2015-01-01

Phase of an electromagnetic wave propagating through a sample-of-interest is well understood in the context of quantitative phase imaging in transmission-mode microscopy. In the past decade, Fourier-domain optical coherence tomography has been used to extend quantitative phase imaging to the reflection-mode. Unlike transmission-mode electromagnetic phase, however, the origin and characteristics of reflection-mode Fourier phase are poorly understood, especially in samples with a slowly varying refractive index. In this paper, the general theory of Fourier phase from first principles is presented, and it is shown that Fourier phase is a joint estimate of subresolution offset and mean spatial frequency of the coherence-gated sample refractive index. It is also shown that both spectral-domain phase microscopy and depth-resolved spatial-domain low-coherence quantitative phase microscopy are special cases of this general theory. Analytical expressions are provided for both, and simulations are presented to explain and support the theoretical results. These results are further used to show how Fourier phase allows the estimation of an axial mean spatial frequency profile of the sample, along with depth-resolved characterization of localized optical density change and sample heterogeneity. Finally, a Fourier phase-based explanation of Doppler optical coherence tomography is also provided. PMID:26831383

16. Fourier phase in Fourier-domain optical coherence tomography.

Science.gov (United States)

Uttam, Shikhar; Liu, Yang

2015-12-01

Phase of an electromagnetic wave propagating through a sample-of-interest is well understood in the context of quantitative phase imaging in transmission-mode microscopy. In the past decade, Fourier-domain optical coherence tomography has been used to extend quantitative phase imaging to the reflection-mode. Unlike transmission-mode electromagnetic phase, however, the origin and characteristics of reflection-mode Fourier phase are poorly understood, especially in samples with a slowly varying refractive index. In this paper, the general theory of Fourier phase from first principles is presented, and it is shown that Fourier phase is a joint estimate of subresolution offset and mean spatial frequency of the coherence-gated sample refractive index. It is also shown that both spectral-domain phase microscopy and depth-resolved spatial-domain low-coherence quantitative phase microscopy are special cases of this general theory. Analytical expressions are provided for both, and simulations are presented to explain and support the theoretical results. These results are further used to show how Fourier phase allows the estimation of an axial mean spatial frequency profile of the sample, along with depth-resolved characterization of localized optical density change and sample heterogeneity. Finally, a Fourier phase-based explanation of Doppler optical coherence tomography is also provided.

17. Spatial correlation in 3D MIMO channels using fourier coefficients of power spectrums

KAUST Repository

Nadeem, Qurrat-Ul-Ain; Kammoun, Abla; Debbah, Mé rouane; Alouini, Mohamed-Slim

2015-01-01

for arbitrary angular distributions and antenna patterns. The resulting expression depends on the underlying angular distributions and antenna patterns through the Fourier Series (FS) coefficients of power azimuth and elevation spectrums. The novelty

18. Fourier analysis: from cloaking to imaging

Science.gov (United States)

Wu, Kedi; Cheng, Qiluan; Wang, Guo Ping

2016-04-01

Regarding invisibility cloaks as an optical imaging system, we present a Fourier approach to analytically unify both Pendry cloaks and complementary media-based invisibility cloaks into one kind of cloak. By synthesizing different transfer functions, we can construct different devices to realize a series of interesting functions such as hiding objects (events), creating illusions, and performing perfect imaging. In this article, we give a brief review on recent works of applying Fourier approach to analysis invisibility cloaks and optical imaging through scattering layers. We show that, to construct devices to conceal an object, no constructive materials with extreme properties are required, making most, if not all, of the above functions realizable by using naturally occurring materials. As instances, we experimentally verify a method of directionally hiding distant objects and create illusions by using all-dielectric materials, and further demonstrate a non-invasive method of imaging objects completely hidden by scattering layers.

19. Fourier analysis: from cloaking to imaging

International Nuclear Information System (INIS)

Wu, Kedi; Ping Wang, Guo; Cheng, Qiluan

2016-01-01

Regarding invisibility cloaks as an optical imaging system, we present a Fourier approach to analytically unify both Pendry cloaks and complementary media-based invisibility cloaks into one kind of cloak. By synthesizing different transfer functions, we can construct different devices to realize a series of interesting functions such as hiding objects (events), creating illusions, and performing perfect imaging. In this article, we give a brief review on recent works of applying Fourier approach to analysis invisibility cloaks and optical imaging through scattering layers. We show that, to construct devices to conceal an object, no constructive materials with extreme properties are required, making most, if not all, of the above functions realizable by using naturally occurring materials. As instances, we experimentally verify a method of directionally hiding distant objects and create illusions by using all-dielectric materials, and further demonstrate a non-invasive method of imaging objects completely hidden by scattering layers. (review)

20. The PROSAIC Laplace and Fourier Transform

International Nuclear Information System (INIS)

Smith, G.A.

1994-01-01

Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today's emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting

1. Applying multilevel model to the relationship of dietary patterns and colorectal cancer: an ongoing case-control study in Córdoba, Argentina.

Science.gov (United States)

Pou, Sonia Alejandra; Díaz, María del Pilar; Osella, Alberto Rubén

2012-09-01

Scientific literature has consistently shown the effects of certain diets on health but regional variations of dietary habits, and their relationship colorectal cancer (CRC) has been poorly studied in Argentina. Our aims were to identify dietary patterns and estimate their effect on CRC occurrence and to quantify the association between family history of CRC and CRC occurrence by applying multilevel models to estimate and interpret measures of variation. Principal components factor analysis was performed to identify dietary patterns that were then used in a multilevel logistic regression applied to an ongoing case-control data about dietary exposure and CRC occurrence taking into account familiar clustering. Three dietary patterns were identified: "Southern Cone pattern" (red meat, wine, and starchy vegetables), "High-sugar drinks pattern", and "Prudent pattern". The study considered 41 cases and 95 controls. There was a significant promoting effects on CRC of "Southern Cone" (OR 1.5, 95%CI 1.0-2.2) and "High-sugar drinks" (OR 3.8, 95%CI 2.0-7.1) patterns, whereas "Prudent pattern" (OR 0.3, 95%CI 0.2-0.4) showed a significant protective effect at third tertile level. BMI, use of NSAIDs, and to have medical insurance showed significant effects. Variance of the random effect of family history of CRC was highly significant. This novel approach for Argentina showed that Southern Cone and High-sugar drinks patterns were associated with a higher risk of CRC, whereas the Prudent pattern showed a protective effect. There was a significant clustering effect of family history of CRC.

2. Fast Fourier single-pixel imaging via binary illumination.

Science.gov (United States)

Zhang, Zibang; Wang, Xueying; Zheng, Guoan; Zhong, Jingang

2017-09-20

Fourier single-pixel imaging (FSI) employs Fourier basis patterns for encoding spatial information and is capable of reconstructing high-quality two-dimensional and three-dimensional images. Fourier-domain sparsity in natural scenes allows FSI to recover sharp images from undersampled data. The original FSI demonstration, however, requires grayscale Fourier basis patterns for illumination. This requirement imposes a limitation on the imaging speed as digital micro-mirror devices (DMDs) generate grayscale patterns at a low refreshing rate. In this paper, we report a new strategy to increase the speed of FSI by two orders of magnitude. In this strategy, we binarize the Fourier basis patterns based on upsampling and error diffusion dithering. We demonstrate a 20,000 Hz projection rate using a DMD and capture 256-by-256-pixel dynamic scenes at a speed of 10 frames per second. The reported technique substantially accelerates image acquisition speed of FSI. It may find broad imaging applications at wavebands that are not accessible using conventional two-dimensional image sensors.

3. Fourier analysis in dynamic non periodic phenomena in nuclear medicine

International Nuclear Information System (INIS)

Constantinesco, A.; Lallot, C.

1984-01-01

The success of Fourier analysis in assessing cardiac function has led us to investigate other possible uses of this technique. We show that phase analysis applied to dynamic non periodic activity changes gives useful parametric functional images. The phase image is comparable to a transit time image, the amplitude image is comparable to the maximum variations of activity and the mean image corresponds to a normalized sum of images. Exemples of this powerful application of Fourier analysis are discussed [fr

4. Fourier analysis and stochastic processes

CERN Document Server

Brémaud, Pierre

2014-01-01

This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). A careful review of the prerequisites (integration and probability theory in the appendix, Hilbert spa...

5. Quadrature formulas for Fourier coefficients

KAUST Repository

Bojanov, Borislav; Petrova, Guergana

2009-01-01

We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node

6. Symplectic geometry and Fourier analysis

CERN Document Server

Wallach, Nolan R

2018-01-01

Suitable for graduate students in mathematics, this monograph covers differential and symplectic geometry, homogeneous symplectic manifolds, Fourier analysis, metaplectic representation, quantization, Kirillov theory. Includes Appendix on Quantum Mechanics by Robert Hermann. 1977 edition.

7. Multivariate temporal pattern analysis applied to the study of rat behavior in the elevated plus maze: methodological and conceptual highlights.

Science.gov (United States)

Casarrubea, M; Magnusson, M S; Roy, V; Arabo, A; Sorbera, F; Santangelo, A; Faulisi, F; Crescimanno, G

2014-08-30

8. Optical Pattern Recognition

Science.gov (United States)

Yu, Francis T. S.; Jutamulia, Suganda

2008-10-01

Contributors; Preface; 1. Pattern recognition with optics Francis T. S. Yu and Don A. Gregory; 2. Hybrid neural networks for nonlinear pattern recognition Taiwei Lu; 3. Wavelets, optics, and pattern recognition Yao Li and Yunglong Sheng; 4. Applications of the fractional Fourier transform to optical pattern recognition David Mendlovic, Zeev Zalesky and Haldum M. Oxaktas; 5. Optical implementation of mathematical morphology Tien-Hsin Chao; 6. Nonlinear optical correlators with improved discrimination capability for object location and recognition Leonid P. Yaroslavsky; 7. Distortion-invariant quadratic filters Gregory Gheen; 8. Composite filter synthesis as applied to pattern recognition Shizhou Yin and Guowen Lu; 9. Iterative procedures in electro-optical pattern recognition Joseph Shamir; 10. Optoelectronic hybrid system for three-dimensional object pattern recognition Guoguang Mu, Mingzhe Lu and Ying Sun; 11. Applications of photrefractive devices in optical pattern recognition Ziangyang Yang; 12. Optical pattern recognition with microlasers Eung-Gi Paek; 13. Optical properties and applications of bacteriorhodopsin Q. Wang Song and Yu-He Zhang; 14. Liquid-crystal spatial light modulators Aris Tanone and Suganda Jutamulia; 15. Representations of fully complex functions on real-time spatial light modulators Robert W. Cohn and Laurence G. Hassbrook; Index.

9. Fourier transform nuclear magnetic resonance

International Nuclear Information System (INIS)

Geick, R.

1981-01-01

This review starts with the basic principles of resonance phenomena in physical systems. Especially, the connection is shown between the properties of these systems and Fourier transforms. Next, we discuss the principles of nuclear magnetic resonance. Starting from the general properties of physical systems showing resonance phenomena and from the special properties of nuclear spin systems, the main part of this paper reviews pulse and Fourier methods in nuclear magnetic resonance. Among pulse methods, an introduction will be given to spin echoes, and, apart from the principle of Fourier transform nuclear magnetic resonance, an introduction to the technical problems of this method, e.g. resolution in the frequency domain, aliasing, phase and intensity errors, stationary state of the spin systems for repetitive measurements, proton decoupling, and application of Fourier methods to systems in a nonequilibrium state. The last section is devoted to special applications of Fourier methods and recent developments, e.g. measurement of relaxation times, solvent peak suppression, 'rapid scan'-method, methods for suppressing the effects of dipolar coupling in solids, two-dimensional Fourier transform nuclear magnetic resonance, and spin mapping or zeugmatography. (author)

10. MODELING OF PATTERN FORMING PROCESS OF AUTOMATIC RADIO DIRECTION FINDER OF PHASE VHF IN THE DEVELOPMENT ENVIRONMENT OF LabVIEW APPLIED PROGRAMS

Directory of Open Access Journals (Sweden)

G. K. Aslanov

2015-01-01

Full Text Available In the article is developed the model demonstrating the forming process of pattern of antenna system of aerodrome quasidopler automatic radiodirection-finder station in the development environment of LabVIEW applied programs of National Instrument company.

11. Application of Fourier analysis to multispectral/spatial recognition

Science.gov (United States)

Hornung, R. J.; Smith, J. A.

1973-01-01

One approach for investigating spectral response from materials is to consider spatial features of the response. This might be accomplished by considering the Fourier spectrum of the spatial response. The Fourier Transform may be used in a one-dimensional to multidimensional analysis of more than one channel of data. The two-dimensional transform represents the Fraunhofer diffraction pattern of the image in optics and has certain invariant features. Physically the diffraction pattern contains spatial features which are possibly unique to a given configuration or classification type. Different sampling strategies may be used to either enhance geometrical differences or extract additional features.

12. Corrected Fourier series and its application to function approximation

Directory of Open Access Journals (Sweden)

Qing-Hua Zhang

2005-01-01

Full Text Available Any quasismooth function f(x in a finite interval [0,x0], which has only a finite number of finite discontinuities and has only a finite number of extremes, can be approximated by a uniformly convergent Fourier series and a correction function. The correction function consists of algebraic polynomials and Heaviside step functions and is required by the aperiodicity at the endpoints (i.e., f(0≠f(x0 and the finite discontinuities in between. The uniformly convergent Fourier series and the correction function are collectively referred to as the corrected Fourier series. We prove that in order for the mth derivative of the Fourier series to be uniformly convergent, the order of the polynomial need not exceed (m+1. In other words, including the no-more-than-(m+1 polynomial has eliminated the Gibbs phenomenon of the Fourier series until its mth derivative. The corrected Fourier series is then applied to function approximation; the procedures to determine the coefficients of the corrected Fourier series are illustrated in detail using examples.

13. Fourier transform resampling: Theory and application

International Nuclear Information System (INIS)

Hawkins, W.G.

1996-01-01

One of the most challenging problems in medical imaging is the development of reconstruction algorithms for nonstandard geometries. This work focuses on the application of Fourier analysis to the problem of resampling or rebinning. Conventional resampling methods utilizing some form of interpolation almost always result in a loss of resolution in the tomographic image. Fourier Transform Resampling (FTRS) offers potential improvement because the Modulation Transfer Function (MTF) of the process behaves like an ideal low pass filter. The MTF, however, is nonstationary if the coordinate transformation is nonlinear. FTRS may be viewed as a generalization of the linear coordinate transformations of standard Fourier analysis. Simulated MTF's were obtained by projecting point sources at different transverse positions in the flat fan beam detector geometry. These MTF's were compared to the closed form expression for FIRS. Excellent agreement was obtained for frequencies at or below the estimated cutoff frequency. The resulting FTRS algorithm is applied to simulations with symmetric fan beam geometry, an elliptical orbit and uniform attenuation, with a normalized root mean square error (NRME) of 0.036. Also, a Tc-99m point source study (1 cm dia., placed in air 10 cm from the COR) for a circular fan beam acquisition was reconstructed with a hybrid resampling method. The FWHM of the hybrid resampling method was 11.28 mm and compares favorably with a direct reconstruction (FWHM: 11.03 mm)

14. Sets of Fourier coefficients using numerical quadrature

International Nuclear Information System (INIS)

Lyness, J. N.

2001-01-01

One approach to the calculation of Fourier trigonometric coefficients f(r) of a given function f(x) is to apply the trapezoidal quadrature rule to the integral representation f(r)=(line i ntegral)(sub 0)(sup 1) f(x)e(sup -2(pi)irx)dx. Some of the difficulties in this approach are discussed. A possible way of overcoming many of these is by means of a subtraction function. Thus, one sets f(x)= h(sub p-1)(x)+ g(sub p)(x), where h(sub -1)(x) is an algebraic polynomial of degree p-1, specified in such a way that the Fourier series of g(sub p)(x) converges more rapidly than that of f(x). To obtain the Fourier coefficients of f(x), one uses an analytic expression for those of h(sub p-1)(x) and numerical quadrature to approximately those of g(sub p)(x)

15. Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans.

Science.gov (United States)

Magnes, Jenny; Hastings, Harold M; Raley-Susman, Kathleen M; Alivisatos, Clara; Warner, Adam; Hulsey-Vincent, Miranda

2017-09-13

This manuscript describes how to classify nematodes using temporal far-field diffraction signatures. A single C. elegans is suspended in a water column inside an optical cuvette. A 632 nm continuous wave HeNe laser is directed through the cuvette using front surface mirrors. A significant distance of at least 20-30 cm traveled after the light passes through the cuvette ensures a useful far-field (Fraunhofer) diffraction pattern. The diffraction pattern changes in real time as the nematode swims within the laser beam. The photodiode is placed off-center in the diffraction pattern. The voltage signal from the photodiode is observed in real time and recorded using a digital oscilloscope. This process is repeated for 139 wild type and 108 "roller" C. elegans. Wild type worms exhibit a rapid oscillation pattern in solution. The "roller" worms have a mutation in a key component of the cuticle that interferes with smooth locomotion. Time intervals that are not free of saturation and inactivity are discarded. It is practical to divide each average by its maximum to compare relative intensities. The signal for each worm is Fourier transformed so that the frequency pattern for each worm emerges. The signal for each type of worm is averaged. The averaged Fourier spectra for the wild type and the "roller" C. elegans are distinctly different and reveal that the dynamic worm shapes of the two different worm strains can be distinguished using Fourier analysis. The Fourier spectra of each worm strain match an approximate model using two different binary worm shapes that correspond to locomotory moments. The envelope of the averaged frequency distribution for actual and modeled worms confirms the model matches the data. This method can serve as a baseline for Fourier analysis for many microscopic species, as every microorganism will have its unique Fourier spectrum.

16. Constellation of phase singularities in a speckle-like pattern for optical vortex metrology applied to biological kinematic analysis

DEFF Research Database (Denmark)

Wang, Wei; Qiao, Yu; Ishijima, Reika

2008-01-01

A novel technique for biological kinematic analysis is proposed that makes use of the pseudophase singularities in a complex signal generated from a speckle-like pattern. In addition to the information about the locations and the anisotropic core structures of the pseudophase singularities, we al...... are presented, which demonstrate the validity of the proposed technique. (c) 2008 Optical Society of America....

17. General Correlation Theorem for Trinion Fourier Transform

OpenAIRE

Bahri, Mawardi

2017-01-01

- The trinion Fourier transform is an extension of the Fourier transform in the trinion numbers setting. In this work we derive the correlation theorem for the trinion Fourier transform by using the relation between trinion convolution and correlation definitions in the trinion Fourier transform domains.

18. Fourier Series, the DFT and Shape Modelling

DEFF Research Database (Denmark)

Skoglund, Karl

2004-01-01

This report provides an introduction to Fourier series, the discrete Fourier transform, complex geometry and Fourier descriptors for shape analysis. The content is aimed at undergraduate and graduate students who wish to learn about Fourier analysis in general, as well as its application to shape...

19. Fourier series, Fourier transform and their applications to mathematical physics

CERN Document Server

Serov, Valery

2017-01-01

This text serves as an introduction to the modern theory of analysis and differential equations with applications in mathematical physics and engineering sciences.  Having outgrown from a series of half-semester courses given at University of Oulu, this book consists of four self-contained parts. The first part, Fourier Series and the Discrete Fourier Transform, is devoted to the classical one-dimensional trigonometric Fourier series with some applications to PDEs and signal processing.  The second part, Fourier Transform and Distributions, is concerned with distribution theory of L. Schwartz and its applications to the Schrödinger and magnetic Schrödinger operations.  The third part, Operator Theory and Integral Equations, is devoted mostly to the self-adjoint but unbounded operators in Hilbert spaces and their applications to integral equations in such spaces. The fourth and final part, Introduction to Partial Differential Equations, serves as an introduction to modern methods for classical theory o...

20. Fourier series and orthogonal polynomials

CERN Document Server

Jackson, Dunham

2004-01-01

This text for undergraduate and graduate students illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Starting with a definition and explanation of the elements of Fourier series, the text follows with examinations of Legendre polynomials and Bessel functions. Boundary value problems consider Fourier series in conjunction with Laplace's equation in an infinite strip and in a rectangle, with a vibrating string, in three dimensions, in a sphere, and in other circumstances. An overview of Pearson frequency functions is followe

1. Experimental display of Fourier analysis through the optical physics and its didatical utilization

International Nuclear Information System (INIS)

Oliveira, S.M.M. de.

1983-01-01

The properties of Fourier analysis through physical optics are displayed experimentally. Within physical optics topics that illustrate didactically Fourier analysis, a subject usually considered purely mathematical are selected. The most important properties of Fourier transform and their utilization in cleaning up images through spatial filtering are presented, in this way the properties of convolution to analyse image formation and characterize some diffraction patterns are also used. (Author) [pt

2. Closed form fourier-based transmit beamforming for MIMO radar

KAUST Repository

Lipor, John J.; Ahmed, Sajid; Alouini, Mohamed-Slim

2014-01-01

-pattern, current research uses iterative algorithms, first to synthesize the waveform covariance matrix, R, then to design the actual waveforms to realize R. In contrast to this, we present a closed form method to design R that exploits discrete Fourier transform

3. Detailed semantic analyses of human error incidents occurring at nuclear power plants. Extraction of periodical transition of error occurrence patterns by applying multivariate analysis

International Nuclear Information System (INIS)

Hirotsu, Yuko; Suzuki, Kunihiko; Takano, Kenichi; Kojima, Mitsuhiro

2000-01-01

It is essential for preventing the recurrence of human error incidents to analyze and evaluate them with the emphasis on human factor. Detailed and structured analyses of all incidents at domestic nuclear power plants (NPPs) reported during last 31 years have been conducted based on J-HPES, in which total 193 human error cases are identified. Results obtained by the analyses have been stored into the J-HPES database. In the previous study, by applying multivariate analysis to above case studies, it was suggested that there were several occurrence patterns identified of how errors occur at NPPs. It was also clarified that the causes related to each human error are different depending on age of their occurrence. This paper described the obtained results in respects of periodical transition of human error occurrence patterns. By applying multivariate analysis to the above data, it was suggested there were two types of error occurrence patterns as to each human error type. First type is common occurrence patterns, not depending on the age, and second type is the one influenced by periodical characteristics. (author)

4. FOURIER SERIES MODELS THROUGH TRANSFORMATION

African Journals Online (AJOL)

DEPT

monthly temperature data (1996 – 2005) collected from the National Root ... KEY WORDS: Fourier series, square transformation, multiplicative model, ... fluctuations or movements are often periodic(Ekpeyong,2005). .... significant trend or not, if the trend is not significant, the grand mean may be used as an estimate of trend.

5. Fourier diffraction theorem for diffusion-based thermal tomography

International Nuclear Information System (INIS)

2006-01-01

There has been much recent interest in thermal imaging as a method of non-destructive testing and for non-invasive medical imaging. The basic idea of applying heat or cold to an area and observing the resulting temperature change with an infrared camera has led to the development of rapid and relatively inexpensive inspection systems. However, the main drawback to date has been that such an approach provides mainly qualitative results. In order to advance the quantitative results that are possible via thermal imaging, there is interest in applying techniques and algorithms from conventional tomography. Many tomography algorithms are based on the Fourier diffraction theorem, which is inapplicable to thermal imaging without suitable modification to account for the attenuative nature of thermal waves. In this paper, the Fourier diffraction theorem for thermal tomography is derived and discussed. The intent is for this thermal-diffusion based Fourier diffraction theorem to form the basis of tomographic reconstruction algorithms for quantitative thermal imaging

6. Encoding plaintext by Fourier transform hologram in double random phase encoding using fingerprint keys

Science.gov (United States)

Takeda, Masafumi; Nakano, Kazuya; Suzuki, Hiroyuki; Yamaguchi, Masahiro

2012-09-01

It has been shown that biometric information can be used as a cipher key for binary data encryption by applying double random phase encoding. In such methods, binary data are encoded in a bit pattern image, and the decrypted image becomes a plain image when the key is genuine; otherwise, decrypted images become random images. In some cases, images decrypted by imposters may not be fully random, such that the blurred bit pattern can be partially observed. In this paper, we propose a novel bit coding method based on a Fourier transform hologram, which makes images decrypted by imposters more random. Computer experiments confirm that the method increases the randomness of images decrypted by imposters while keeping the false rejection rate as low as in the conventional method.

7. Encoding plaintext by Fourier transform hologram in double random phase encoding using fingerprint keys

International Nuclear Information System (INIS)

Takeda, Masafumi; Nakano, Kazuya; Suzuki, Hiroyuki; Yamaguchi, Masahiro

2012-01-01

It has been shown that biometric information can be used as a cipher key for binary data encryption by applying double random phase encoding. In such methods, binary data are encoded in a bit pattern image, and the decrypted image becomes a plain image when the key is genuine; otherwise, decrypted images become random images. In some cases, images decrypted by imposters may not be fully random, such that the blurred bit pattern can be partially observed. In this paper, we propose a novel bit coding method based on a Fourier transform hologram, which makes images decrypted by imposters more random. Computer experiments confirm that the method increases the randomness of images decrypted by imposters while keeping the false rejection rate as low as in the conventional method. (paper)

8. Detection of boiling by Piety's on-line PSD-pattern recognition algorithm applied to neutron noise signals in the SAPHIR reactor

International Nuclear Information System (INIS)

Spiekerman, G.

1988-09-01

A partial blockage of the cooling channels of a fuel element in a swimming pool reactor could lead to vapour generation and to burn-out. To detect such anomalies, a pattern recognition algorithm based on power spectra density (PSD) proposed by Piety was further developed and implemented on a PDP 11/23 for on-line applications. This algorithm identifies anomalies by measuring the PSD on the process signal and comparing them with a standard baseline previously formed. Up to 8 decision discriminants help to recognize spectral changes due to anomalies. In our application, to detect boiling as quickly as possible with sufficient sensitivity, Piety's algorithm was modified using overlapped Fast-Fourier-Transform-Processing and the averaging of the PSDs over a large sample of preceding instantaneous PSDs. This processing allows high sensitivity in detecting weak disturbances without reducing response time. The algorithm was tested with simulation-of-boiling experiments where nitrogen in a cooling channel of a mock-up of a fuel element was injected. Void fractions higher than 30 % in the channel can be detected. In the case of boiling, it is believed that this limit is lower because collapsing bubbles could give rise to stronger fluctuations. The algorithm was also tested with a boiling experiment where the reactor coolant flow was actually reduced. The results showed that the discriminant D5 of Piety's algorithm based on neutron noise obtained from the existing neutron chambers of the reactor control system could sensitively recognize boiling. The detection time amounts to 7-30 s depending on the strength of the disturbances. Other events, which arise during a normal reactor run like scrams, removal of isotope elements without scramming or control rod movements and which could lead to false alarms, can be distinguished from boiling. 49 refs., 104 figs., 5 tabs

9. Do's and don'ts in Fourier analysis of steady-state potentials.

Science.gov (United States)

Bach, M; Meigen, T

1999-01-01

Fourier analysis is a powerful tool in signal analysis that can be very fruitfully applied to steady-state evoked potentials (flicker ERG, pattern ERG, VEP, etc.). However, there are some inherent assumptions in the underlying discrete Fourier transform (DFT) that are not necessarily fulfilled in typical electrophysiological recording and analysis conditions. Furthermore, engineering software-packages may be ill-suited and/or may not fully exploit the information of steady-state recordings. Specifically: * In the case of steady-state stimulation we know more about the stimulus than in standard textbook situations (exact frequency, phase stability), so 'windowing' and calculation of the 'periodogram' are not necessary. * It is mandatory to choose an integer relationship between sampling rate and frame rate when employing a raster-based CRT stimulator. * The analysis interval must comprise an exact integer number (e.g., 10) of stimulus periods. * The choice of the number of stimulus periods per analysis interval needs a wise compromise: A high number increases the frequency resolution, but makes artifact removal difficult; a low number 'spills' noise into the response frequency. * There is no need to feel tied to a power-of-two number of data points as required by standard FFT, 'resampling' is an easy and efficient alternative. * Proper estimates of noise-corrected Fourier magnitude and statistical significance can be calculated that take into account the non-linear superposition of signal and noise. These aspects are developed in an intuitive approach with examples using both simulations and recordings. Proper use of Fourier analysis of our electrophysiological records will reduce recording time and/or increase the reliability of physiologic or pathologic interpretations.

10. Comparative study on γ energy spectrum denoise by fourier and wavelet transforms

International Nuclear Information System (INIS)

Shi Dongsheng; Di Yuming; Zhou Chunlin

2007-01-01

This paper introduces the basic principle of wavelet and Fourier transforms, applies wavelet transform method to denoise γ energy spectrum of 60 Co and compares it with Fourier transform method. The result of simulation with MATLAB software tool showed that as compared with traditional Fourier transform, wavelet transform has comparatively higher accuracy for γ energy spectrum denoising and is more feasible to γ energy spectrum denoising. (authors)

11. Porphyrin pattern and methemoglobin levels in Columba livia applied to assess toxicological risk by air pollution in urban areas.

Science.gov (United States)

Sicolo, Matteo; Tringali, Maria; Orsi, Federica; Santagostino, Angela

2009-11-01

The study has explored two conservative biomarkers, porphyrin pattern in guano and methemoglobin levels in blood of Columba livia, in order to assay their potential use for monitoring toxic effects induced by exposure to urban air pollution. Fieldwork was conducted between October 2003 and June 2005 in the city of Milan, Italy, by sampling the pigeons in different areas almost twice a week. Six air contaminants, CO, PM10, NO(2), O(3), SO(2), and C(6)H(6), plus polycyclic aromatic hydrocarbons (PAHs) in fine particles, temperature, and UV index, were considered. Protoporphyrins from pigeon excreta sampled outdoors were always higher than in indoor animals, particularly in winter. A positive correlation (p urban air showed significant differences from season to season but only in summer and autumn did the outdoor pigeons show higher values than indoor animals. In summer, a regression model with a positive correlation between O(3) and benzene was determined (p urban air pollution as well as for detecting complex interactions between contaminants in the urban air pollutant mixture was discussed.

12. Small area estimation of obesity prevalence and dietary patterns: a model applied to Rio de Janeiro city, Brazil.

Science.gov (United States)

Cataife, Guido

2014-03-01

We propose the use of previously developed small area estimation techniques to monitor obesity and dietary habits in developing countries and apply the model to Rio de Janeiro city. We estimate obesity prevalence rates at the Census Tract through a combinatorial optimization spatial microsimulation model that matches body mass index and socio-demographic data in Brazil's 2008-9 family expenditure survey with Census 2010 socio-demographic data. Obesity ranges from 8% to 25% in most areas and affects the poor almost as much as the rich. Male and female obesity rates are uncorrelated at the small area level. The model is an effective tool to understand the complexity of the problem and to aid in policy design. © 2013 Published by Elsevier Ltd.

13. From Fourier analysis to wavelets

CERN Document Server

Gomes, Jonas

2015-01-01

This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints.  Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform.  The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed. Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets.  Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis.  Basic knowledge of signal and image processing is desirable. This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.

14. Compact Microwave Fourier Spectrum Analyzer

Science.gov (United States)

Savchenkov, Anatoliy; Matsko, Andrey; Strekalov, Dmitry

2009-01-01

A compact photonic microwave Fourier spectrum analyzer [a Fourier-transform microwave spectrometer, (FTMWS)] with no moving parts has been proposed for use in remote sensing of weak, natural microwave emissions from the surfaces and atmospheres of planets to enable remote analysis and determination of chemical composition and abundances of critical molecular constituents in space. The instrument is based on a Bessel beam (light modes with non-zero angular momenta) fiber-optic elements. It features low power consumption, low mass, and high resolution, without a need for any cryogenics, beyond what is achievable by the current state-of-the-art in space instruments. The instrument can also be used in a wide-band scatterometer mode in active radar systems.

15. Uncertainty Principles and Fourier Analysis

analysis on the part of the reader. Those who are not fa- miliar with Fourier analysis are encouraged to look up Box. 1 along with [3]. (A) Heisenberg's inequality: Let us measure concentration in terms of standard deviation i.e. for a square integrable func-. 00 tion defined on 1R and normalized so that J If(x)12d,x = 1,. -00. 00.

16. Fourier transformation methods in the field of gamma spectrometry

The basic principles of a new version of Fourier transformation is presented. This new version was applied to solve some main problems such as smoothing, and denoising in gamma spectroscopy. The mathematical procedures were first tested by simulated data and then by actual experimental data.

17. A new analytical solution to the diffusion problem: Fourier series ...

African Journals Online (AJOL)

This paper reviews briefly the origin of Fourier Series Method. The paper then gives a vivid description of how the method can be applied to solve a diffusion problem, subject to some boundary conditions. The result obtained is quite appealing as it can be used to solve similar examples of diffusion equations. JONAMP Vol.

18. Prototypes and matrix relevance learning in complex fourier space

NARCIS (Netherlands)

Straat, M.; Kaden, M.; Gay, M.; Villmann, T.; Lampe, Alexander; Seiffert, U.; Biehl, M.; Melchert, F.

2017-01-01

In this contribution, we consider the classification of time-series and similar functional data which can be represented in complex Fourier coefficient space. We apply versions of Learning Vector Quantization (LVQ) which are suitable for complex-valued data, based on the so-called Wirtinger

19. An introduction to Fourier series and integrals

CERN Document Server

Seeley, Robert T

2006-01-01

This compact guide emphasizes the relationship between physics and mathematics, introducing Fourier series in the way that Fourier himself used them: as solutions of the heat equation in a disk. 1966 edition.

20. Feasibility of applying the life history calendar in a population of chronic opioid users to identify patterns of drug use and addiction treatment.

Science.gov (United States)

Fikowski, Jill; Marchand, Kirsten; Palis, Heather; Oviedo-Joekes, Eugenia

2014-01-01

Uncovering patterns of drug use and treatment access is essential to improving treatment for opioid dependence. The life history calendar (LHC) could be a valuable instrument for capturing time-sensitive data on lifetime patterns of drug use and addiction treatment. This study describes the methodology applied when collecting data using the LHC in a sample of individuals with long-term opioid dependence and aims to identify specific factors that impact the feasibility of administering the LHC interview. In this study, the LHC allowed important events such as births, intimate relationships, housing, or incarcerations to become reference points for recalling details surrounding drug use and treatment access. The paper concludes that the administration of the LHC was a resource-intensive process and required special attention to interviewer training and experience with the study population. These factors should be considered and integrated into study plans by researchers using the LHC in addiction research.

1. The prosaic Laplace and Fourier transform

International Nuclear Information System (INIS)

Smith, G.A.

1995-01-01

Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today's emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting. copyright 1995 American Institute of Physics

2. Elementary kinetic modelling applied to solid oxide fuel cell pattern anodes and a direct flame fuel cell system

Energy Technology Data Exchange (ETDEWEB)

Vogler, Marcel

2009-05-27

In the course of this thesis a model for the prediction of polarisation characteristics of solid oxide fuel cells (SOFC) was developed. The model is based on an elementary kinetic description of electrochemical reactions and the fundamental conservation principles of mass and energy. The model allows to predict the current-voltage relation of an SOFC and offers ideal possibilities for model validation. The aim of this thesis is the identification of rate-limiting processes and the determination of the elementary pathway during charge transfer. The numerical simulation of experiments with model anodes allowed to identify a hydrogen transfer to be the most probable charge-transfer reaction and revealed the influence of diffusive transport. Applying the hydrogen oxidation kinetics to the direct flame fuel cell system (DFFC) showed that electrochemical oxidation of CO is possible based on the same mechanism. Based on the quantification of loss processes in the DFFC system, improvements on cell design, predicting 80% increase of efficiency, were proposed. (orig.)

3. Properties of the distributional finite Fourier transform

OpenAIRE

Carmichael, Richard D.

2016-01-01

The analytic functions in tubes which obtain the distributional finite Fourier transform as boundary value are shown to have a strong boundedness property and to be recoverable as a Fourier-Laplace transform, a distributional finite Fourier transform, and as a Cauchy integral of a distribution associated with the boundary value.

4. Fourier techniques in X-ray timing

NARCIS (Netherlands)

van der Klis, M.

1988-01-01

Basic principles of Fourier techniques often used in X-ray time series analysis are reviewed. The relation between the discrete Fourier transform and the continuous Fourier transform is discussed to introduce the concepts of windowing and aliasing. The relation is derived between the power spectrum

5. Fourier analysis of temporal NDVI in the Southern African and American continents

NARCIS (Netherlands)

Azzali, S.; Menenti, M.

1996-01-01

Results of applying Fourier analysis of temporal NDVI in southern Africa and southern America are summarized. The decomposition of complex time series of images in simpler periodic components by Fourier analysis allowed the factors that affect the vegetation cover to be analysed much easier. The

6. Solution of two-dimensional diffusion equation for hexagonal cells by the finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1975-01-01

A method of solution is presented for a monoenergetic diffusion equation in two-dimensional hexagonal cells by a finite Fourier transformation. Up to the present, the solution by the finite Fourier transformation has been developed for x-y, r-z and x-y-z geometries, and the flux and current at the boundary are obtained in terms of Fourier series. It is shown here that the method can be applied to hexagonal cells and the expansion of boundary values in a Legendre polynomials gives numerically a higher accuracy than is obtained by a Fourier series. (orig.) [de

7. Fourier-Based Fast Multipole Method for the Helmholtz Equation

KAUST Repository

Cecka, Cris

2013-01-01

The fast multipole method (FMM) has had great success in reducing the computational complexity of solving the boundary integral form of the Helmholtz equation. We present a formulation of the Helmholtz FMM that uses Fourier basis functions rather than spherical harmonics. By modifying the transfer function in the precomputation stage of the FMM, time-critical stages of the algorithm are accelerated by causing the interpolation operators to become straightforward applications of fast Fourier transforms, retaining the diagonality of the transfer function, and providing a simplified error analysis. Using Fourier analysis, constructive algorithms are derived to a priori determine an integration quadrature for a given error tolerance. Sharp error bounds are derived and verified numerically. Various optimizations are considered to reduce the number of quadrature points and reduce the cost of computing the transfer function. © 2013 Society for Industrial and Applied Mathematics.

8. Fourier-transform optical microsystems

Science.gov (United States)

Collins, S. D.; Smith, R. L.; Gonzalez, C.; Stewart, K. P.; Hagopian, J. G.; Sirota, J. M.

1999-01-01

The design, fabrication, and initial characterization of a miniature single-pass Fourier-transform spectrometer (FTS) that has an optical bench that measures 1 cm x 5 cm x 10 cm is presented. The FTS is predicated on the classic Michelson interferometer design with a moving mirror. Precision translation of the mirror is accomplished by microfabrication of dovetailed bearing surfaces along single-crystal planes in silicon. Although it is miniaturized, the FTS maintains a relatively high spectral resolution, 0.1 cm-1, with adequate optical throughput.

9. Fourier analysis and its applications

CERN Document Server

Folland, Gerald B

2009-01-01

This book presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. It includes material on Bessel functions, orthogonal polynomials, and Laplace transforms, and it concludes with chapters on generalized functions and Green's functions for ordinary and partial differential equations. The book deals almost exclusively with aspects of these subjects that are useful in physics and engineering, and includes a wide variety of applications. On the theoretical side, it uses ideas from modern ana

10. Fourier Transform Methods. Chapter 4

Science.gov (United States)

Kaplan, Simon G.; Quijada, Manuel A.

2015-01-01

This chapter describes the use of Fourier transform spectrometers (FTS) for accurate spectrophotometry over a wide spectral range. After a brief exposition of the basic concepts of FTS operation, we discuss instrument designs and their advantages and disadvantages relative to dispersive spectrometers. We then examine how common sources of error in spectrophotometry manifest themselves when using an FTS and ways to reduce the magnitude of these errors. Examples are given of applications to both basic and derived spectrophotometric quantities. Finally, we give recommendations for choosing the right instrument for a specific application, and how to ensure the accuracy of the measurement results..

11. Novel myopic refractive correction with transepithelial very high-fluence collagen cross-linking applied in a customized pattern: early clinical results of a feasibility study

Directory of Open Access Journals (Sweden)

Kanellopoulos AJ

2014-04-01

Full Text Available Anastasios John Kanellopoulos LaserVision.gr Institute, Athens, Greece, and New York Medical School, New York, NY, USA Background: The purpose of this study is to report the safety and efficacy of a new application of collagen cross-linking using a novel device to achieve predictable refractive myopic changes in virgin corneas. Methods: Four cases were treated with a novel device employing very high-fluence collagen cross-linking applied in a myopic pattern. Prior to treatment, riboflavin solution was applied to the intact epithelium. The collagen cross-linking device was then engaged for a total of 12 J/cm2, to be applied transepithelially in a predetermined pattern. Cornea clarity, corneal keratometry, and corneal topography were evaluated by both Placido disc and Scheimpflug imaging, along with cornea anterior segment optical coherence tomography and endothelial cell counts. Results: An average of 2.3 diopters was achieved in the first week in all four cases treated with the very high-fluence myopic collagen cross-linking intervention. There was a slight regression to 1.44 diopters at 1 month, which remained stable at 6-month follow-up. The mean keratometry change was from 44.90 diopters to 43.46 diopters. There was no significant change in endothelial cell counts or corneal clarity. There was some mild change in epithelial thickness distribution, with the treated area showing a slight but homogeneous reduction in mean thickness from 52 µm to 44 µm. Conclusion: This report describes the novel application of very high-fluence collagen cross-linking with a predictable well defined myopic refractive (flattening corneal effect. This technique has the advantages of essentially no postoperative morbidity, immediate visual rehabilitation, and the potential for tapering until the desired result is achieved. Keywords: myopia, refractive correction, high-fluence collagen cross-linking, clinical results

12. Pointwise convergence of Fourier series

CERN Document Server

Arias de Reyna, Juan

2002-01-01

This book contains a detailed exposition of Carleson-Hunt theorem following the proof of Carleson: to this day this is the only one giving better bounds. It points out the motivation of every step in the proof. Thus the Carleson-Hunt theorem becomes accessible to any analyst.The book also contains the first detailed exposition of the fine results of Hunt, Sjölin, Soria, etc on the convergence of Fourier Series. Its final chapters present original material. With both Fefferman's proof and the recent one of Lacey and Thiele in print, it becomes more important than ever to understand and compare these two related proofs with that of Carleson and Hunt. These alternative proofs do not yield all the results of the Carleson-Hunt proof. The intention of this monograph is to make Carleson's proof accessible to a wider audience, and to explain its consequences for the pointwise convergence of Fourier series for functions in spaces near $äcal Lü^1$, filling a well-known gap in the literature.

13. Eliminating the zero spectrum in Fourier transform profilometry using empirical mode decomposition.

Science.gov (United States)

Li, Sikun; Su, Xianyu; Chen, Wenjing; Xiang, Liqun

2009-05-01

Empirical mode decomposition is introduced into Fourier transform profilometry to extract the zero spectrum included in the deformed fringe pattern without the need for capturing two fringe patterns with pi phase difference. The fringe pattern is subsequently demodulated using a standard Fourier transform profilometry algorithm. With this method, the deformed fringe pattern is adaptively decomposed into a finite number of intrinsic mode functions that vary from high frequency to low frequency by means of an algorithm referred to as a sifting process. Then the zero spectrum is separated from the high-frequency components effectively. Experiments validate the feasibility of this method.

14. Handbook of Fourier analysis & its applications

CERN Document Server

Marks, Robert J

2009-01-01

Fourier analysis has many scientific applications - in physics, number theory, combinatorics, signal processing, probability theory, statistics, option pricing, cryptography, acoustics, oceanography, optics and diffraction, geometry, and other areas. In signal processing and related fields, Fourier analysis is typically thought of as decomposing a signal into its component frequencies and their amplitudes. This practical, applications-based professional handbook comprehensively covers the theory and applications of Fourier Analysis, spanning topics from engineering mathematics, signal process

15. Fourier transform n.m.r. spectroscopy

International Nuclear Information System (INIS)

Shaw, D.

1976-01-01

This book is orientated to techniques rather than applications. The basic theory of n.m.r. is dealt with in a unified approach to the Fourier theory. The middle section of the book concentrates on the practical aspects of Fourier n.m.r., both instrumental and experimental. The final chapters briefly cover general application of n.m.r., but concentrate strongly on those areas where Fourier n.m.r. can give information which is not available by conventional techniques

16. A simple approach to Fourier aliasing

International Nuclear Information System (INIS)

2007-01-01

In the context of discrete Fourier transforms the idea of aliasing as due to approximation errors in the integral defining Fourier coefficients is introduced and explained. This has the positive pedagogical effect of getting to the heart of sampling and the discrete Fourier transform without having to delve into effective, but otherwise long and structured, introductions to the topic, commonly met in advanced, specialized books

17. Tunable fractional-order Fourier transformer

International Nuclear Information System (INIS)

Malyutin, A A

2006-01-01

A fractional two-dimensional Fourier transformer whose orders are tuned by means of optical quadrupoles is described. It is shown that in the optical scheme considered, the Fourier-transform order a element of [0,1] in one of the mutually orthogonal planes corresponds to the transform order (2-a) in another plane, i.e., to inversion and inverse Fourier transform of the order a. (laser modes and beams)

18. Fourier transform n. m. r. spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Shaw, D [Varian Ltd., Walton (UK)

1976-01-01

This book is orientated to techniques rather than applications. The basic theory of n.m.r. is dealt with in a unified approach to the Fourier theory. The middle section of the book concentrates on the practical aspects of Fourier n.m.r., both instrumental and experimental. The final chapters briefly cover general application of n.m.r., but concentrate strongly on those areas where Fourier n.m.r. can give information which is not available by conventional techniques.

19. Geographical traceability of Marsdenia tenacissima by Fourier transform infrared spectroscopy and chemometrics

Science.gov (United States)

Li, Chao; Yang, Sheng-Chao; Guo, Qiao-Sheng; Zheng, Kai-Yan; Wang, Ping-Li; Meng, Zhen-Gui

2016-01-01

A combination of Fourier transform infrared spectroscopy with chemometrics tools provided an approach for studying Marsdenia tenacissima according to its geographical origin. A total of 128 M. tenacissima samples from four provinces in China were analyzed with FTIR spectroscopy. Six pattern recognition methods were used to construct the discrimination models: support vector machine-genetic algorithms, support vector machine-particle swarm optimization, K-nearest neighbors, radial basis function neural network, random forest and support vector machine-grid search. Experimental results showed that K-nearest neighbors was superior to other mathematical algorithms after data were preprocessed with wavelet de-noising, with a discrimination rate of 100% in both the training and prediction sets. This study demonstrated that FTIR spectroscopy coupled with K-nearest neighbors could be successfully applied to determine the geographical origins of M. tenacissima samples, thereby providing reliable authentication in a rapid, cheap and noninvasive way.

20. Pattern recognition neural-net by spatial mapping of biology visual field

Science.gov (United States)

Lin, Xin; Mori, Masahiko

2000-05-01

The method of spatial mapping in biology vision field is applied to artificial neural networks for pattern recognition. By the coordinate transform that is called the complex-logarithm mapping and Fourier transform, the input images are transformed into scale- rotation- and shift- invariant patterns, and then fed into a multilayer neural network for learning and recognition. The results of computer simulation and an optical experimental system are described.

1. Spectrums Transform Operators in Bases of Fourier and Walsh Functions

Directory of Open Access Journals (Sweden)

V. V. Syuzev

2017-01-01

Full Text Available The problems of synthesis of the efficient algorithms for digital processing of discrete signals require transforming the signal spectra from one basis system into other. The rational solution to this problem is to construct the Fourier kernel, which is a spectrum of some basis functions, according to the system of functions of the other basis. However, Fourier kernel properties are not equally studied and described for all basis systems of practical importance. The article sets a task and presents an original way to solve the problem of mutual transformation of trigonometric Fourier spectrum into Walsh spectrum of different basis systems.The relevance of this theoretical and applied problem is stipulated, on the one hand, by the prevalence of trigonometric Fourier basis for harmonic representation of digital signals, and, on the other hand, by the fact that Walsh basis systems allow us to have efficient algorithms to simulate signals. The problem solution is achieved through building the Fourier kernel of a special structure that allows us to establish independent groups of Fourier and Walsh spectrum coefficients for further reducing the computational complexity of the transform algorithms.The article analyzes the properties of the system of trigonometric Fourier functions and shows its completeness. Considers the Walsh function basis systems in three versions, namely those of Hadamard, Paley, and Hartmut giving different ordering and analytical descriptions of the functions that make up the basis. Proves a completeness of these systems.Sequentially, for each of the three Walsh systems the analytical curves for the Fourier kernel components are obtained, and Fourier kernel themselves are built with binary rational number of samples of basis functions. The kernels are presented in matrix form and, as an example, recorded for a particular value of the discrete interval of N, equal to 8. The analysis spectral coefficients of the Fourier kernel

2. Fourier-based magnetic induction tomography for mapping resistivity

International Nuclear Information System (INIS)

2011-01-01

Magnetic induction tomography is used as an experimental tool for mapping the passive electromagnetic properties of conductors, with the potential for imaging biological tissues. Our numerical approach to solving the inverse problem is to obtain a Fourier expansion of the resistivity and the stream functions of the magnetic fields and eddy current density. Thus, we are able to solve the inverse problem of determining the resistivity from the applied and measured magnetic fields for a two-dimensional conducting plane. When we add noise to the measured magnetic field, we find the fidelity of the measured to the true resistivity is quite robust for increasing levels of noise and increasing distances of the applied and measured field coils from the conducting plane, when properly filtered. We conclude that Fourier methods provide a reliable alternative for solving the inverse problem.

3. Algorithm, applications and evaluation for protein comparison by Ramanujan Fourier transform.

Science.gov (United States)

Zhao, Jian; Wang, Jiasong; Hua, Wei; Ouyang, Pingkai

2015-12-01

The amino acid sequence of a protein determines its chemical properties, chain conformation and biological functions. Protein sequence comparison is of great importance to identify similarities of protein structures and infer their functions. Many properties of a protein correspond to the low-frequency signals within the sequence. Low frequency modes in protein sequences are linked to the secondary structures, membrane protein types, and sub-cellular localizations of the proteins. In this paper, we present Ramanujan Fourier transform (RFT) with a fast algorithm to analyze the low-frequency signals of protein sequences. The RFT method is applied to similarity analysis of protein sequences with the Resonant Recognition Model (RRM). The results show that the proposed fast RFT method on protein comparison is more efficient than commonly used discrete Fourier transform (DFT). RFT can detect common frequencies as significant feature for specific protein families, and the RFT spectrum heat-map of protein sequences demonstrates the information conservation in the sequence comparison. The proposed method offers a new tool for pattern recognition, feature extraction and structural analysis on protein sequences. Copyright © 2015 Elsevier Ltd. All rights reserved.

4. Fourier expansions and multivariable Bessel functions concerning radiation programmes

International Nuclear Information System (INIS)

Dattoli, G.; Richetta, M.; Torre, A.; Chiccoli, C.; Lorenzutta, S.; Maino, G.

1996-01-01

The link between generalized Bessel functions and other special functions is investigated using the Fourier series and the generalized Jacobi-Anger expansion. A new class of multivariable Hermite polynomials is then introduced and their relevance to physical problems discussed. As an example of the power of the method, applied to radiation physics, we analyse the role played by multi-variable Bessel functions in the description of radiation emitted by a charge constrained to a nonlinear oscillation. (author)

5. Fast Fourier transformation results from gamma-ray burst profiles

Science.gov (United States)

Kouveliotou, Chryssa; Norris, Jay P.; Fishman, Gerald J.; Meegan, Charles A.; Wilson, Robert B.; Paciesas, W. S.

1992-01-01

Several gamma-ray bursts in the BATSE data have sufficiently long durations and complex temporal structures with pulses that appear to be spaced quasi-periodically. In order to test and quantify these periods we have applied fast Fourier transformations (FFT) to all these events. We have also performed cross spectral analyses of the FFT of the two extreme (high-low) energy bands in each case to determine the lead/lag of the pulses in different energies.

6. Quantum arithmetic with the Quantum Fourier Transform

OpenAIRE

Ruiz-Perez, Lidia; Garcia-Escartin, Juan Carlos

2014-01-01

The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their capabilities. Among the new circuits, we propose a quantum method to compute the weighted average of a series of inputs in the transform domain.

7. On the inverse windowed Fourier transform

OpenAIRE

Rebollo Neira, Laura; Fernández Rubio, Juan Antonio

1999-01-01

The inversion problem concerning the windowed Fourier transform is considered. It is shown that, out of the infinite solutions that the problem admits, the windowed Fourier transform is the "optimal" solution according to a maximum-entropy selection criterion. Peer Reviewed

8. Wigner distribution and fractional Fourier transform

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.; Boashash, B.

2003-01-01

We have described the relationship between the fractional Fourier transform and the Wigner distribution by using the Radon-Wigner transform, which is a set of projections of the Wigner distribution as well as a set of squared moduli of the fractional Fourier transform. We have introduced the concept

9. Pattern formation in superdiffusion Oregonator model

Science.gov (United States)

Feng, Fan; Yan, Jia; Liu, Fu-Cheng; He, Ya-Feng

2016-10-01

Pattern formations in an Oregonator model with superdiffusion are studied in two-dimensional (2D) numerical simulations. Stability analyses are performed by applying Fourier and Laplace transforms to the space fractional reaction-diffusion systems. Antispiral, stable turing patterns, and travelling patterns are observed by changing the diffusion index of the activator. Analyses of Floquet multipliers show that the limit cycle solution loses stability at the wave number of the primitive vector of the travelling hexagonal pattern. We also observed a transition between antispiral and spiral by changing the diffusion index of the inhibitor. Project supported by the National Natural Science Foundation of China (Grant Nos. 11205044 and 11405042), the Research Foundation of Education Bureau of Hebei Province, China (Grant Nos. Y2012009 and ZD2015025), the Program for Young Principal Investigators of Hebei Province, China, and the Midwest Universities Comprehensive Strength Promotion Project.

10. Precise and fast spatial-frequency analysis using the iterative local Fourier transform.

Science.gov (United States)

Lee, Sukmock; Choi, Heejoo; Kim, Dae Wook

2016-09-19

The use of the discrete Fourier transform has decreased since the introduction of the fast Fourier transform (fFT), which is a numerically efficient computing process. This paper presents the iterative local Fourier transform (ilFT), a set of new processing algorithms that iteratively apply the discrete Fourier transform within a local and optimal frequency domain. The new technique achieves 210 times higher frequency resolution than the fFT within a comparable computation time. The method's superb computing efficiency, high resolution, spectrum zoom-in capability, and overall performance are evaluated and compared to other advanced high-resolution Fourier transform techniques, such as the fFT combined with several fitting methods. The effectiveness of the ilFT is demonstrated through the data analysis of a set of Talbot self-images (1280 × 1024 pixels) obtained with an experimental setup using grating in a diverging beam produced by a coherent point source.

11. The fractional Fourier transform and applications

Science.gov (United States)

Bailey, David H.; Swarztrauber, Paul N.

1991-01-01

This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.

12. Teaching Fourier optics through ray matrices

International Nuclear Information System (INIS)

Moreno, I; Sanchez-Lopez, M M; Ferreira, C; Davis, J A; Mateos, F

2005-01-01

In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this derivation to fractional Fourier transform optical systems, and derive the order of the transform from the ray matrix. Some examples are provided to stress this point of view, both with classical and with graded index lenses. This formulation cannot replace the complete explanation of Fourier optics provided by the wave theory, but it is a complementary tool useful to simplify many aspects of Fourier optics and to relate them to geometrical optics

13. Application of the fractional Fourier transformation to digital holography recorded by an elliptical, astigmatic Gaussian beam

NARCIS (Netherlands)

Nicolas, F.; Coëtmellec, S.; Brunel, M.; Allano, D.; Lebrun, D.; Janssen, A.J.E.M.

2005-01-01

The authors have studied the diffraction pattern produced by a particle field illuminated by an elliptic and astigmatic Gaussian beam. They demonstrate that the bidimensional fractional Fourier transformation is a mathematically suitable tool to analyse the diffraction pattern generated not only by

14. The Geostationary Fourier Transform Spectrometer

Science.gov (United States)

Key, Richard; Sander, Stanley; Eldering, Annmarie; Blavier, Jean-Francois; Bekker, Dmitriy; Manatt, Ken; Rider, David; Wu, Yen-Hung

2012-01-01

The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for a geostationary orbit (GEO) earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. GEO allows GeoFTS to continuously stare at a region of the earth for frequent sampling to capture the variability of biogenic fluxes and anthropogenic emissions from city to continental spatial scales and temporal scales from diurnal, synoptic, seasonal to interannual. The measurement strategy provides a process based understanding of the carbon cycle from contiguous maps of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and chlorophyll fluorescence (CF) collected many times per day at high spatial resolution (2.7kmx2.7km at nadir). The CO2/CH4/CO/CF measurement suite in the near infrared spectral region provides the information needed to disentangle natural and anthropogenic contributions to atmospheric carbon concentrations and to minimize uncertainties in the flow of carbon between the atmosphere and surface. The half meter cube size GeoFTS instrument is based on a Michelson interferometer design that uses all high TRL components in a modular configuration to reduce complexity and cost. It is self-contained and as independent of the spacecraft as possible with simple spacecraft interfaces, making it ideal to be a "hosted" payload on a commercial communications satellite mission. The hosted payload approach for measuring the major carbon-containing gases in the atmosphere from the geostationary vantage point will affordably advance the scientific understating of carbon cycle processes and climate change.

15. Accelerated radial Fourier-velocity encoding using compressed sensing

International Nuclear Information System (INIS)

Hilbert, Fabian; Han, Dietbert

2014-01-01

Purpose:Phase Contrast Magnetic Resonance Imaging (MRI) is a tool for non-invasive determination of flow velocities inside blood vessels. Because Phase Contrast MRI only measures a single mean velocity per voxel, it is only applicable to vessels significantly larger than the voxel size. In contrast, Fourier Velocity Encoding measures the entire velocity distribution inside a voxel, but requires a much longer acquisition time. For accurate diagnosis of stenosis in vessels on the scale of spatial resolution, it is important to know the velocity distribution of a voxel. Our aim was to determine velocity distributions with accelerated Fourier Velocity Encoding in an acquisition time required for a conventional Phase Contrast image. Materials and Methods:We imaged the femoral artery of healthy volunteers with ECG - triggered, radial CINE acquisition. Data acquisition was accelerated by undersampling, while missing data were reconstructed by Compressed Sensing. Velocity spectra of the vessel were evaluated by high resolution Phase Contrast images and compared to spectra from fully sampled and undersampled Fourier Velocity Encoding. By means of undersampling, it was possible to reduce the scan time for Fourier Velocity Encoding to the duration required for a conventional Phase Contrast image. Results:Acquisition time for a fully sampled data set with 12 different Velocity Encodings was 40 min. By applying a 12.6 - fold retrospective undersampling, a data set was generated equal to 3:10 min acquisition time, which is similar to a conventional Phase Contrast measurement. Velocity spectra from fully sampled and undersampled Fourier Velocity Encoded images are in good agreement and show the same maximum velocities as compared to velocity maps from Phase Contrast measurements. Conclusion: Compressed Sensing proved to reliably reconstruct Fourier Velocity Encoded data. Our results indicate that Fourier Velocity Encoding allows an accurate determination of the velocity

16. Accelerated radial Fourier-velocity encoding using compressed sensing

Energy Technology Data Exchange (ETDEWEB)

Hilbert, Fabian; Han, Dietbert [Wuerzburg Univ. (Germany). Inst. of Radiology; Wech, Tobias; Koestler, Herbert [Wuerzburg Univ. (Germany). Inst. of Radiology; Wuerzburg Univ. (Germany). Comprehensive Heart Failure Center (CHFC)

2014-10-01

Purpose:Phase Contrast Magnetic Resonance Imaging (MRI) is a tool for non-invasive determination of flow velocities inside blood vessels. Because Phase Contrast MRI only measures a single mean velocity per voxel, it is only applicable to vessels significantly larger than the voxel size. In contrast, Fourier Velocity Encoding measures the entire velocity distribution inside a voxel, but requires a much longer acquisition time. For accurate diagnosis of stenosis in vessels on the scale of spatial resolution, it is important to know the velocity distribution of a voxel. Our aim was to determine velocity distributions with accelerated Fourier Velocity Encoding in an acquisition time required for a conventional Phase Contrast image. Materials and Methods:We imaged the femoral artery of healthy volunteers with ECG - triggered, radial CINE acquisition. Data acquisition was accelerated by undersampling, while missing data were reconstructed by Compressed Sensing. Velocity spectra of the vessel were evaluated by high resolution Phase Contrast images and compared to spectra from fully sampled and undersampled Fourier Velocity Encoding. By means of undersampling, it was possible to reduce the scan time for Fourier Velocity Encoding to the duration required for a conventional Phase Contrast image. Results:Acquisition time for a fully sampled data set with 12 different Velocity Encodings was 40 min. By applying a 12.6 - fold retrospective undersampling, a data set was generated equal to 3:10 min acquisition time, which is similar to a conventional Phase Contrast measurement. Velocity spectra from fully sampled and undersampled Fourier Velocity Encoded images are in good agreement and show the same maximum velocities as compared to velocity maps from Phase Contrast measurements. Conclusion: Compressed Sensing proved to reliably reconstruct Fourier Velocity Encoded data. Our results indicate that Fourier Velocity Encoding allows an accurate determination of the velocity

17. Accelerated radial Fourier-velocity encoding using compressed sensing.

Science.gov (United States)

Hilbert, Fabian; Wech, Tobias; Hahn, Dietbert; Köstler, Herbert

2014-09-01

Phase Contrast Magnetic Resonance Imaging (MRI) is a tool for non-invasive determination of flow velocities inside blood vessels. Because Phase Contrast MRI only measures a single mean velocity per voxel, it is only applicable to vessels significantly larger than the voxel size. In contrast, Fourier Velocity Encoding measures the entire velocity distribution inside a voxel, but requires a much longer acquisition time. For accurate diagnosis of stenosis in vessels on the scale of spatial resolution, it is important to know the velocity distribution of a voxel. Our aim was to determine velocity distributions with accelerated Fourier Velocity Encoding in an acquisition time required for a conventional Phase Contrast image. We imaged the femoral artery of healthy volunteers with ECG-triggered, radial CINE acquisition. Data acquisition was accelerated by undersampling, while missing data were reconstructed by Compressed Sensing. Velocity spectra of the vessel were evaluated by high resolution Phase Contrast images and compared to spectra from fully sampled and undersampled Fourier Velocity Encoding. By means of undersampling, it was possible to reduce the scan time for Fourier Velocity Encoding to the duration required for a conventional Phase Contrast image. Acquisition time for a fully sampled data set with 12 different Velocity Encodings was 40 min. By applying a 12.6-fold retrospective undersampling, a data set was generated equal to 3:10 min acquisition time, which is similar to a conventional Phase Contrast measurement. Velocity spectra from fully sampled and undersampled Fourier Velocity Encoded images are in good agreement and show the same maximum velocities as compared to velocity maps from Phase Contrast measurements. Compressed Sensing proved to reliably reconstruct Fourier Velocity Encoded data. Our results indicate that Fourier Velocity Encoding allows an accurate determination of the velocity distribution in vessels in the order of the voxel size. Thus

18. An Exact Method to Determine the Photonic Resonances of Quasicrystals Based on Discrete Fourier Harmonics of Higher-Dimensional Atomic Surfaces

Directory of Open Access Journals (Sweden)

2016-08-01

Full Text Available A rigorous method for obtaining the diffraction patterns of quasicrystals is presented. Diffraction patterns are an essential analytical tool in the study of quasicrystals, since they can be used to determine their photonic resonances. Previous methods for approximating the diffraction patterns of quasicrystals have relied on evaluating the Fourier transform of finite-sized super-lattices. Our approach, on the other hand, is exact in the sense that it is based on a technique that embeds quasicrystals into higher dimensional periodic hyper-lattices, thereby completely capturing the properties of the infinite structure. The periodicity of the unit cell in the higher dimensional space can be exploited to obtain the Fourier series expansion in closed-form of the corresponding atomic surfaces. The utility of the method is demonstrated by applying it to one-dimensional Fibonacci and two-dimensional Penrose quasicrystals. The results are verified by comparing them to those obtained by using the conventional super-lattice method. It is shown that the conventional super-cell approach can lead to inaccurate results due to the continuous nature of the Fourier transform, since quasicrystals have a discrete spectrum, whereas the approach introduced in this paper generates discrete Fourier harmonics. Furthermore, the conventional approach requires very large super-cells and high-resolution sampling of the reciprocal space in order to produce accurate results leading to a very large computational burden, whereas the proposed method generates accurate results with a relatively small number of terms. Finally, we propose how this approach can be generalized from the vertex model, which assumes identical particles at all vertices, to a more realistic case where the quasicrystal is composed of different atoms.

19. The short time Fourier transform and local signals

Science.gov (United States)

Okumura, Shuhei

In this thesis, I examine the theoretical properties of the short time discrete Fourier transform (STFT). The STFT is obtained by applying the Fourier transform by a fixed-sized, moving window to input series. We move the window by one time point at a time, so we have overlapping windows. I present several theoretical properties of the STFT, applied to various types of complex-valued, univariate time series inputs, and their outputs in closed forms. In particular, just like the discrete Fourier transform, the STFT's modulus time series takes large positive values when the input is a periodic signal. One main point is that a white noise time series input results in the STFT output being a complex-valued stationary time series and we can derive the time and time-frequency dependency structure such as the cross-covariance functions. Our primary focus is the detection of local periodic signals. I present a method to detect local signals by computing the probability that the squared modulus STFT time series has consecutive large values exceeding some threshold after one exceeding observation following one observation less than the threshold. We discuss a method to reduce the computation of such probabilities by the Box-Cox transformation and the delta method, and show that it works well in comparison to the Monte Carlo simulation method.

20. Modeling and forecasting monthly movement of annual average solar insolation based on the least-squares Fourier-model

International Nuclear Information System (INIS)

Yang, Zong-Chang

2014-01-01

Highlights: • Introduce a finite Fourier-series model for evaluating monthly movement of annual average solar insolation. • Present a forecast method for predicting its movement based on the extended Fourier-series model in the least-squares. • Shown its movement is well described by a low numbers of harmonics with approximately 6-term Fourier series. • Predict its movement most fitting with less than 6-term Fourier series. - Abstract: Solar insolation is one of the most important measurement parameters in many fields. Modeling and forecasting monthly movement of annual average solar insolation is of increasingly importance in areas of engineering, science and economics. In this study, Fourier-analysis employing finite Fourier-series is proposed for evaluating monthly movement of annual average solar insolation and extended in the least-squares for forecasting. The conventional Fourier analysis, which is the most common analysis method in the frequency domain, cannot be directly applied for prediction. Incorporated with the least-square method, the introduced Fourier-series model is extended to predict its movement. The extended Fourier-series forecasting model obtains its optimums Fourier coefficients in the least-square sense based on its previous monthly movements. The proposed method is applied to experiments and yields satisfying results in the different cities (states). It is indicated that monthly movement of annual average solar insolation is well described by a low numbers of harmonics with approximately 6-term Fourier series. The extended Fourier forecasting model predicts the monthly movement of annual average solar insolation most fitting with less than 6-term Fourier series

1. Replica Fourier Transform: Properties and applications

International Nuclear Information System (INIS)

Crisanti, A.; De Dominicis, C.

2015-01-01

The Replica Fourier Transform is the generalization of the discrete Fourier Transform to quantities defined on an ultrametric tree. It finds use in conjunction of the replica method used to study thermodynamics properties of disordered systems such as spin glasses. Its definition is presented in a systematic and simple form and its use illustrated with some representative examples. In particular we give a detailed discussion of the diagonalization in the Replica Fourier Space of the Hessian matrix of the Gaussian fluctuations about the mean field saddle point of spin glass theory. The general results are finally discussed for a generic spherical spin glass model, where the Hessian can be computed analytically

2. Fourier transforms in radar and signal processing

CERN Document Server

Brandwood, David

2011-01-01

Fourier transforms are used widely, and are of particular value in the analysis of single functions and combinations of functions found in radar and signal processing. Still, many problems that could have been tackled by using Fourier transforms may have gone unsolved because they require integration that is difficult and tedious. This newly revised and expanded edition of a classic Artech House book provides you with an up-to-date, coordinated system for performing Fourier transforms on a wide variety of functions. Along numerous updates throughout the book, the Second Edition includes a crit

3. An introduction to Laplace transforms and Fourier series

CERN Document Server

Dyke, Phil

2014-01-01

Laplace transforms continue to be a very important tool for the engineer, physicist and applied mathematician. They are also now useful to financial, economic and biological modellers as these disciplines become more quantitative. Any problem that has underlying linearity and with solution based on initial values can be expressed as an appropriate differential equation and hence be solved using Laplace transforms. In this book, there is a strong emphasis on application with the necessary mathematical grounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter on wavelets. Only knowledge of elementary trigonometry and calculus are required as prerequisites. An Introduction to Laplace Transforms and Fourier Series will be useful for second and third year undergraduate students in engineering, physics or mathematics, as well as for graduates in any discipline such as financial mathematics, econometrics and ...

4. Matrix-Vector Based Fast Fourier Transformations on SDR Architectures

Directory of Open Access Journals (Sweden)

Y. He

2008-05-01

Full Text Available Today Discrete Fourier Transforms (DFTs are applied in various radio standards based on OFDM (Orthogonal Frequency Division Multiplex. It is important to gain a fast computational speed for the DFT, which is usually achieved by using specialized Fast Fourier Transform (FFT engines. However, in face of the Software Defined Radio (SDR development, more general (parallel processor architectures are often desirable, which are not tailored to FFT computations. Therefore, alternative approaches are required to reduce the complexity of the DFT. Starting from a matrix-vector based description of the FFT idea, we will present different factorizations of the DFT matrix, which allow a reduction of the complexity that lies between the original DFT and the minimum FFT complexity. The computational complexities of these factorizations and their suitability for implementation on different processor architectures are investigated.

5. Fourier acceleration of iterative processes in disordered systems

International Nuclear Information System (INIS)

Batrouni, G.G.; Hansen, A.

1988-01-01

Technical details are given on how to use Fourier acceleration with iterative processes such as relaxation and conjugate gradient methods. These methods are often used to solve large linear systems of equations, but become hopelessly slow very rapidly as the size of the set of equations to be solved increases. Fourier acceleration is a method designed to alleviate these problems and result in a very fast algorithm. The method is explained for the Jacobi relaxation and conjugate gradient methods and is applied to two models: the random resistor network and the random central-force network. In the first model, acceleration works very well; in the second, little is gained. We discuss reasons for this. We also include a discussion of stopping criteria

6. Generalization of the Fourier Convergence Analysis in the Neutron Diffusion Eigenvalue Problem

International Nuclear Information System (INIS)

Lee, Hyun Chul; Noh, Jae Man; Joo, Hyung Kook

2005-01-01

Fourier error analysis has been a standard technique for the stability and convergence analysis of linear and nonlinear iterative methods. Lee et al proposed new 2- D/1-D coupling methods and demonstrated several advantages of the new methods by performing a Fourier convergence analysis of the methods as well as two existing methods for a fixed source problem. We demonstrated the Fourier convergence analysis of one of the 2-D/1-D coupling methods applied to a neutron diffusion eigenvalue problem. However, the technique cannot be used directly to analyze the convergence of the other 2-D/1-D coupling methods since some algorithm-specific features were used in our previous study. In this paper we generalized the Fourier convergence analysis technique proposed and analyzed the convergence of the 2-D/1-D coupling methods applied to a neutron diffusion Eigenvalue problem using the generalized technique

7. Complex Networks Dynamics Based on Events-Phase Synchronization and Intensity Correlation Applied to The Anomaly Patterns and Extremes in The Tropical African Climate System

Science.gov (United States)

Oluoch, K.; Marwan, N.; Trauth, M.; Loew, A.; Kurths, J.

2012-04-01

The African continent lie almost entirely within the tropics and as such its (tropical) climate systems are predominantly governed by the heterogeneous, spatial and temporal variability of the Hadley and Walker circulations. The variabilities in these meridional and zonal circulations lead to intensification or suppression of the intensities, durations and frequencies of the Inter-tropical Convergence Zone (ICTZ) migration, trade winds and subtropical high-pressure regions and the continental monsoons. The above features play a central role in determining the African rainfall spatial and temporal variability patterns. The current understanding of these climate features and their influence on the rainfall patterns is not sufficiently understood. Like many real-world systems, atmospheric-oceanic processes exhibit non-linear properties that can be better explored using non-linear (NL) methods of time-series analysis. Over the recent years, the complex network approach has evolved as a powerful new player in understanding spatio-temporal dynamics and evolution of complex systems. Together with NL techniques, it is continuing to find new applications in many areas of science and technology including climate research. We would like to use these two powerful methods to understand the spatial structure and dynamics of African rainfall anomaly patterns and extremes. The method of event synchronization (ES) developed by Quiroga et al., 2002 and first applied to climate networks by Malik et al., 2011 looks at correlations with a dynamic time lag and as such, it is a more intuitive way to correlate a complex and heterogeneous system like climate networks than a fixed time delay most commonly used. On the other hand, the short comings of ES is its lack of vigorous test statistics for the significance level of the correlations, and the fact that only the events' time indices are synchronized while all information about how the relative intensities propagate within network

8. Evaluation of the response of a round hole scintillation camera collimator by the Fourier analysis method

International Nuclear Information System (INIS)

Hernandez, A.; Millan, S.; Yzuel, M.J.

1986-01-01

The Fourier analysis method was used to investigate the response of scintillation camera collimators with parallel holes. This method which takes into account the septal penetration was applied to the case of round hole collimators having a hexagonal distribution. Modulation transfer functions, MTF have been determined to verify the accuracy of the computed Fourier coefficients of the collimator function. Comparisons between the geometric and the penetrating plus geometric transfer function are shown for round and hexagonal holes. (author)

9. Products of multiple Fourier series with application to the multiblade transformation

Science.gov (United States)

Kunz, D. L.

1981-01-01

A relatively simple and systematic method for forming the products of multiple Fourier series using tensor like operations is demonstrated. This symbolic multiplication can be performed for any arbitrary number of series, and the coefficients of a set of linear differential equations with periodic coefficients from a rotating coordinate system to a nonrotating system is also demonstrated. It is shown that using Fourier operations to perform this transformation make it easily understood, simple to apply, and generally applicable.

10. On sharp estimates of the convergence of double Fourier-Bessel series

Science.gov (United States)

Abilov, V. A.; Abilova, F. V.; Kerimov, M. K.

2017-11-01

The problem of approximation of a differentiable function of two variables by partial sums of a double Fourier-Bessel series is considered. Sharp estimates of the rate of convergence of the double Fourier-Bessel series on the class of differentiable functions of two variables characterized by a generalized modulus of continuity are obtained. The proofs of four theorems on this issue, which can be directly applied to solving particular problems of mathematical physics, approximation theory, etc., are presented.

11. Miniaturized Fourier-plane fiber scanner for OCT endoscopy

International Nuclear Information System (INIS)

Vilches, Sergio; Kretschmer, Simon; Ataman, Çağlar; Zappe, Hans

2017-01-01

A forward-looking endoscopic optical coherence tomography (OCT) probe featuring a Fourier-plane fiber scanner is designed, manufactured and characterized. In contrast to common image-plane fiber scanners, the Fourier-plane scanner is a telecentric arrangement that eliminates vignetting and spatial resolution variations across the image plane. To scan the OCT beam in a spiral pattern, a tubular piezoelectric actuator is used to resonate an optical fiber bearing a collimating GRIN lens at its tip. The free-end of the GRIN lens sits at the back focal plane of an objective lens, such that its rotation replicates the beam angles in the collimated region of a classical telecentric 4f optical system. Such an optical arrangement inherently has a low numerical aperture combined with a relatively large field-of-view, rendering it particularly useful for endoscopic OCT imaging. Furthermore, the optical train of the Fourier-plane scanner is shorter than that of a comparable image-plane scanner by one focal length of the objective lens, significantly shortening the final arrangement. As a result, enclosed within a 3D printed housing of 2.5 mm outer diameter and 15 mm total length, the developed probe is the most compact forward-looking endoscopic OCT imager to date. Due to its compact form factor and compatibility with real-time OCT imaging, the developed probe is also ideal for use in the working channel of flexible endoscopes as a potential optical biopsy tool. (paper)

12. Miniaturized Fourier-plane fiber scanner for OCT endoscopy

Science.gov (United States)

Vilches, Sergio; Kretschmer, Simon; Ataman, Çağlar; Zappe, Hans

2017-10-01

A forward-looking endoscopic optical coherence tomography (OCT) probe featuring a Fourier-plane fiber scanner is designed, manufactured and characterized. In contrast to common image-plane fiber scanners, the Fourier-plane scanner is a telecentric arrangement that eliminates vignetting and spatial resolution variations across the image plane. To scan the OCT beam in a spiral pattern, a tubular piezoelectric actuator is used to resonate an optical fiber bearing a collimating GRIN lens at its tip. The free-end of the GRIN lens sits at the back focal plane of an objective lens, such that its rotation replicates the beam angles in the collimated region of a classical telecentric 4f optical system. Such an optical arrangement inherently has a low numerical aperture combined with a relatively large field-of-view, rendering it particularly useful for endoscopic OCT imaging. Furthermore, the optical train of the Fourier-plane scanner is shorter than that of a comparable image-plane scanner by one focal length of the objective lens, significantly shortening the final arrangement. As a result, enclosed within a 3D printed housing of 2.5 mm outer diameter and 15 mm total length, the developed probe is the most compact forward-looking endoscopic OCT imager to date. Due to its compact form factor and compatibility with real-time OCT imaging, the developed probe is also ideal for use in the working channel of flexible endoscopes as a potential optical biopsy tool.

13. New focus on Fourier optics techniques

NARCIS (Netherlands)

Calvo, M.L.; Alieva, T.; Bastiaans, M.J.; Rodrigo Martín-Romo, J.A.; Rodríguez Merlo, D.; Vlad, V.I.

2004-01-01

We present a short overview on the application of fractional cyclic and linear canonical transformations to optical signal processing and dedicate some of the discussions to the particular features found in the fractional Fourier transform domain.

14. The finite Fourier transform of classical polynomials

OpenAIRE

Dixit, Atul; Jiu, Lin; Moll, Victor H.; Vignat, Christophe

2014-01-01

The finite Fourier transform of a family of orthogonal polynomials $A_{n}(x)$, is the usual transform of the polynomial extended by $0$ outside their natural domain. Explicit expressions are given for the Legendre, Jacobi, Gegenbauer and Chebyshev families.

15. On the Scaled Fractional Fourier Transformation Operator

International Nuclear Information System (INIS)

Hong-Yi, Fan; Li-Yun, Hu

2008-01-01

Based on our previous study [Chin. Phys. Lett. 24 (2007) 2238] in which the Fresnel operator corresponding to classical Fresnel transform was introduced, we derive the fractional Fourier transformation operator, and the optical operator method is then enriched

16. Mountain Wave Analysis Using Fourier Methods

National Research Council Canada - National Science Library

2007-01-01

...) their requirements for only a coarse horizontal background state. Common traits of Fourier mountain wave models include use of the Boussinesq approximation and neglect of moisture and Coriolis terms...

17. A new twist to fourier transforms

CERN Document Server

Meikle, Hamish D

2004-01-01

Making use of the inherent helix in the Fourier transform expression, this book illustrates both Fourier transforms and their properties in the round. The author draws on elementary complex algebra to manipulate the transforms, presenting the ideas in such a way as to avoid pages of complicated mathematics. Similarly, abbreviations are not used throughout and the language is kept deliberately clear so that the result is a text that is accessible to a much wider readership.The treatment is extended with the use of sampled data to finite and discrete transforms, the fast Fourier transform, or FFT, being a special case of a discrete transform. The application of Fourier transforms in statistics is illustrated for the first time using the examples operational research and later radar detection. In addition, a whole chapter on tapering or weighting functions is added for reference. The whole is rounded off by a glossary and examples of diagrams in three dimensions made possible by today's mathematics programs

18. 360-degrees profilometry using strip-light projection coupled to Fourier phase-demodulation.

Science.gov (United States)

Servin, Manuel; Padilla, Moises; Garnica, Guillermo

2016-01-11

360 degrees (360°) digitalization of three dimensional (3D) solids using a projected light-strip is a well-established technique in academic and commercial profilometers. These profilometers project a light-strip over the digitizing solid while the solid is rotated a full revolution or 360-degrees. Then, a computer program typically extracts the centroid of this light-strip, and by triangulation one obtains the shape of the solid. Here instead of using intensity-based light-strip centroid estimation, we propose to use Fourier phase-demodulation for 360° solid digitalization. The advantage of Fourier demodulation over strip-centroid estimation is that the accuracy of phase-demodulation linearly-increases with the fringe density, while in strip-light the centroid-estimation errors are independent. Here we proposed first to construct a carrier-frequency fringe-pattern by closely adding the individual light-strip images recorded while the solid is being rotated. Next, this high-density fringe-pattern is phase-demodulated using the standard Fourier technique. To test the feasibility of this Fourier demodulation approach, we have digitized two solids with increasing topographic complexity: a Rubik's cube and a plastic model of a human-skull. According to our results, phase demodulation based on the Fourier technique is less noisy than triangulation based on centroid light-strip estimation. Moreover, Fourier demodulation also provides the amplitude of the analytic signal which is a valuable information for the visualization of surface details.

19. Mapped Fourier Methods for stiff problems in toroidal geometry

OpenAIRE

Guillard , Herve

2014-01-01

Fourier spectral or pseudo-spectral methods are usually extremely efficient for periodic problems. However this efficiency is lost if the solutions have zones of rapid variations or internal layers. For these cases, a large number of Fourier modes are required and this makes the Fourier method unpractical in many cases. This work investigates the use of mapped Fourier method as a way to circumvent this problem. Mapped Fourier method uses instead of the usual Fourier interpolant the compositio...

20. Non-Fourier heat conduction and phase transition in laser ablation of polytetrafluoroethylene (PTFE)

Science.gov (United States)

Zhang, Yu; Zhang, Daixian; Wu, Jianjun; Li, Jian; He, Zhaofu

2017-11-01

The phase transition in heat conduction of polytetrafluoroethylene-like polymers was investigated and applied in many fields of science and engineering. Considering more details including internal absorption of laser radiation, reflectivity of material and non-Fourier effect etc., the combined heat conduction and phase transition in laser ablation of polytetrafluoroethylene were modeled and investigated numerically. The thermal and mechanic issues in laser ablation were illustrated and analyzed. Especially, the phenomenon of temperature discontinuity formed in the combined phase transition and non-Fourier heat conduction was discussed. Comparisons of target temperature profiles between Fourier and non-Fourier heat conduction in melting process were implemented. It was indicated that the effect of non-Fourier plays an important role in the temperature evolvement. The effect of laser fluence was proven to be significant and the thermal wave propagation was independent on the laser intensity for the non-Fourier heat conduction. Besides, the effect of absorption coefficients on temperature evolvements was studied. For different ranges of absorption coefficients, different temperature evolvements can be achieved. The above numerical simulation provided insight into physical processes of combined non-Fourier heat conduction and phase transition in laser ablation.

1. Fourier analysis of conductive heat transfer for glazed roofing materials

Energy Technology Data Exchange (ETDEWEB)

Roslan, Nurhana Lyana; Bahaman, Nurfaradila; Almanan, Raja Noorliyana Raja; Ismail, Razidah [Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor (Malaysia); Zakaria, Nor Zaini [Faculty of Applied Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor (Malaysia)

2014-07-10

For low-rise buildings, roof is the most exposed surface to solar radiation. The main mode of heat transfer from outdoor via the roof is conduction. The rate of heat transfer and the thermal impact is dependent on the thermophysical properties of roofing materials. Thus, it is important to analyze the heat distribution for the various types of roofing materials. The objectives of this paper are to obtain the Fourier series for the conductive heat transfer for two types of glazed roofing materials, namely polycarbonate and polyfilled, and also to determine the relationship between the ambient temperature and the conductive heat transfer for these materials. Ambient and surface temperature data were collected from an empirical field investigation in the campus of Universiti Teknologi MARA Shah Alam. The roofing materials were installed on free-standing structures in natural ventilation. Since the temperature data are generally periodic, Fourier series and numerical harmonic analysis are applied. Based on the 24-point harmonic analysis, the eleventh order harmonics is found to generate an adequate Fourier series expansion for both glazed roofing materials. In addition, there exists a linear relationship between the ambient temperature and the conductive heat transfer for both glazed roofing materials. Based on the gradient of the graphs, lower heat transfer is indicated through polyfilled. Thus polyfilled would have a lower thermal impact compared to polycarbonate.

2. Evaluation of gastric motility by Fourier analysis of condensed images

International Nuclear Information System (INIS)

Linke, R.; Muenzing, W.; Hahn, K.; Tatsch, K.

2000-01-01

In this study Fourier analysis was applied to condensed images of gastric emptying with the aim of evaluating the amplitude and frequency of gastric contractions as well as gastric emptying in patients with various well-defined disorders. In 15 controls, 65 patients with progressive systemic sclerosis (PSS), 41 patients with diabetes mellitus type I (DM), 12 patients with pyloric stenosis and 9 patients who had undergone gastric surgery, gastric emptying was determined after ingestion of a semi-solid test meal. In addition, condensed images were generated to evaluate the amplitude and frequency of gastric contractions by means of Fourier analysis. In PSS and DM patients, gastric emptying and contraction amplitudes were significantly reduced (P<0.01). Patients with pyloric stenosis displayed regular peristalsis but significantly delayed emptying (P<0.01). Patients who had undergone gastric surgery showed normal or rapid gastric emptying associated with decreased amplitudes (P<0.01). The frequency of gastric contractions in the patient groups was not different from that in controls. This study showed Fourier analysis of condensed images to be a rapid and feasible approach for the evaluation of gastric contractions. Depending on the underlying disorder, gastric emptying and peristalsis showed both corresponding and discrepant findings. Data on gastric contractions provided additional information compared with results obtained by conventional emptying studies. Therefore, both parameters should be routinely assessed to further improve characterisation of gastric dysfunction by scintigraphy. (orig.)

3. Error Analysis for Fourier Methods for Option Pricing

KAUST Repository

Häppölä, Juho

2016-01-06

We provide a bound for the error committed when using a Fourier method to price European options when the underlying follows an exponential Levy dynamic. The price of the option is described by a partial integro-differential equation (PIDE). Applying a Fourier transformation to the PIDE yields an ordinary differential equation that can be solved analytically in terms of the characteristic exponent of the Levy process. Then, a numerical inverse Fourier transform allows us to obtain the option price. We present a novel bound for the error and use this bound to set the parameters for the numerical method. We analyze the properties of the bound for a dissipative and pure-jump example. The bound presented is independent of the asymptotic behaviour of option prices at extreme asset prices. The error bound can be decomposed into a product of terms resulting from the dynamics and the option payoff, respectively. The analysis is supplemented by numerical examples that demonstrate results comparable to and superior to the existing literature.

4. Evaluation of gastric motility by Fourier analysis of condensed images

Energy Technology Data Exchange (ETDEWEB)

Linke, R.; Muenzing, W.; Hahn, K.; Tatsch, K. [Dept. of Nuclear Medicine, Univ. of Munich, Munich (Germany)

2000-10-01

In this study Fourier analysis was applied to condensed images of gastric emptying with the aim of evaluating the amplitude and frequency of gastric contractions as well as gastric emptying in patients with various well-defined disorders. In 15 controls, 65 patients with progressive systemic sclerosis (PSS), 41 patients with diabetes mellitus type I (DM), 12 patients with pyloric stenosis and 9 patients who had undergone gastric surgery, gastric emptying was determined after ingestion of a semi-solid test meal. In addition, condensed images were generated to evaluate the amplitude and frequency of gastric contractions by means of Fourier analysis. In PSS and DM patients, gastric emptying and contraction amplitudes were significantly reduced (P<0.01). Patients with pyloric stenosis displayed regular peristalsis but significantly delayed emptying (P<0.01). Patients who had undergone gastric surgery showed normal or rapid gastric emptying associated with decreased amplitudes (P<0.01). The frequency of gastric contractions in the patient groups was not different from that in controls. This study showed Fourier analysis of condensed images to be a rapid and feasible approach for the evaluation of gastric contractions. Depending on the underlying disorder, gastric emptying and peristalsis showed both corresponding and discrepant findings. Data on gastric contractions provided additional information compared with results obtained by conventional emptying studies. Therefore, both parameters should be routinely assessed to further improve characterisation of gastric dysfunction by scintigraphy. (orig.)

5. Fourier acceleration in lattice gauge theories. I. Landau gauge fixing

International Nuclear Information System (INIS)

Davies, C.T.H.; Batrouni, G.G.; Katz, G.R.; Kronfeld, A.S.; Lepage, G.P.; Wilson, K.G.; Rossi, P.; Svetitsky, B.

1988-01-01

Fourier acceleration is a useful technique which can be applied to many different numerical algorithms in order to alleviate the problem of critical slowing down. Here we describe its application to an optimization problem in the simulation of lattice gauge theories, that of gauge fixing a configuration of link fields to the Landau gauge (partial/sub μ/A/sup μ/ = 0). We find that a steepest-descents method of gauge fixing link fields at β = 5.8 on an 8 4 lattice can be made 5 times faster using Fourier acceleration. This factor will grow as the volume of the lattice is increased. We also discuss other gauges that are useful to lattice-gauge-theory simulations, among them one that is a combination of the axial and Landau gauges. This seems to be the optimal gauge to impose for the Fourier acceleration of two other important algorithms, the inversion of the fermion matrix and the updating of gauge field configurations

6. Deploying Fourier Coefficients to Unravel Soybean Canopy Diversity.

Science.gov (United States)

Jubery, Talukder Z; Shook, Johnathon; Parmley, Kyle; Zhang, Jiaoping; Naik, Hsiang S; Higgins, Race; Sarkar, Soumik; Singh, Arti; Singh, Asheesh K; Ganapathysubramanian, Baskar

2016-01-01

Soybean canopy outline is an important trait used to understand light interception ability, canopy closure rates, row spacing response, which in turn affects crop growth and yield, and directly impacts weed species germination and emergence. In this manuscript, we utilize a methodology that constructs geometric measures of the soybean canopy outline from digital images of canopies, allowing visualization of the genetic diversity as well as a rigorous quantification of shape parameters. Our choice of data analysis approach is partially dictated by the need to efficiently store and analyze large datasets, especially in the context of planned high-throughput phenotyping experiments to capture time evolution of canopy outline which will produce very large datasets. Using the Elliptical Fourier Transformation (EFT) and Fourier Descriptors (EFD), canopy outlines of 446 soybean plant introduction (PI) lines from 25 different countries exhibiting a wide variety of maturity, seed weight, and stem termination were investigated in a field experiment planted as a randomized complete block design with up to four replications. Canopy outlines were extracted from digital images, and subsequently chain coded, and expanded into a shape spectrum by obtaining the Fourier coefficients/descriptors. These coefficients successfully reconstruct the canopy outline, and were used to measure traditional morphometric traits. Highest phenotypic diversity was observed for roundness, while solidity showed the lowest diversity across all countries. Some PI lines had extraordinary shape diversity in solidity. For interpretation and visualization of the complexity in shape, Principal Component Analysis (PCA) was performed on the EFD. PI lines were grouped in terms of origins, maturity index, seed weight, and stem termination index. No significant pattern or similarity was observed among the groups; although interestingly when genetic marker data was used for the PCA, patterns similar to canopy

7. Fourier phasing with phase-uncertain mask

International Nuclear Information System (INIS)

Fannjiang, Albert; Liao, Wenjing

2013-01-01

Fourier phasing is the problem of retrieving Fourier phase information from Fourier intensity data. The standard Fourier phase retrieval (without a mask) is known to have many solutions which cause the standard phasing algorithms to stagnate and produce wrong or inaccurate solutions. In this paper Fourier phase retrieval is carried out with the introduction of a randomly fabricated mask in measurement and reconstruction. Highly probable uniqueness of solution, up to a global phase, was previously proved with exact knowledge of the mask. Here the uniqueness result is extended to the case where only rough information about the mask’s phases is assumed. The exponential probability bound for uniqueness is given in terms of the uncertainty-to-diversity ratio of the unknown mask. New phasing algorithms alternating between the object update and the mask update are systematically tested and demonstrated to have the capability of recovering both the object and the mask (within the object support) simultaneously, consistent with the uniqueness result. Phasing with a phase-uncertain mask is shown to be robust with respect to the correlation in the mask as well as the Gaussian and Poisson noises. (paper)

8. Fourier-based reconstruction via alternating direction total variation minimization in linear scan CT

International Nuclear Information System (INIS)

Cai, Ailong; Wang, Linyuan; Yan, Bin; Zhang, Hanming; Li, Lei; Xi, Xiaoqi; Li, Jianxin

2015-01-01

In this study, we consider a novel form of computed tomography (CT), that is, linear scan CT (LCT), which applies a straight line trajectory. Furthermore, an iterative algorithm is proposed for pseudo-polar Fourier reconstruction through total variation minimization (PPF-TVM). Considering that the sampled Fourier data are distributed in pseudo-polar coordinates, the reconstruction model minimizes the TV of the image subject to the constraint that the estimated 2D Fourier data for the image are consistent with the 1D Fourier transform of the projection data. PPF-TVM employs the alternating direction method (ADM) to develop a robust and efficient iteration scheme, which ensures stable convergence provided that appropriate parameter values are given. In the ADM scheme, PPF-TVM applies the pseudo-polar fast Fourier transform and its adjoint to iterate back and forth between the image and frequency domains. Thus, there is no interpolation in the Fourier domain, which makes the algorithm both fast and accurate. PPF-TVM is particularly useful for limited angle reconstruction in LCT and it appears to be robust against artifacts. The PPF-TVM algorithm was tested with the FORBILD head phantom and real data in comparisons with state-of-the-art algorithms. Simulation studies and real data verification suggest that PPF-TVM can reconstruct higher accuracy images with lower time consumption

9. Designing Fresnel microlenses for focusing astigmatic multi-Gaussian beams by using fractional order Fourier transforms

International Nuclear Information System (INIS)

Patino, A; Durand, P-E; Fogret, E; Pellat-Finet, P

2011-01-01

According to a scalar theory of diffraction, light propagation can be expressed by two-dimensional fractional order Fourier transforms. Since the fractional Fourier transform of a chirp function is a Dirac distribution, focusing a light beam is optically achieved by using a diffractive screen whose transmission function is a two-dimensional chirp function. This property is applied to designing Fresnel microlenses, and the orders of the involved Fourier fractional transforms depend on diffraction distances as well as on emitter and receiver radii of curvature. If the emitter is astigmatic (with two principal radii of curvature), the diffraction phenomenon involves two one-dimensional fractional Fourier transforms whose orders are different. This degree of freedom allows us to design microlenses that can focus astigmatic Gaussian beams, as produced by a line-shaped laser diode source.

10. Practical protocols for fast histopathology by Fourier transform infrared spectroscopic imaging

Science.gov (United States)

Keith, Frances N.; Reddy, Rohith K.; Bhargava, Rohit

2008-02-01

Fourier transform infrared (FT-IR) spectroscopic imaging is an emerging technique that combines the molecular selectivity of spectroscopy with the spatial specificity of optical microscopy. We demonstrate a new concept in obtaining high fidelity data using commercial array detectors coupled to a microscope and Michelson interferometer. Next, we apply the developed technique to rapidly provide automated histopathologic information for breast cancer. Traditionally, disease diagnoses are based on optical examinations of stained tissue and involve a skilled recognition of morphological patterns of specific cell types (histopathology). Consequently, histopathologic determinations are a time consuming, subjective process with innate intra- and inter-operator variability. Utilizing endogenous molecular contrast inherent in vibrational spectra, specially designed tissue microarrays and pattern recognition of specific biochemical features, we report an integrated algorithm for automated classifications. The developed protocol is objective, statistically significant and, being compatible with current tissue processing procedures, holds potential for routine clinical diagnoses. We first demonstrate that the classification of tissue type (histology) can be accomplished in a manner that is robust and rigorous. Since data quality and classifier performance are linked, we quantify the relationship through our analysis model. Last, we demonstrate the application of the minimum noise fraction (MNF) transform to improve tissue segmentation.

11. Magneto-sensor circuit efficiency incremented by Fourier-transformation

KAUST Repository

Talukdar, Abdul Hafiz Ibne; Useinov, Arthur; Hussain, Muhammad Mustafa

2011-01-01

In this paper detection by recognized intelligent algorithm for different magnetic films with the aid of a cost-effective and simple high efficient circuit are realized. Well-known, magnetic films generate oscillating frequencies when they stay a part of an LC- oscillatory circuit. These frequencies can be further analyzed to gather information about their magnetic properties. For the first time in this work we apply the signal analysis in frequency domain to create the Fourier frequency spectra which was used to detect the sample properties and their recognition. In this paper we have summarized both the simulation and experimental results. © 2011 Elsevier Ltd. All rights reserved.

12. Magneto-sensor circuit efficiency incremented by Fourier-transformation

KAUST Repository

Talukdar, Abdul Hafiz Ibne

2011-10-01

In this paper detection by recognized intelligent algorithm for different magnetic films with the aid of a cost-effective and simple high efficient circuit are realized. Well-known, magnetic films generate oscillating frequencies when they stay a part of an LC- oscillatory circuit. These frequencies can be further analyzed to gather information about their magnetic properties. For the first time in this work we apply the signal analysis in frequency domain to create the Fourier frequency spectra which was used to detect the sample properties and their recognition. In this paper we have summarized both the simulation and experimental results. © 2011 Elsevier Ltd. All rights reserved.

13. Fourier transform infrared studies in solid egg white lysozyme

International Nuclear Information System (INIS)

Rivzi, T.Z.

1994-12-01

Fourier Transform Infrared (FTIR) Spectroscopy is the most recent addition to the arsenal of bioanalytical techniques capable of providing information about the secondary structure of proteins in a variety of environments. FTIR spectra have been obtained in solid egg white lysozyme. The spectra display the usual amide I, II and III bands. Secondary structural information obtained from the spectra after applying resolution enhancement techniques to the amide I band has been found consistent with the x-ray crystallographic data of the protein and also to the spectroscopic data of the protein in aqueous solution. (author). 17 refs, 6 figs, 2 tabs

14. Transfer Function Identification Using Orthogonal Fourier Transform Modeling Functions

Science.gov (United States)

Morelli, Eugene A.

2013-01-01

A method for transfer function identification, including both model structure determination and parameter estimation, was developed and demonstrated. The approach uses orthogonal modeling functions generated from frequency domain data obtained by Fourier transformation of time series data. The method was applied to simulation data to identify continuous-time transfer function models and unsteady aerodynamic models. Model fit error, estimated model parameters, and the associated uncertainties were used to show the effectiveness of the method for identifying accurate transfer function models from noisy data.

15. High-resolution extraction of particle size via Fourier Ptychography

Science.gov (United States)

Li, Shengfu; Zhao, Yu; Chen, Guanghua; Luo, Zhenxiong; Ye, Yan

2017-11-01

This paper proposes a method which can extract the particle size information with a resolution beyond λ/NA. This is achieved by applying Fourier Ptychographic (FP) ideas to the present problem. In a typical FP imaging platform, a 2D LED array is used as light sources for angle-varied illuminations, a series of low-resolution images was taken by a full sequential scan of the array of LEDs. Here, we demonstrate the particle size information is extracted by turning on each single LED on a circle. The simulated results show that the proposed method can reduce the total number of images, without loss of reliability in the results.

16. Differentiating Fragmentation Pathways of Cholesterol by Two-Dimensional Fourier Transform Ion Cyclotron Resonance Mass Spectrometry.

Science.gov (United States)

van Agthoven, Maria A; Barrow, Mark P; Chiron, Lionel; Coutouly, Marie-Aude; Kilgour, David; Wootton, Christopher A; Wei, Juan; Soulby, Andrew; Delsuc, Marc-André; Rolando, Christian; O'Connor, Peter B

2015-12-01

Two-dimensional Fourier transform ion cyclotron resonance mass spectrometry is a data-independent analytical method that records the fragmentation patterns of all the compounds in a sample. This study shows the implementation of atmospheric pressure photoionization with two-dimensional (2D) Fourier transform ion cyclotron resonance mass spectrometry. In the resulting 2D mass spectrum, the fragmentation patterns of the radical and protonated species from cholesterol are differentiated. This study shows the use of fragment ion lines, precursor ion lines, and neutral loss lines in the 2D mass spectrum to determine fragmentation mechanisms of known compounds and to gain information on unknown ion species in the spectrum. In concert with high resolution mass spectrometry, 2D Fourier transform ion cyclotron resonance mass spectrometry can be a useful tool for the structural analysis of small molecules. Graphical Abstract ᅟ.

17. Closed fringe demodulation using phase decomposition by Fourier basis functions.

Science.gov (United States)

Kulkarni, Rishikesh; Rastogi, Pramod

2016-06-01

We report a new technique for the demodulation of a closed fringe pattern by representing the phase as a weighted linear combination of a certain number of linearly independent Fourier basis functions in a given row/column at a time. A state space model is developed with the weights of the basis functions as the elements of the state vector. The iterative extended Kalman filter is effectively utilized for the robust estimation of the weights. A coarse estimate of the fringe density based on the fringe frequency map is used to determine the initial row/column to start with and subsequently the optimal number of basis functions. The performance of the proposed method is evaluated with several noisy fringe patterns. Experimental results are also reported to support the practical applicability of the proposed method.

18. Harmonic analysis from Fourier to wavelets

CERN Document Server

Pereyra, Maria Cristina

2012-01-01

In the last 200 years, harmonic analysis has been one of the most influential bodies of mathematical ideas, having been exceptionally significant both in its theoretical implications and in its enormous range of applicability throughout mathematics, science, and engineering. In this book, the authors convey the remarkable beauty and applicability of the ideas that have grown from Fourier theory. They present for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization). While concentrating on the Fourier and Haar cases, the book touches on aspects of the world that lies between these two different ways of decomposing functions: time-frequency analysis (wavelets). Both finite and continuous perspectives are presented, allowing for the introd...

19. Projective Fourier duality and Weyl quantization

International Nuclear Information System (INIS)

Aldrovandi, R.; Saeger, L.A.

1996-08-01

The Weyl-Wigner correspondence prescription, which makes large use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for non-commutative Fourier analysis allowing for that property. It is shown how the standard Kac structure has to be extended in order to accommodate the physical requirements. An Abelian and a symmetric projective Kac algebras are shown to provide, in close parallel to the standard case, a new dual framework and a well-defined notion of projective Fourier duality for the group of translations on the plane. The Weyl formula arises naturally as an irreducible component of the duality mapping between these projective algebras. (author). 29 refs

20. Fourier duality as a quantization principle

International Nuclear Information System (INIS)

Aldrovandi, R.; Saeger, L.A.

1996-08-01

The Weyl-Wigner prescription for quantization on Euclidean phase spaces makes essential use of Fourier duality. The extension of this property to more general phase spaces requires the use of Kac algebras, which provide the necessary background for the implementation of Fourier duality on general locally groups. Kac algebras - and the duality they incorporate are consequently examined as candidates for a general quantization framework extending the usual formalism. Using as a test case the simplest non-trivial phase space, the half-plane, it is shown how the structures present in the complete-plane case must be modified. Traces, for example, must be replaced by their noncommutative generalizations - weights - and the correspondence embodied in the Weyl-Wigner formalism is no more complete. Provided the underlying algebraic structure is suitably adapted to each case, Fourier duality is shown to be indeed a very powerful guide to the quantization of general physical systems. (author). 30 refs

1. Methods of Fourier analysis and approximation theory

CERN Document Server

Tikhonov, Sergey

2016-01-01

Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.

2. Fourier analysis and boundary value problems

CERN Document Server

Gonzalez-Velasco, Enrique A

1996-01-01

Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics.A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.Key Features* Topics are covered from a historical perspective with biographical information on key contributors to the field* The text contains more than 500 exercises* Includes practical applicati...

3. Group-invariant finite Fourier transforms

International Nuclear Information System (INIS)

Shenefelt, M.H.

1988-01-01

The computation of the finite Fourier transform of functions is one of the most used computations in crystallography. Since the Fourier transform involved in 3-dimensional, the size of the computation becomes very large even for relatively few sample points along each edge. In this thesis, there is a family of algorithms that reduce the computation of Fourier transform of functions respecting the symmetries. Some properties of these algorithms are: (1) The algorithms make full use of the group of symmetries of a crystal. (2) The algorithms can be factored and combined according to the prime factorization of the number of points in the sample space. (3) The algorithms are organized into a family using the group structure of the crystallographic groups to make iterative procedures possible

4. An optical Fourier transform coprocessor with direct phase determination.

Science.gov (United States)

Macfaden, Alexander J; Gordon, George S D; Wilkinson, Timothy D

2017-10-20

The Fourier transform is a ubiquitous mathematical operation which arises naturally in optics. We propose and demonstrate a practical method to optically evaluate a complex-to-complex discrete Fourier transform. By implementing the Fourier transform optically we can overcome the limiting O(nlogn) complexity of fast Fourier transform algorithms. Efficiently extracting the phase from the well-known optical Fourier transform is challenging. By appropriately decomposing the input and exploiting symmetries of the Fourier transform we are able to determine the phase directly from straightforward intensity measurements, creating an optical Fourier transform with O(n) apparent complexity. Performing larger optical Fourier transforms requires higher resolution spatial light modulators, but the execution time remains unchanged. This method could unlock the potential of the optical Fourier transform to permit 2D complex-to-complex discrete Fourier transforms with a performance that is currently untenable, with applications across information processing and computational physics.

5. Specialization Patterns

DEFF Research Database (Denmark)

Schultz, Ulrik Pagh; Lawall, Julia Laetitia; Consel, Charles

2000-01-01

Design patterns offer many advantages for software development, but can introduce inefficiency into the final program. Program specialization can eliminate such overheads, but is most effective when targeted by the user to specific bottlenecks. Consequently, we propose that these concepts...... are complementary. Program specialization can optimize programs written using design patterns, and design patterns provide information about the program structure that can guide specialization. Concretely, we propose specialization patterns, which describe how to apply program specialization to optimize uses...... of design patterns. In this paper, we analyze the specialization opportunities provided by specific uses of design patterns. Based on the analysis of each design pattern, we define the associated specialization pattern. These specialization opportunities can be declared using the specialization classes...

6. Fourier transforms and convolutions for the experimentalist

CERN Document Server

Jennison, RC

1961-01-01

Fourier Transforms and Convolutions for the Experimentalist provides the experimentalist with a guide to the principles and practical uses of the Fourier transformation. It aims to bridge the gap between the more abstract account of a purely mathematical approach and the rule of thumb calculation and intuition of the practical worker. The monograph springs from a lecture course which the author has given in recent years and for which he has drawn upon a number of sources, including a set of notes compiled by the late Dr. I. C. Browne from a series of lectures given by Mr. J . A. Ratcliffe of t

7. Electro-optic imaging Fourier transform spectrometer

Science.gov (United States)

Chao, Tien-Hsin (Inventor); Znod, Hanying (Inventor)

2009-01-01

An Electro-Optic Imaging Fourier Transform Spectrometer (EOIFTS) for Hyperspectral Imaging is described. The EOIFTS includes an input polarizer, an output polarizer, and a plurality of birefringent phase elements. The relative orientations of the polarizers and birefringent phase elements can be changed mechanically or via a controller, using ferroelectric liquid crystals, to substantially measure the spectral Fourier components of light propagating through the EIOFTS. When achromatic switches are used as an integral part of the birefringent phase elements, the EIOFTS becomes suitable for broadband applications, with over 1 micron infrared bandwidth.

8. Isogyres - Manifestation of Spin-orbit interaction in uniaxial crystal: A closed-fringe Fourier analysis of conoscopic interference

Science.gov (United States)

Samlan, C. T.; Naik, Dinesh N.; Viswanathan, Nirmal K.

2016-09-01

Discovered in 1813, the conoscopic interference pattern observed due to light propagating through a crystal, kept between crossed polarizers, shows isochromates and isogyres, respectively containing information about the dynamic and geometric phase acquired by the beam. We propose and demonstrate a closed-fringe Fourier analysis method to disentangle the isogyres from the isochromates, leading us to the azimuthally varying geometric phase and its manifestation as isogyres. This azimuthally varying geometric phase is shown to be the underlying mechanism for the spin-to-orbital angular momentum conversion observed in a diverging optical field propagating through a z-cut uniaxial crystal. We extend the formalism to study the optical activity mediated uniaxial-to-biaxial transformation due to a weak transverse electric field applied across the crystal. Closely associated with the phase and polarization singularities of the optical field, the formalism enables us to understand crystal optics in a new way, paving the way to anticipate several emerging phenomena.

9. Wavelet-based feature extraction applied to small-angle x-ray scattering patterns from breast tissue: a tool for differentiating between tissue types

International Nuclear Information System (INIS)

Falzon, G; Pearson, S; Murison, R; Hall, C; Siu, K; Evans, A; Rogers, K; Lewis, R

2006-01-01

This paper reports on the application of wavelet decomposition to small-angle x-ray scattering (SAXS) patterns from human breast tissue produced by a synchrotron source. The pixel intensities of SAXS patterns of normal, benign and malignant tissue types were transformed into wavelet coefficients. Statistical analysis found significant differences between the wavelet coefficients describing the patterns produced by different tissue types. These differences were then correlated with position in the image and have been linked to the supra-molecular structural changes that occur in breast tissue in the presence of disease. Specifically, results indicate that there are significant differences between healthy and diseased tissues in the wavelet coefficients that describe the peaks produced by the axial d-spacing of collagen. These differences suggest that a useful classification tool could be based upon the spectral information within the axial peaks

10. The periodogram at the Fourier frequencies

NARCIS (Netherlands)

Kokoszka, P; Mikosch, T

In the time series literature one can often find the claim that the periodogram ordinates of an lid sequence at the Fourier frequencies behave like an lid standard exponential sequence. We review some results about functions of these periodogram ordinates, including the convergence of extremes,

11. Pi, Fourier Transform and Ludolph van Ceulen

NARCIS (Netherlands)

Vajta, Miklos

2000-01-01

The paper describes an interesting (and unexpected) application of the Fast Fourier transform in number theory. Calculating more and more decimals of p (first by hand and then from the mid-20th century, by digital computers) not only fascinated mathematicians from ancient times but kept them busy as

12. Fourier transform infrared spectrometery: an undergraduate experiment

International Nuclear Information System (INIS)

Lerner, L

2016-01-01

Simple apparatus is developed, providing undergraduate students with a solid understanding of Fourier transform (FT) infrared (IR) spectroscopy in a hands on experiment. Apart from its application to measuring the mid-IR spectra of organic molecules, the experiment introduces several techniques with wide applicability in physics, including interferometry, the FT, digital data analysis, and control theory. (paper)

13. Wigner distribution and fractional Fourier transform

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.

2001-01-01

The connection between the Wigner distribution and the squared modulus of the fractional Fourier transform - which are both well-known time-frequency representations of a signal - is established. In particular the Radon-Wigner transform is used, which relates projections of the Wigner distribution

14. The Fourier transform of tubular densities

KAUST Repository

Prior, C B; Goriely, A

2012-01-01

molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one

15. Geometric Representations for Discrete Fourier Transforms

Science.gov (United States)

Cambell, C. W.

1986-01-01

Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.

16. Fourier analysis in combinatorial number theory

International Nuclear Information System (INIS)

Shkredov, Il'ya D

2010-01-01

In this survey applications of harmonic analysis to combinatorial number theory are considered. Discussion topics include classical problems of additive combinatorics, colouring problems, higher-order Fourier analysis, theorems about sets of large trigonometric sums, results on estimates for trigonometric sums over subgroups, and the connection between combinatorial and analytic number theory. Bibliography: 162 titles.

17. Fourier analysis in combinatorial number theory

Energy Technology Data Exchange (ETDEWEB)

Shkredov, Il' ya D [M. V. Lomonosov Moscow State University, Moscow (Russian Federation)

2010-09-16

In this survey applications of harmonic analysis to combinatorial number theory are considered. Discussion topics include classical problems of additive combinatorics, colouring problems, higher-order Fourier analysis, theorems about sets of large trigonometric sums, results on estimates for trigonometric sums over subgroups, and the connection between combinatorial and analytic number theory. Bibliography: 162 titles.

18. A Fourier analysis of extremal events

DEFF Research Database (Denmark)

Zhao, Yuwei

is the extremal periodogram. The extremal periodogram shares numerous asymptotic properties with the periodogram of a linear process in classical time series analysis: the asymptotic distribution of the periodogram ordinates at the Fourier frequencies have a similar form and smoothed versions of the periodogram...

19. Bernoulli Polynomials, Fourier Series and Zeta Numbers

DEFF Research Database (Denmark)

Scheufens, Ernst E

2013-01-01

Fourier series for Bernoulli polynomials are used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent...

20. The Fourier modal method for aperiodic structures

NARCIS (Netherlands)

Pisarenco, M.; Maubach, J.M.L.; Setija, I.D.; Mattheij, R.M.M.

2010-01-01

This paper extends the area of application of the Fourier modal method from periodic structures to non-periodic ones illuminated under arbitrary angles. This is achieved by placing perfectly matched layers at the lateral boundaries and reformulating the problem in terms of a contrast field.

1. Discrete Fourier analysis of multigrid algorithms

NARCIS (Netherlands)

van der Vegt, Jacobus J.W.; Rhebergen, Sander

2011-01-01

The main topic of this report is a detailed discussion of the discrete Fourier multilevel analysis of multigrid algorithms. First, a brief overview of multigrid methods is given for discretizations of both linear and nonlinear partial differential equations. Special attention is given to the

2. Euler Polynomials, Fourier Series and Zeta Numbers

DEFF Research Database (Denmark)

Scheufens, Ernst E

2012-01-01

Fourier series for Euler polynomials is used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent series....

3. Fourier inversion on a reductive symmetric space

NARCIS (Netherlands)

Ban, E.P. van den

1999-01-01

Let X be a semisimple symmetric space. In previous papers, [8] and [9], we have dened an explicit Fourier transform for X and shown that this transform is injective on the space C 1 c (X) ofcompactly supported smooth functions on X. In the present paper, which is a continuation of these papers, we

4. Fractional-Fourier-domain weighted Wigner distribution

NARCIS (Netherlands)

Stankovic, L.; Alieva, T.; Bastiaans, M.J.

2001-01-01

A fractional-Fourier-domain realization of the weighted Wigner distribution (or S-method), producing auto-terms close to the ones in the Wigner distribution itself, but with reduced cross-terms, is presented. The computational cost of this fractional-domain realization is the same as the

5. Fourier transforms on a semisimple symmetric space

NARCIS (Netherlands)

Ban, E.P. van den; Schlichtkrull, H.

1994-01-01

Let G=H be a semisimple symmetric space, that is, G is a connected semisimple real Lie group with an involution ?, and H is an open subgroup of the group of xed points for ? in G. The main purpose of this paper is to study an explicit Fourier transform on G=H. In terms of general representation

6. Fourier transforms on a semisimple symmetric space

NARCIS (Netherlands)

Ban, E.P. van den; Carmona, J.; Delorme, P.

1997-01-01

Let G=H be a semisimple symmetric space, that is, G is a connected semisimple real Lie group with an involution ?, and H is an open subgroup of the group of xed points for ? in G. The main purpose of this paper is to study an explicit Fourier transform on G=H. In terms of general representation

7. Application of the fractional Fourier transformation to digital holography recorded by an elliptical, astigmatic Gaussian beam.

Science.gov (United States)

Nicolas, F; Coëtmellec, S; Brunel, M; Allano, D; Lebrun, D; Janssen, A J E M

2005-11-01

The authors have studied the diffraction pattern produced by a particle field illuminated by an elliptic and astigmatic Gaussian beam. They demonstrate that the bidimensional fractional Fourier transformation is a mathematically suitable tool to analyse the diffraction pattern generated not only by a collimated plane wave [J. Opt. Soc. Am A 19, 1537 (2002)], but also by an elliptic and astigmatic Gaussian beam when two different fractional orders are considered. Simulations and experimental results are presented.

8. Causal Correlation Functions and Fourier Transforms: Application in Calculating Pressure Induced Shifts

Science.gov (United States)

Ma, Q.; Tipping, R. H.; Lavrentieva, N. N.

2012-01-01

By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct.

9. Maximum-entropy data restoration using both real- and Fourier-space analysis

International Nuclear Information System (INIS)

Anderson, D.M.; Martin, D.C.; Thomas, E.L.

1989-01-01

An extension of the maximum-entropy (ME) data-restoration method is presented that is sensitive to periodic correlations in data. The method takes advantage of the higher signal-to-noise ratio for periodic information in Fourier space, thus enhancing statistically significant frequencies in a manner which avoids the user bias inherent in conventional Fourier filtering. This procedure incorporates concepts underlying new approaches in quantum mechanics that consider entropies in both position and momentum spaces, although the emphasis here is on data restoration rather than quantum physics. After a fast Fourier transform of the image, the phases are saved and the array of Fourier moduli are restored using the maximum-entropy criterion. A first-order continuation method is introduced that speeds convergence of the ME computation. The restored moduli together with the original phases are then Fourier inverted to yield a new image; traditional real-space ME restoration is applied to this new image completing one stage in the restoration process. In test cases improvement can be obtained from two to four stages of iteration. It is shown that in traditional Fourier filtering spurious features can be induced by selection or elimination of Fourier components without regard to their statistical significance. With the present approach there is no such freedom for the user to exert personal bias, so that features present in the final image and power spectrum are those which have survived the tests of statistical significance in both real and Fourier space. However, it is still possible for periodicities to 'bleed' across sharp boundaries. An 'uncertainty' relation is derived describing the inverse relationship between the resolution of these boundaries and the level of noise that can be eliminated. (orig./BHO)

10. Applying machine learning methods for characterization of hexagonal prisms from their 2D scattering patterns - an investigation using modelled scattering data

Science.gov (United States)

Salawu, Emmanuel Oluwatobi; Hesse, Evelyn; Stopford, Chris; Davey, Neil; Sun, Yi

2017-11-01

Better understanding and characterization of cloud particles, whose properties and distributions affect climate and weather, are essential for the understanding of present climate and climate change. Since imaging cloud probes have limitations of optical resolution, especially for small particles (with diameter < 25 μm), instruments like the Small Ice Detector (SID) probes, which capture high-resolution spatial light scattering patterns from individual particles down to 1 μm in size, have been developed. In this work, we have proposed a method using Machine Learning techniques to estimate simulated particles' orientation-averaged projected sizes (PAD) and aspect ratio from their 2D scattering patterns. The two-dimensional light scattering patterns (2DLSP) of hexagonal prisms are computed using the Ray Tracing with Diffraction on Facets (RTDF) model. The 2DLSP cover the same angular range as the SID probes. We generated 2DLSP for 162 hexagonal prisms at 133 orientations for each. In a first step, the 2DLSP were transformed into rotation-invariant Zernike moments (ZMs), which are particularly suitable for analyses of pattern symmetry. Then we used ZMs, summed intensities, and root mean square contrast as inputs to the advanced Machine Learning methods. We created one random forests classifier for predicting prism orientation, 133 orientation-specific (OS) support vector classification models for predicting the prism aspect-ratios, 133 OS support vector regression models for estimating prism sizes, and another 133 OS Support Vector Regression (SVR) models for estimating the size PADs. We have achieved a high accuracy of 0.99 in predicting prism aspect ratios, and a low value of normalized mean square error of 0.004 for estimating the particle's size and size PADs.

11. Laplace-Fourier-domain dispersion analysis of an average derivative optimal scheme for scalar-wave equation

Science.gov (United States)

Chen, Jing-Bo

2014-06-01

By using low-frequency components of the damped wavefield, Laplace-Fourier-domain full waveform inversion (FWI) can recover a long-wavelength velocity model from the original undamped seismic data lacking low-frequency information. Laplace-Fourier-domain modelling is an important foundation of Laplace-Fourier-domain FWI. Based on the numerical phase velocity and the numerical attenuation propagation velocity, a method for performing Laplace-Fourier-domain numerical dispersion analysis is developed in this paper. This method is applied to an average-derivative optimal scheme. The results show that within the relative error of 1 per cent, the Laplace-Fourier-domain average-derivative optimal scheme requires seven gridpoints per smallest wavelength and smallest pseudo-wavelength for both equal and unequal directional sampling intervals. In contrast, the classical five-point scheme requires 23 gridpoints per smallest wavelength and smallest pseudo-wavelength to achieve the same accuracy. Numerical experiments demonstrate the theoretical analysis.

12. Simple example of track finding by Fourier transform and possibilities for vector or optical processors

International Nuclear Information System (INIS)

Underwood, D.

1986-01-01

Simple examples of finding tracks by Fourier transform with filter or correlation function are presented. Possibilities for using this method in more complicated real situations and the processing times which might be achieved are discussed. The method imitates the simplest examples in the literature on optical pattern recognition and optical processing. The possible benefits of the method are in speed of processing in the optical Fourier transform wherein an entire picture is processed simultaneously. The speed of a computer vector processor may be competitive with present electro-optical devices. 2 refs., 6 figs

13. Automatic Fourier transform and self-Fourier beams due to parabolic potential

Energy Technology Data Exchange (ETDEWEB)

Zhang, Yiqi, E-mail: zhangyiqi@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Liu, Xing [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Belić, Milivoj R., E-mail: milivoj.belic@qatar.tamu.edu [Science Program, Texas A& M University at Qatar, P.O. Box 23874 Doha (Qatar); Zhong, Weiping [Department of Electronic and Information Engineering, Shunde Polytechnic, Shunde 528300 (China); Petrović, Milan S. [Institute of Physics, P.O. Box 68, 11001 Belgrade (Serbia); Zhang, Yanpeng, E-mail: ypzhang@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)

2015-12-15

We investigate the propagation of light beams including Hermite–Gauss, Bessel–Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams—that is, the beams whose Fourier transforms are the beams themselves.

14. Fourier-based automatic alignment for improved Visual Cryptography schemes.

Science.gov (United States)

Machizaud, Jacques; Chavel, Pierre; Fournel, Thierry

2011-11-07

In Visual Cryptography, several images, called "shadow images", that separately contain no information, are overlapped to reveal a shared secret message. We develop a method to digitally register one printed shadow image acquired by a camera with a purely digital shadow image, stored in memory. Using Fourier techniques derived from Fourier Optics concepts, the idea is to enhance and exploit the quasi periodicity of the shadow images, composed by a random distribution of black and white patterns on a periodic sampling grid. The advantage is to speed up the security control or the access time to the message, in particular in the cases of a small pixel size or of large numbers of pixels. Furthermore, the interest of visual cryptography can be increased by embedding the initial message in two shadow images that do not have identical mathematical supports, making manual registration impractical. Experimental results demonstrate the successful operation of the method, including the possibility to directly project the result onto the printed shadow image.

15. (Anti)symmetric multivariate exponential functions and corresponding Fourier transforms

International Nuclear Information System (INIS)

Klimyk, A U; Patera, J

2007-01-01

We define and study symmetrized and antisymmetrized multivariate exponential functions. They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. These functions are eigenfunctions of the Laplace operator on the corresponding fundamental domains satisfying certain boundary conditions. To symmetric and antisymmetric multivariate exponential functions there correspond Fourier transforms. There are three types of such Fourier transforms: expansions into the corresponding Fourier series, integral Fourier transforms and multivariate finite Fourier transforms. Eigenfunctions of the integral Fourier transforms are found

16. SU-E-QI-08: Fourier Properties of Cone Beam CT Projection

International Nuclear Information System (INIS)

Bai, T; Yan, H; Jia, X; Jiang, Steve B.; Mou, X

2014-01-01

Purpose: To explore the Fourier properties of cone beam CT (CBCT) projections and apply the property to directly estimate noise level of CBCT projections without any prior information. Methods: By utilizing the property of Bessel function, we derivate the Fourier properties of the CBCT projections for an arbitrary point object. It is found that there exists a double-wedge shaped region in the Fourier space where the intensity is approximately zero. We further derivate the Fourier properties of independent noise added to CBCT projections. The expectation of the square of the module in any point of the Fourier space is constant and the value approximately equals to noise energy. We further validate the theory in numerical simulations for both a delta function object and a NCAT phantom with different levels of noise added. Results: Our simulation confirmed the existence of the double-wedge shaped region in Fourier domain for the x-ray projection image. The boundary locations of this region agree well with theoretical predictions. In the experiments of estimating noise level, the mean relative error between the theory estimation and the ground truth values is 2.697%. Conclusion: A novel theory on the Fourier properties of CBCT projections has been discovered. Accurate noise level estimation can be achieved by applying this theory directly to the measured CBCT projections. This work was supported in part by NIH(1R01CA154747-01), NSFC((No. 61172163), Research Fund for the Doctoral Program of Higher Education of China (No. 20110201110011) and China Scholarship Council

17. Reflector modelization in neutronic and optimization methods applied to fuel loading pattern; Modelisation du reflecteur en neutronique et methodes doptimisation appliquees aux plans de rechargement

Energy Technology Data Exchange (ETDEWEB)

Argaud, J P

1995-12-01

I Physical description of P.W.R nuclear core can be handled by multigroup neutronic diffusion model. We are interested in two problems, using the same approach for the optimization aspect. To deal with some differences between calculations and measurements, the question of their reduction is then introduced. A reflector parameters identification from core measurements is then purposed, the reflector being at the present time the less known part of core diffusion model. This approach conducts to study the reflector model, in particular by an analysis of its transport origin. It leads finally to a new model of reflector described by boundary operators using an integral formulation on the core/reflector interface. That is on this new model that a parameter identification formulation of calculations-measurements differences reduction is given, using an adjoint state formulation to minimize errors by a gradient method. Furthermore, nuclear fuel reload of P.W.R core needs an optimal distribution of fuel assemblies, namely a loading pattern. This combinatorial optimization problem is then expressed as a cost function minimization, the cost function describing the power spatial distribution. Various methods (linear programming, simulated annealing,...), used to solve this problem, are detailed, given in particular a practical search example. A new approach is then proposed, using the gradient of the cost function to direct the search in the patterns discrete space. Final results of complete patterns search trials are presented, and compared to those obtained by other methods. In particular the results are obtained very quickly. (author). 81 refs., 55 figs., 5 appends.

18. Anthropometric geography applied to the analysis of socioeconomic disparities: cohort trends and spatial patterns of height and robustness in 20th-century Spain.

Science.gov (United States)

Camara, Antonio D; Roman, Joan Garcia

2015-11-01

Anthropometrics have been widely used to study the influence of environmental factors on health and nutritional status. In contrast, anthropometric geography has not often been employed to approximate the dynamics of spatial disparities associated with socioeconomic and demographic changes. Spain exhibited intense disparity and change during the middle decades of the 20 th century, with the result that the life courses of the corresponding cohorts were associated with diverse environmental conditions. This was also true of the Spanish territories. This paper presents insights concerning the relationship between socioeconomic changes and living conditions by combining the analysis of cohort trends and the anthropometric cartography of height and physical build. This analysis is conducted for Spanish male cohorts born 1934-1973 that were recorded in the Spanish military statistics. This information is interpreted in light of region-level data on GDP and infant mortality. Our results show an anthropometric convergence across regions that, nevertheless, did not substantially modify the spatial patterns of robustness, featuring primarily robust northeastern regions and weak Central-Southern regions. These patterns persisted until the 1990s (cohorts born during the 1970s). For the most part, anthropometric disparities were associated with socioeconomic disparities, although the former lessened over time to a greater extent than the latter. Interestingly, the various anthropometric indicators utilized here do not point to the same conclusions. Some discrepancies between height and robustness patterns have been found that moderate the statements from the analysis of cohort height alone regarding the level and evolution of living conditions across Spanish regions.

19. Multichannel Dynamic Fourier-Transform IR Spectrometer

Science.gov (United States)

Balashov, A. A.; Vaguine, V. A.; Golyak, Il. S.; Morozov, A. N.; Khorokhorin, A. I.

2017-09-01

A design of a multichannel continuous scan Fourier-transform IR spectrometer for simultaneous recording and analysis of the spectral characteristics of several objects is proposed. For implementing the design, a multi-probe fiber is used, constructed from several optical fibers connected into a single optical connector and attached at the output of the interferometer. The Fourier-transform spectrometer is used as a signal modulator. Each fiber is individually mated with an investigated sample and a dedicated radiation detector. For the developed system, the radiation intensity of the spectrometer is calculated from the condition of the minimum spectral resolution and parameters of the optical fibers. Using the proposed design, emission spectra of a gas-discharge neon lamp have been recorded using a single fiber 1 mm in diameter with a numerical aperture NA = 0.22.

20. Discrete Fourier transform in nanostructures using scattering

International Nuclear Information System (INIS)

Leuenberger, Michael N.; Flatte, Michael E.; Loss, Daniel; Awschalom, D.D.

2004-01-01

In this article, we show that the discrete Fourier transform (DFT) can be performed by scattering a coherent particle or laser beam off an electrically controllable two-dimensional (2D) potential that has the shape of rings or peaks. After encoding the initial vector into the two-dimensional potential by means of electric gates, the Fourier-transformed vector can be read out by detectors surrounding the potential. The wavelength of the laser beam determines the necessary accuracy of the 2D potential, which makes our method very fault-tolerant. Since the time to perform the DFT is much smaller than the clock cycle of today's computers, our proposed device performs DFTs at the frequency of the computer clock speed

1. Fourier transform of momentum distribution in vanadium

International Nuclear Information System (INIS)

Singh, A.K.; Manuel, A.A.; Peter, M.; Singru, R.M.

1985-01-01

Experimental Compton profile and 2D-angular correlation of positron annihilation radiation data from vanadium are analyzed by the mean of their Fourier transform. They are compared with the functions calculated with the help of both the linear muffin-tin orbital and the Hubbard-Mijnarends band structure methods. The results show that the functions are influenced by the positron wave function, by the e + -e - many-body correlations and by the differences in the electron wave functions used for the band structure calculations. It is concluded that Fourier analysis is a sensitive approach to investigate the momentum distributions in transition metals and to understnad the effects of the positron. (Auth.)

2. Correcting sample drift using Fourier harmonics.

Science.gov (United States)

Bárcena-González, G; Guerrero-Lebrero, M P; Guerrero, E; Reyes, D F; Braza, V; Yañez, A; Nuñez-Moraleda, B; González, D; Galindo, P L

2018-07-01

During image acquisition of crystalline materials by high-resolution scanning transmission electron microscopy, the sample drift could lead to distortions and shears that hinder their quantitative analysis and characterization. In order to measure and correct this effect, several authors have proposed different methodologies making use of series of images. In this work, we introduce a methodology to determine the drift angle via Fourier analysis by using a single image based on the measurements between the angles of the second Fourier harmonics in different quadrants. Two different approaches, that are independent of the angle of acquisition of the image, are evaluated. In addition, our results demonstrate that the determination of the drift angle is more accurate by using the measurements of non-consecutive quadrants when the angle of acquisition is an odd multiple of 45°. Copyright © 2018 Elsevier Ltd. All rights reserved.

3. Genetic Algorithm with Maximum-Minimum Crossover (GA-MMC) Applied in Optimization of Radiation Pattern Control of Phased-Array Radars for Rocket Tracking Systems

Science.gov (United States)

Silva, Leonardo W. T.; Barros, Vitor F.; Silva, Sandro G.

2014-01-01

In launching operations, Rocket Tracking Systems (RTS) process the trajectory data obtained by radar sensors. In order to improve functionality and maintenance, radars can be upgraded by replacing antennas with parabolic reflectors (PRs) with phased arrays (PAs). These arrays enable the electronic control of the radiation pattern by adjusting the signal supplied to each radiating element. However, in projects of phased array radars (PARs), the modeling of the problem is subject to various combinations of excitation signals producing a complex optimization problem. In this case, it is possible to calculate the problem solutions with optimization methods such as genetic algorithms (GAs). For this, the Genetic Algorithm with Maximum-Minimum Crossover (GA-MMC) method was developed to control the radiation pattern of PAs. The GA-MMC uses a reconfigurable algorithm with multiple objectives, differentiated coding and a new crossover genetic operator. This operator has a different approach from the conventional one, because it performs the crossover of the fittest individuals with the least fit individuals in order to enhance the genetic diversity. Thus, GA-MMC was successful in more than 90% of the tests for each application, increased the fitness of the final population by more than 20% and reduced the premature convergence. PMID:25196013

4. Closed form fourier-based transmit beamforming for MIMO radar

KAUST Repository

Lipor, John J.

2014-05-01

In multiple-input multiple-output (MIMO) radar setting, it is often desirable to design correlated waveforms such that power is transmitted only to a given set of locations, a process known as beampattern design. To design desired beam-pattern, current research uses iterative algorithms, first to synthesize the waveform covariance matrix, R, then to design the actual waveforms to realize R. In contrast to this, we present a closed form method to design R that exploits discrete Fourier transform and Toeplitz matrix. The resulting covariance matrix fulfills the practical constraints and performance is similar to that of iterative methods. Next, we present a radar architecture for the desired beampattern that does not require the synthesis of covariance matrix nor the design of correlated waveforms. © 2014 IEEE.

5. Fourier evaluation of broad Moessbauer spectra

International Nuclear Information System (INIS)

Vincze, I.

1981-01-01

It is shown by the Fourier analysis of broad Moessbauer spectra that the even part of the distribution of the dominant hyperfine interaction (hyperfine field or quadrupole splitting) can be obtained directly without using least-square fitting procedures. Also the odd part of this distribution correlated with other hyperfine parameters (e.g. isomer shift) can be directly determined. Examples for amorphous magnetic and paramagnetic iron-based alloys are presented. (author)

6. Fourier evaluation of broad Moessbauer spectra

International Nuclear Information System (INIS)

Vincze, I.

1981-09-01

It is shown by the Fourier analysis of broad Moessbauer spectra that the even part of the distribution of the dominant hyperfine interaction (hyperfine field or quadrupole splitting) can be obtained directly without using least-square fitting procedures. Also the odd part of this distribution correlated with other hyperfine parameters (e.g. isomer shift) can be directly determined. Examples covering the case of amorphous magnetic and paramagnetic iron-based alloys are presented. (author)

7. Quantum Fourier Transform Over Galois Rings

OpenAIRE

Zhang, Yong

2009-01-01

Galois rings are regarded as "building blocks" of a finite commutative ring with identity. There have been many papers on classical error correction codes over Galois rings published. As an important warm-up before exploring quantum algorithms and quantum error correction codes over Galois rings, we study the quantum Fourier transform (QFT) over Galois rings and prove it can be efficiently preformed on a quantum computer. The properties of the QFT over Galois rings lead to the quantum algorit...

8. Fourier Transform Spectrometer Controller for Partitioned Architectures

DEFF Research Database (Denmark)

Tamas-Selicean, Domitian; Keymeulen, D.; Berisford, D.

2013-01-01

The current trend in spacecraft computing is to integrate applications of different criticality levels on the same platform using no separation. This approach increases the complexity of the development, verification and integration processes, with an impact on the whole system life cycle. Resear......, such as avionics and automotive. In this paper we investigate the challenges of developing and the benefits of integrating a scientific instrument, namely a Fourier Transform Spectrometer, in such a partitioned architecture....

9. A Fourier analysis of extreme events

DEFF Research Database (Denmark)

Mikosch, Thomas Valentin; Zhao, Yuwei

2014-01-01

The extremogram is an asymptotic correlogram for extreme events constructed from a regularly varying stationary sequence. In this paper, we define a frequency domain analog of the correlogram: a periodogram generated from a suitable sequence of indicator functions of rare events. We derive basic ...... properties of the periodogram such as the asymptotic independence at the Fourier frequencies and use this property to show that weighted versions of the periodogram are consistent estimators of a spectral density derived from the extremogram....

10. Ion-cyclotron-resonance- and Fourier-transform-ion-cyclotron-resonance spectroscopy: technology and application

International Nuclear Information System (INIS)

Luederwald, I.

1977-01-01

Instrumentation and technology of Ion-Cyclotron-Resonance and Fourier-Transform-Ion-Cyclotron-Resonance Spectroscopy are described. The method can be applied to studies of ion/molecule reactions in gas phase, to obtain thermodynamic data as gas phase acidity or basicity, proton and electron affinity, and to establish reaction mechanisms and ion structures. (orig.) [de

11. Limitations and potential of spectral subtractions in fourier-transform infrared (FTIR) spectroscopy of soil samples

Science.gov (United States)

Soil science research is increasingly applying Fourier transform infrared (FTIR) spectroscopy for analysis of soil organic matter (SOM). However, the compositional complexity of soils and the dominance of the mineral component can limit spectroscopic resolution of SOM and other minor components. The...

12. Description of the electron-hydrogen collision by the Coulomb Fourier transform method

International Nuclear Information System (INIS)

Levin, S.B.

2005-01-01

A recently developed Coulomb Fourier Transform method is applied to the system containing one heavy ion and two electrons. The transformed Hamiltonian is described with a controlled accuracy in an effective finite basis set as a finite dimensional operator matrix. The kernels of interaction are formulated in terms of the so called Nordsieck integrals

13. Fourier Descriptor Analysis and Unification of Voice Range Profile Contours: Method and Applications

Science.gov (United States)

Pabon, Peter; Ternstrom, Sten; Lamarche, Anick

2011-01-01

Purpose: To describe a method for unified description, statistical modeling, and comparison of voice range profile (VRP) contours, even from diverse sources. Method: A morphologic modeling technique, which is based on Fourier descriptors (FDs), is applied to the VRP contour. The technique, which essentially involves resampling of the curve of the…

14. The derivative-free Fourier shell identity for photoacoustics.

Science.gov (United States)

2016-01-01

In X-ray tomography, the Fourier slice theorem provides a relationship between the Fourier components of the object being imaged and the measured projection data. The Fourier slice theorem is the basis for X-ray Fourier-based tomographic inversion techniques. A similar relationship, referred to as the 'Fourier shell identity' has been previously derived for photoacoustic applications. However, this identity relates the pressure wavefield data function and its normal derivative measured on an arbitrary enclosing aperture to the three-dimensional Fourier transform of the enclosed object evaluated on a sphere. Since the normal derivative of pressure is not normally measured, the applicability of the formulation is limited in this form. In this paper, alternative derivations of the Fourier shell identity in 1D, 2D polar and 3D spherical polar coordinates are presented. The presented formulations do not require the normal derivative of pressure, thereby lending the formulas directly adaptable for Fourier based absorber reconstructions.

15. Nonlinear refractive index measuring using a double-grating interferometer in pump–probe configuration and Fourier transform analysis

International Nuclear Information System (INIS)

Rasouli, Saifollah; Ghorbani, Mahnaz

2012-01-01

In this paper, we have presented a simple, stable, highly sensitive and timesaving method based on a double-grating interferometer in conjunction with a pump–probe technique for measuring the nonlinear refractive index. A pump laser beam is aligned collinearly with an expanded plane parallel probe beam by a dichroic mirror. These beams pass through the sample, while right behind the sample using a suitable bandpass filter the pump beam is intercepted. The distorted probe beam then passes through a double-grating interferometer. One of the lateral shearing interference patterns is recorded by use of a CCD camera and, after digitization, has been stored in a computer. The interference pattern is analyzed by means of a Fourier transform algorithm. The refractive index changes have been obtained from phase distribution of the recorded fringe patterns. The implementation of the technique is straightforward and the arrangement is very simple and stable yet its sensitivity is comparable with other interferometry methods. It is also not a time consuming method. The method is applied for measuring the thermal nonlinear refractive index n 2 of colloidal gold nanoparticles in water solution. (paper)

16. Ultrafast and versatile spectroscopy by temporal Fourier transform

Science.gov (United States)

Zhang, Chi; Wei, Xiaoming; Marhic, Michel E.; Wong, Kenneth K. Y.

2014-06-01

One of the most remarkable and useful properties of a spatially converging lens system is its inherent ability to perform the Fourier transform; the same applies for the time-lens system. At the back focal plane of the time-lens, the spectral information can be instantaneously obtained in the time axis. By implementing temporal Fourier transform for spectroscopy applications, this time-lens-based architecture can provide orders of magnitude improvement over the state-of-art spatial-dispersion-based spectroscopy in terms of the frame rate. On the other hand, in addition to the single-lens structure, the multi-lens structures (e.g. telescope or wide-angle scope) will provide very versatile operating conditions. Leveraging the merit of instantaneous response, as well as the flexible lens structure, here we present a 100-MHz frame rate spectroscopy system - the parametric spectro-temporal analyzer (PASTA), which achieves 17 times zoom in/out ratio for different observation ranges.

17. A Note on Fourier and the Greenhouse Effect

OpenAIRE

Postma, Joseph E.

2015-01-01

Joseph Fourier's discovery of the greenhouse effect is discussed and is compared to the modern conception of the greenhouse effect. It is confirmed that what Fourier discovered is analogous to the modern concept of the greenhouse effect. However, the modern concept of the greenhouse effect is found to be based on a paradoxical analogy to Fourier's greenhouse work and so either Fourier's greenhouse work, the modern conception of the greenhouse effect, or the modern definition of heat is incorr...

18. Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series

Science.gov (United States)

Zhang, Zhihua

2014-01-01

Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the corresponding Fourier cosine coefficients decay very fast. Although our research is in the setting of stochastic processes, our results are also new for deterministic functions. PMID:25147842

19. Regional distribution of ventilation assessed by Kr-81m scintigraphy employing temporal Fourier transform

International Nuclear Information System (INIS)

Slosman, D.; Susskind, H.; Cinotti, L.; van Giessen, J.W.; Brill, A.B.

1986-01-01

Temporal Fourier analysis was applied to Kr-81m ventilation scintigraphy to determine the amplitude (AMP1) and phase (PHA1) of the first harmonic of a single composite respiratory cycle and to compare regional patterns in subjects with obstructive pulmonary disease (COPD) and nonobstructed subjects. Six nonobstructed subjects, three subjects with small airway disease, six subjects with COPD, and one subject with restrictive disease were investigated. The mean value of the functional PHA1 image (PHA1m) correlated negatively with 1-second forced expiratory volume (FEV1) (r = -0.801, P less than .001), with %FEV1/FVC (r = -0.636, P less than .01) and maximum midexpiratory flow rate (FEF25-75%) (r = -0.723, P less than .002), and correlated positively with residual volume (r = 0.640, P less than .01). PHA1m values for the six subjects with COPD were significantly higher (t = 2.359, P less than .05) than for the ten nonobstructed subjects. Display of phase and amplitude functional images permits a visual evaluation of the regional distribution of ventilation to be made. Regional abnormalities of air flow were detected in obstructed subjects, and the presence of airway obstruction could be predicted. Dynamic ventilation imaging, therefore, appears to be a potentially useful noninvasive technique to assess lung impairment on a localized level

20. Binary zone-plate array for a parallel joint transform correlator applied to face recognition.

Science.gov (United States)

Kodate, K; Hashimoto, A; Thapliya, R

1999-05-10

Taking advantage of small aberrations, high efficiency, and compactness, we developed a new, to our knowledge, design procedure for a binary zone-plate array (BZPA) and applied it to a parallel joint transform correlator for the recognition of the human face. Pairs of reference and unknown images of faces are displayed on a liquid-crystal spatial light modulator (SLM), Fourier transformed by the BZPA, intensity recorded on an optically addressable SLM, and inversely Fourier transformed to obtain correlation signals. Consideration of the bandwidth allows the relations among the channel number, the numerical aperture of the zone plates, and the pattern size to be determined. Experimentally a five-channel parallel correlator was implemented and tested successfully with a 100-person database. The design and the fabrication of a 20-channel BZPA for phonetic character recognition are also included.

1. Some Applications of Fourier's Great Discovery for Beginners

Science.gov (United States)

Kraftmakher, Yaakov

2012-01-01

Nearly two centuries ago, Fourier discovered that any periodic function of period T can be presented as a sum of sine waveforms of frequencies equal to an integer times the fundamental frequency [omega] = 2[pi]/T (Fourier's series). It is impossible to overestimate the importance of Fourier's discovery, and all physics or engineering students…

2. Fourier Transforms Simplified: Computing an Infrared Spectrum from an Interferogram

Science.gov (United States)

Hanley, Quentin S.

2012-01-01

Fourier transforms are used widely in chemistry and allied sciences. Examples include infrared, nuclear magnetic resonance, and mass spectroscopies. A thorough understanding of Fourier methods assists the understanding of microscopy, X-ray diffraction, and diffraction gratings. The theory of Fourier transforms has been presented in this "Journal",…

3. Big Data Usage Patterns in the Health Care Domain: A Use Case Driven Approach Applied to the Assessment of Vaccination Benefits and Risks

Science.gov (United States)

Liyanage, H.; Liaw, S-T.; Kuziemsky, C.; Mold, F.; Krause, P.; Fleming, D.; Jones, S.

2014-01-01

Summary Background Generally benefits and risks of vaccines can be determined from studies carried out as part of regulatory compliance, followed by surveillance of routine data; however there are some rarer and more long term events that require new methods. Big data generated by increasingly affordable personalised computing, and from pervasive computing devices is rapidly growing and low cost, high volume, cloud computing makes the processing of these data inexpensive. Objective To describe how big data and related analytical methods might be applied to assess the benefits and risks of vaccines. Method: We reviewed the literature on the use of big data to improve health, applied to generic vaccine use cases, that illustrate benefits and risks of vaccination. We defined a use case as the interaction between a user and an information system to achieve a goal. We used flu vaccination and pre-school childhood immunisation as exemplars. Results We reviewed three big data use cases relevant to assessing vaccine benefits and risks: (i) Big data processing using crowd-sourcing, distributed big data processing, and predictive analytics, (ii) Data integration from heterogeneous big data sources, e.g. the increasing range of devices in the “internet of things”, and (iii) Real-time monitoring for the direct monitoring of epidemics as well as vaccine effects via social media and other data sources. Conclusions Big data raises new ethical dilemmas, though its analysis methods can bring complementary real-time capabilities for monitoring epidemics and assessing vaccine benefit-risk balance. PMID:25123718

4. Fourier descriptors analysis of anisotropy and preferred Orientation in geological samples

International Nuclear Information System (INIS)

Santiago Buey, C. de

2011-01-01

This study focuses on the use of Fourier descriptors to evaluate and quantify two specific fabric characteristics of geological materials: anisotropy of particles or voids morphologies and particle orientation. To this end, a theoretical section of a rock was created, made of ellipses and rectangles of different axes ratios and different orientations. The Fourier descriptors method was applied to calculate the anisotropy and orientation of each particle and, finally, a rose diagram was constructed to represent the particles orientations distribution and to observe the presence or not of any preferred orientation. (Author) 15 refs.

5. Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus

International Nuclear Information System (INIS)

Aerts, Diederik; Czachor, Marek; Kuna, Maciej

2016-01-01

Highlights: • Fractal arithmetic allows to define Fourier transforms on Cantor-like sets. • General construction is illustrated on the example of a sawtooth signal. • The formalism is much simpler than the approaches discussed so far in the literature. - Abstract: Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration, and complex structure. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has all the required basic properties. As an example we discuss a sawtooth signal on the ternary middle-third Cantor set. The formalism works also for fractals that are not self-similar.

6. New development for the reverse time of flight analysis of spectra measured using Fourier Diffractometer Facilities

CERN Document Server

Maayouf, R M A

2002-01-01

The present work introduces a new design to replace the (Finnish make) reverse time of flight (RTOF) analyzer used for the Fourier diffractometer facilities. The new design applies a data acquisition system, a special interface card and software program installed in a PC computer, to perform the cross-correlation functions between signals received from the chopper-decoder and detector. It has been found from test measurements performed with the Cairo Fourier diffractometer facility (CFDF) and the similar high resolution one at JINR (Dubna-Russia) that the new design can successfully replace the Finnish make RTOF analyzer.

7. Fringe pattern analysis for optical metrology theory, algorithms, and applications

CERN Document Server

2014-01-01

The main objective of this book is to present the basic theoretical principles and practical applications for the classical interferometric techniques and the most advanced methods in the field of modern fringe pattern analysis applied to optical metrology. A major novelty of this work is the presentation of a unified theoretical framework based on the Fourier description of phase shifting interferometry using the Frequency Transfer Function (FTF) along with the theory of Stochastic Process for the straightforward analysis and synthesis of phase shifting algorithms with desired properties such

8. Quantum diffraction and interference of spatially correlated photon pairs and its Fourier-optical analysis

International Nuclear Information System (INIS)

Shimizu, Ryosuke; Edamatsu, Keiichi; Itoh, Tadashi

2006-01-01

We present one- and two-photon diffraction and interference experiments involving parametric down-converted photon pairs. By controlling the divergence of the pump beam in parametric down-conversion, the diffraction-interference pattern produced by an object changes from a quantum (perfectly correlated) case to a classical (uncorrelated) one. The observed diffraction and interference patterns are accurately reproduced by Fourier-optical analysis taking into account the quantum spatial correlation. We show that the relation between the spatial correlation and the object size plays a crucial role in the formation of both one- and two-photon diffraction-interference patterns

9. Paraconsistents artificial neural networks applied to the study of mutational patterns of the F subtype of the viral strains of HIV-1 to antiretroviral therapy

Directory of Open Access Journals (Sweden)

PAULO C.C. DOS SANTOS

2016-03-01

Full Text Available ABSTRACT The high variability of HIV-1 as well as the lack of efficient repair mechanisms during the stages of viral replication, contribute to the rapid emergence of HIV-1 strains resistant to antiretroviral drugs. The selective pressure exerted by the drug leads to fixation of mutations capable of imparting varying degrees of resistance. The presence of these mutations is one of the most important factors in the failure of therapeutic response to medications. Thus, it is of critical to understand the resistance patterns and mechanisms associated with them, allowing the choice of an appropriate therapeutic scheme, which considers the frequency, and other characteristics of mutations. Utilizing Paraconsistents Artificial Neural Networks, seated in Paraconsistent Annotated Logic Et which has the capability of measuring uncertainties and inconsistencies, we have achieved levels of agreement above 90% when compared to the methodology proposed with the current methodology used to classify HIV-1 subtypes. The results demonstrate that Paraconsistents Artificial Neural Networks can serve as a promising tool of analysis.

10. Application of Fourier analysis to the study of roughness profiles of eroded samples

International Nuclear Information System (INIS)

Bethencourt, M.; Botana, F.J.; Calvino, J.J.; Marcos, M.; Rodriguez-Chacon, M.A.

1998-01-01

Fourier transforms are applied to analyse surface roughness profiles recorded on samples coming from erosion-corrosion essays. The information retrieved using this method clearly complements that revealed by the more classical roughness amplitude parameters. The analysis procedure here proposed can be applied not only to characterise the surface of corroded samples but, in general, to evaluate the quality of any surface after application of finishing treatments. (Author) 7 refs

11. New significance test methods for Fourier analysis of geophysical time series

Directory of Open Access Journals (Sweden)

Z. Zhang

2011-09-01

Full Text Available When one applies the discrete Fourier transform to analyze finite-length time series, discontinuities at the data boundaries will distort its Fourier power spectrum. In this paper, based on a rigid statistics framework, we present a new significance test method which can extract the intrinsic feature of a geophysical time series very well. We show the difference in significance level compared with traditional Fourier tests by analyzing the Arctic Oscillation (AO and the Nino3.4 time series. In the AO, we find significant peaks at about 2.8, 4.3, and 5.7 yr periods and in Nino3.4 at about 12 yr period in tests against red noise. These peaks are not significant in traditional tests.

12. Application of the Fourier descriptors method to the morphological classification of particles in geological materials

International Nuclear Information System (INIS)

Manzanas Lopez, J.; Santiago Buey, C.

2010-01-01

This study focuses on the use of Fourier descriptors to quantitatively describe the morphology of particles aggregates or pores in geological materials. Firstly, the mathematical fundaments of the method are explained. Then, the Fourier descriptors method is applied to the Krumbein Scale, a system of measuring roundness and sphericity of particles. the analysis of the comparison shows that there is good correlation between the Sphericity parameter at the Krumbein classifications and the value of the modulus of the Fourier descriptor No-1. This good correlation, along with the mathematical precision which allows to prevent subjective valorisations in the morphological description, corroborates the validity of the method to quantify the sphericity elongation of particles in geological materials. (Author) 12 refs.

13. Fourier transforms in NMR, optical, and mass spectrometry

International Nuclear Information System (INIS)

Marshall, A.G.; Verdun, F.R.; Ohio State Univ., Columbus, OH

1990-01-01

This book is a teaching and reference text for Fourier transform methods as they are applied in spectroscopy. It offers a unified treatment of the three most popular types of FT/spectroscopy. Non-ideal effects are treated in detail: noise (source- and detector-limited); non-linear response; limits to spectrometer performance based on finite detection period, finite data size, mis-phasing, etc. Common puzzles and paradoxes are explained: e.g., use of mathematically complex variables to represent physically real quantities; interpretation of negative frequency signals; on-resonance versus off-resonance response; interpolation; ultimate accuracy of discrete representation of an analog signal; differences between linearly- and circularly-polarized radiation; multiplex advantage or disadvantage, etc. (author). refs.; figs.; tabs

14. Alternating multivariate trigonometric functions and corresponding Fourier transforms

International Nuclear Information System (INIS)

Klimyk, A U; Patera, J

2008-01-01

We define and study multivariate sine and cosine functions, symmetric with respect to the alternating group A n , which is a subgroup of the permutation (symmetric) group S n . These functions are eigenfunctions of the Laplace operator. They determine Fourier-type transforms. There exist three types of such transforms: expansions into corresponding sine-Fourier and cosine-Fourier series, integral sine-Fourier and cosine-Fourier transforms, and multivariate finite sine and cosine transforms. In all these transforms, alternating multivariate sine and cosine functions are used as a kernel

15. Validation of Fourier analysis of videokeratographic data.

Science.gov (United States)

Sideroudi, Haris; Labiris, Georgios; Ditzel, Fienke; Tsaragli, Efi; Georgatzoglou, Kimonas; Siganos, Haralampos; Kozobolis, Vassilios

2017-06-15

The aim was to assess the repeatability of Fourier transfom analysis of videokeratographic data using Pentacam in normal (CG), keratoconic (KC) and post-CXL (CXL) corneas. This was a prospective, clinic-based, observational study. One randomly selected eye from all study participants was included in the analysis: 62 normal eyes (CG group), 33 keratoconus eyes (KC group), while 34 eyes, which had already received CXL treatment, formed the CXL group. Fourier analysis of keratometric data were obtained using Pentacam, by two different operators within each of two sessions. Precision, repeatability and Intraclass Correlation Coefficient (ICC), were calculated for evaluating intrassesion and intersession repeatability for the following parameters: Spherical Component (SphRmin, SphEcc), Maximum Decentration (Max Dec), Regular Astigmatism, and Irregularitiy (Irr). Bland-Altman analysis was used for assessing interobserver repeatability. All parameters were presented to be repeatable, reliable and reproductible in all groups. Best intrasession and intersession repeatability and reliability were detected for parameters SphRmin, SphEcc and Max Dec parameters for both operators using ICC (intrasession: ICC > 98%, intersession: ICC > 94.7%) and within subject standard deviation. Best precision and lowest range of agreement was found for the SphRmin parameter (CG: 0.05, KC: 0.16, and CXL: 0.2) in all groups, while the lowest repeatability, reliability and reproducibility was detected for the Irr parameter. The Pentacam system provides accurate measurements of Fourier tranform keratometric data. A single Pentacam scan will be sufficient for most clinical applications.

16. Fourier Analysis: Graphical Animation and Analysis of Experimental Data with Excel

Directory of Open Access Journals (Sweden)

Margarida Oliveira

2012-05-01

Full Text Available According to Fourier formulation, any function that can be represented in a graph may be approximated by the “sum” of infinite sinusoidal functions (Fourier series, termed as “waves”.The adopted approach is accessible to students of the first years of university studies, in which the emphasis is put on the understanding of mathematical concepts through illustrative graphic representations, the students being encouraged to prepare animated Excel-based computational modules (VBA-Visual Basic for Applications.Reference is made to the part played by both trigonometric and complex representations of Fourier series in the concept of discrete Fourier transform. Its connection with the continuous Fourier transform is demonstrated and a brief mention is made of the generalization leading to Laplace transform.As application, the example presented refers to the analysis of vibrations measured on engineering structures: horizontal accelerations of a one-storey building deriving from environment noise. This example is integrated in the curriculum of the discipline “Matemática Aplicada à Engenharia Civil” (Mathematics Applied to Civil Engineering, lectured at ISEL (Instituto Superior de Engenharia de Lisboa. In this discipline, the students have the possibility of performing measurements using an accelerometer and a data acquisition system, which, when connected to a PC, make it possible to record the accelerations measured in a file format recognizable by Excel.

17. Left ventricular wall motion abnormalities evaluated by factor analysis as compared with Fourier analysis

International Nuclear Information System (INIS)

Hirota, Kazuyoshi; Ikuno, Yoshiyasu; Nishikimi, Toshio

1986-01-01

Factor analysis was applied to multigated cardiac pool scintigraphy to evaluate its ability to detect left ventricular wall motion abnormalities in 35 patients with old myocardial infarction (MI), and in 12 control cases with normal left ventriculography. All cases were also evaluated by conventional Fourier analysis. In most cases with normal left ventriculography, the ventricular and atrial factors were extracted by factor analysis. In cases with MI, the third factor was obtained in the left ventricle corresponding to wall motion abnormality. Each case was scored according to the coincidence of findings of ventriculography and those of factor analysis or Fourier analysis. Scores were recorded for three items; the existence, location, and degree of asynergy. In cases of MI, the detection rate of asynergy was 94 % by factor analysis, 83 % by Fourier analysis, and the agreement in respect to location was 71 % and 66 %, respectively. Factor analysis had higher scores than Fourier analysis, but this was not significant. The interobserver error of factor analysis was less than that of Fourier analysis. Factor analysis can display locations and dynamic motion curves of asynergy, and it is regarded as a useful method for detecting and evaluating left ventricular wall motion abnormalities. (author)

18. Generalized formulation of an encryption system based on a joint transform correlator and fractional Fourier transform

International Nuclear Information System (INIS)

Vilardy, Juan M; Millán, María S; Pérez-Cabré, Elisabet; Torres, Yezid

2014-01-01

We propose a generalization of the encryption system based on double random phase encoding (DRPE) and a joint transform correlator (JTC), from the Fourier domain to the fractional Fourier domain (FrFD) by using the fractional Fourier operators, such as the fractional Fourier transform (FrFT), fractional traslation, fractional convolution and fractional correlation. Image encryption systems based on a JTC architecture in the FrFD usually produce low quality decrypted images. In this work, we present two approaches to improve the quality of the decrypted images, which are based on nonlinear processing applied to the encrypted function (that contains the joint fractional power spectrum, JFPS) and the nonzero-order JTC in the FrFD. When the two approaches are combined, the quality of the decrypted image is higher. In addition to the advantages introduced by the implementation of the DRPE using a JTC, we demonstrate that the proposed encryption system in the FrFD preserves the shift-invariance property of the JTC-based encryption system in the Fourier domain, with respect to the lateral displacement of both the key random mask in the decryption process and the retrieval of the primary image. The feasibility of this encryption system is verified and analyzed by computer simulations. (paper)

19. Fourier transforms in the complex domain

CERN Document Server

Wiener, N

1934-01-01

With the aid of Fourier-Mellin transforms as a tool in analysis, the authors were able to attack such diverse analytic questions as those of quasi-analytic functions, Mercer's theorem on summability, Milne's integral equation of radiative equilibrium, the theorems of MÃ¼nz and SzÃ¡sz concerning the closure of sets of powers of an argument, Titchmarsh's theory of entire functions of semi-exponential type with real negative zeros, trigonometric interpolation and developments in polynomials of the form \\sum^N_1A_ne^{i\\lambda_nx}, lacunary series, generalized harmonic analysis in the complex domain,

20. Analog fourier transform channelizer and OFDM receiver

OpenAIRE

2007-01-01

An OFDM receiver having an analog multiplier based I-Q channelizing filter, samples and holds consecutive analog I-Q samples of an I-Q baseband, the I-Q basebands having OFDM sub-channels. A lattice of analog I-Q multipliers and analog I-Q summers concurrently receives the held analog I-Q samples, performs analog I-Q multiplications and analog I-Q additions to concurrently generate a plurality of analog I-Q output signals, representing an N-point discrete Fourier transform of the held analog ...

1. Fourier-Mukai, 34 years on

Science.gov (United States)

Bruzzo, Ugo; Maciocia, Antony

2017-12-01

This special issue celebrates the 34 years since the discovery of the Fourier-Mukai Transform by Shigeru Mukai. It mostly contains papers presented at the conference held in the Mathematics Research Centre of the University of Warwick, 15th to 19th June 2015 as part of a year long Warwick symposium on Derived categories and applications. The conference was also the annual conference of the Vector Bundles on Algebraic Curves series led by Peter Newstead. The symposium was principally supported by the Engineering and Physical Sciences Research Council of the UK and there was further funding from the London Mathematical Society and the Foundation Compositio.

2. Noise figure of amplified dispersive Fourier transformation

International Nuclear Information System (INIS)

Goda, Keisuke; Jalali, Bahram

2010-01-01

Amplified dispersive Fourier transformation (ADFT) is a powerful tool for fast real-time spectroscopy as it overcomes the limitations of traditional optical spectrometers. ADFT maps the spectrum of an optical pulse into a temporal waveform using group-velocity dispersion and simultaneously amplifies it in the optical domain. It greatly simplifies spectroscopy by replacing the diffraction grating and detector array in the conventional spectrometer with a dispersive fiber and single-pixel photodetector, enabling ultrafast real-time spectroscopic measurements. Following our earlier work on the theory of ADFT, here we study the effect of noise on ADFT. We derive the noise figure of ADFT and discuss its dependence on various parameters.

3. Fourier transform infrared spectroscopy of peptides.

Science.gov (United States)

Bakshi, Kunal; Liyanage, Mangala R; Volkin, David B; Middaugh, C Russell

2014-01-01

Fourier transform infrared (FTIR) spectroscopy provides data that are widely used for secondary structure characterization of peptides. A wide array of available sampling methods permits structural analysis of peptides in diverse environments such as aqueous solution (including optically turbid media), powders, detergent micelles, and lipid bilayers. In some cases, side chain vibrations can also be resolved and used for tertiary structure and chemical analysis. Data from several low-resolution spectroscopic techniques, including FTIR, can be combined to generate an empirical phase diagram, an overall picture of peptide structure as a function of environmental conditions that can aid in the global interpretation of large amounts of spectroscopic data.

4. Complex nonlinear Fourier transform and its inverse

International Nuclear Information System (INIS)

Saksida, Pavle

2015-01-01

We study the nonlinear Fourier transform associated to the integrable systems of AKNS-ZS type. Two versions of this transform appear in connection with the AKNS-ZS systems. These two versions can be considered as two real forms of a single complex transform F c . We construct an explicit algorithm for the calculation of the inverse transform (F c ) -1 (h) for an arbitrary argument h. The result is given in the form of a convergent series of functions in the domain space and the terms of this series can be computed explicitly by means of finitely many integrations. (paper)

5. Functional Fourier transforms and the loop equation

International Nuclear Information System (INIS)

Bershadskii, M.A.; Vaisburd, I.D.; Migdal, A.A.

1986-01-01

The Migdal-Makeenko momentum-space loop equation is investigated. This equation is derived from the ordinary loop equation by taking the Fourier transform of the Wilson functional. A perturbation theory is constructed for the new equation and it is proved that the action of the loop operator is determined by vertex functions which coincide with those of the previous equation. It is shown how the ghost loop arises in direct iterations of the momentum-space equation with respect to the coupling constant. A simple example is used to illustrate the mechanism of appearance of an integration in the interior loops in transition to observables

6. Fourier transform spectroscopy of six stars

Energy Technology Data Exchange (ETDEWEB)

Mendoza V, E E [Universidad Nacional Autonoma de Mexico, Mexico City. Inst. de Astronomia

1981-01-01

This paper outlines results from a digital analysis of the Fourier transform spectroscopy of six stars: ..sigma.. Aur, rho Ori, ..cap alpha.. Lyr, zeta Aql and ..cap alpha.. Cyg. Nearly 1200 different spectral lines have been identified in the spectra of these six stars in the wavelength interval 4800-10200 A where the spectra are of very high quality, less than the one per cent level of noise versus signal. ..cap alpha.. Lyr and ..cap alpha.. Cyg show spectral line and profile variations easily seen in their spectra.

7. Generalized Fourier transforms Fk,a

DEFF Research Database (Denmark)

Salem, Ben Said; Kobayashi, Toshiyuki; Ørsted, Bent

2009-01-01

We construct a two-parameter family of actions ωk,a of the Lie algebra by differential-difference operators on . Here, k is a multiplicity-function for the Dunkl operators, and a>0 arises from the interpolation of the Weil representation and the minimal unitary representation of the conformal gro...... of our semigroup Ωk,a provides us with (k,a) -generalized Fourier transforms , which includes the Dunkl transform ( a=2 ) and a new unitary operator ( a=1 ) as a Dunkl-type generalization of the classical Hankel transform....

8. Fourier-transforming with quantum annealers

Directory of Open Access Journals (Sweden)

Itay eHen

2014-07-01

Full Text Available We introduce a set of quantum adiabatic evolutions that we argue may be used as building blocks', or subroutines, in the onstruction of an adiabatic algorithm that executes Quantum Fourier Transform (QFT with the same complexity and resources as its gate-model counterpart. One implication of the above construction is the theoretical feasibility of implementing Shor's algorithm for integer factorization in an optimal manner, and any other algorithm that makes use of QFT, on quantum annealing devices. We discuss the possible advantages, as well as the limitations, of the proposed approach as well as its relation to traditional adiabatic quantum computation.

9. The Fourier transform of tubular densities

KAUST Repository

Prior, C B

2012-05-18

We consider the Fourier transform of tubular volume densities, with arbitrary axial geometry and (possibly) twisted internal structure. This density can be used to represent, among others, magnetic flux or the electron density of biopolymer molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one for which the radius of the tube is less than the curvature of the axis and one for which the radius is greater (which must have density overlap). This expression can accommodate an asymmetric density distribution and a tube structure which has non-uniform twisting. In addition we give several simpler expressions for isotropic densities, densities of finite radius, densities which decay at a rate sufficient to minimize local overlap and finally individual surfaces of the tube manifold. These simplified cases can often be expressed as arclength integrals and can be evaluated using a system of first-order ODEs. © 2012 IOP Publishing Ltd.

10. Fourier transform ion cyclotron resonance mass spectrometry

Science.gov (United States)

Marshall, Alan G.

1998-06-01

As for Fourier transform infrared (FT-IR) interferometry and nuclear magnetic resonance (NMR) spectroscopy, the introduction of pulsed Fourier transform techniques revolutionized ion cyclotron resonance mass spectrometry: increased speed (factor of 10,000), increased sensitivity (factor of 100), increased mass resolution (factor of 10,000-an improvement not shared by the introduction of FT techniques to IR or NMR spectroscopy), increased mass range (factor of 500), and automated operation. FT-ICR mass spectrometry is the most versatile technique for unscrambling and quantifying ion-molecule reaction kinetics and equilibria in the absence of solvent (i.e., the gas phase). In addition, FT-ICR MS has the following analytically important features: speed (~1 second per spectrum); ultrahigh mass resolution and ultrahigh mass accuracy for analysis of mixtures and polymers; attomole sensitivity; MSn with one spectrometer, including two-dimensional FT/FT-ICR/MS; positive and/or negative ions; multiple ion sources (especially MALDI and electrospray); biomolecular molecular weight and sequencing; LC/MS; and single-molecule detection up to 108 Dalton. Here, some basic features and recent developments of FT-ICR mass spectrometry are reviewed, with applications ranging from crude oil to molecular biology.

11. Approximate modal analysis using Fourier decomposition

International Nuclear Information System (INIS)

Kozar, Ivica; Jericevic, Zeljko; Pecak, Tatjana

2010-01-01

The paper presents a novel numerical approach for approximate solution of eigenvalue problem and investigates its suitability for modal analysis of structures with special attention on plate structures. The approach is based on Fourier transformation of the matrix equation into frequency domain and subsequent removal of potentially less significant frequencies. The procedure results in a much reduced problem that is used in eigenvalue calculation. After calculation eigenvectors are expanded and transformed back into time domain. The principles are presented in Jericevic [1]. Fourier transform can be formulated in a way that some parts of the matrix that should not be approximated are not transformed but are fully preserved. In this paper we present formulation that preserves central or edge parts of the matrix and compare it with the formulation that performs transform on the whole matrix. Numerical experiments on transformed structural dynamic matrices describe quality of the approximations obtained in modal analysis of structures. On the basis of the numerical experiments, from the three approaches to matrix reduction one is recommended.

12. The Fourier transform of tubular densities

International Nuclear Information System (INIS)

Prior, C B; Goriely, A

2012-01-01

We consider the Fourier transform of tubular volume densities, with arbitrary axial geometry and (possibly) twisted internal structure. This density can be used to represent, among others, magnetic flux or the electron density of biopolymer molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one for which the radius of the tube is less than the curvature of the axis and one for which the radius is greater (which must have density overlap). This expression can accommodate an asymmetric density distribution and a tube structure which has non-uniform twisting. In addition we give several simpler expressions for isotropic densities, densities of finite radius, densities which decay at a rate sufficient to minimize local overlap and finally individual surfaces of the tube manifold. These simplified cases can often be expressed as arclength integrals and can be evaluated using a system of first-order ODEs. (paper)

13. Fourier transform zero field NMR and NQR

International Nuclear Information System (INIS)

Zax, D.B.

1985-01-01

In many systems the chemical shifts measured by traditional high resolution solid state NMR methods are insufficiently sensitive, or the information contained in the dipole-dipole couplings is more important. In these cases, Fourier transform zero field magnetic resonance may make an important contribution. Zero field NMR and NQR is the subject of this thesis. Chapter I presents the quantum mechanical background and notational formalism for what follows. Chapter II gives a brief review of high resolution magnetic resonance methods, with particular emphasis on techniques applicable to dipole-dipole and quadrupolar couplings. Level crossings between spin-1/2 and quadrupolar spins during demagnetization transfer polarization from high to low λ nuclei. This is the basis of very high sensitivity zero field NQR measurements by field cycling. Chapter III provides a formal presentation of the high resolution Fourier transform zero field NMR method. Theoretical signal functions are calculated for common spin systems, and examples of typical spectra are presented. Chapters IV and V review the experimental progress in zero field NMR of dipole-dipole coupled spin-1/2 nuclei and for quadrupolar spin systems. Variations of the simple experiment describe in earlier chapters that use pulsed dc fields are presented in Chapter VI

14. Resolution optimization with irregularly sampled Fourier data

International Nuclear Information System (INIS)

Ferrara, Matthew; Parker, Jason T; Cheney, Margaret

2013-01-01

Image acquisition systems such as synthetic aperture radar (SAR) and magnetic resonance imaging often measure irregularly spaced Fourier samples of the desired image. In this paper we show the relationship between sample locations, their associated backprojection weights, and image resolution as characterized by the resulting point spread function (PSF). Two new methods for computing data weights, based on different optimization criteria, are proposed. The first method, which solves a maximal-eigenvector problem, optimizes a PSF-derived resolution metric which is shown to be equivalent to the volume of the Cramer–Rao (positional) error ellipsoid in the uniform-weight case. The second approach utilizes as its performance metric the Frobenius error between the PSF operator and the ideal delta function, and is an extension of a previously reported algorithm. Our proposed extension appropriately regularizes the weight estimates in the presence of noisy data and eliminates the superfluous issue of image discretization in the choice of data weights. The Frobenius-error approach results in a Tikhonov-regularized inverse problem whose Tikhonov weights are dependent on the locations of the Fourier data as well as the noise variance. The two new methods are compared against several state-of-the-art weighting strategies for synthetic multistatic point-scatterer data, as well as an ‘interrupted SAR’ dataset representative of in-band interference commonly encountered in very high frequency radar applications. (paper)

15. Fourier transform spectra of quantum dots

Science.gov (United States)

Damian, V.; Ardelean, I.; Armăşelu, Anca; Apostol, D.

2010-05-01

Semiconductor quantum dots are nanometer-sized crystals with unique photochemical and photophysical properties that are not available from either isolated molecules or bulk solids. These nanocrystals absorb light over a very broad spectral range as compared to molecular fluorophores which have very narrow excitation spectra. High-quality QDs are proper to be use in different biological and medical applications (as fluorescent labels, the cancer treatment and the drug delivery). In this article, we discuss Fourier transform visible spectroscopy of commercial quantum dots. We reveal that QDs produced by Evident Technologies when are enlightened by laser or luminescent diode light provides a spectral shift of their fluorescence spectra correlated to exciting emission wavelengths, as shown by the ARCspectroNIR Fourier Transform Spectrometer. In the final part of this paper we show an important biological application of CdSe/ZnS core-shell ODs as microbial labeling both for pure cultures of cyanobacteria (Synechocystis PCC 6803) and for mixed cultures of phototrophic and heterotrophic microorganisms.

16. On localization for double Fourier series

Science.gov (United States)

Goffman, Casper; Waterman, Daniel

1978-01-01

The localization theorems for Fourier series of functions of a single variable are classical and easy to prove. The situation is different for Fourier series of functions of several variables, even if one restricts consideration to rectangular, in particular square, partial sums. We show that the answer to the problem can be obtained by considering the notion of generalized bounded variation, which we introduced. Given a nondecreasing sequence {λn} of positive numbers such that Σ 1/λn diverges, a function g defined on an interval I of R1 is said to be of Λ-bounded variation (ΛBV) if Σ|g(an) — g(bn)|/λn converges for every sequence of nonoverlapping intervals (an, bn) [unk]I. If λn = n, we say that g is of harmonic bounded variation (HBV). The definition suitably modified can be extended to functions of several variables. We show that in the case of two variables the localization principle holds for rectangular partial sums if ΛBV = HBV, and that if ΛBV is not contained in HBV, then the localization principle does not hold for ΛBV even in the case of square partial sums. PMID:16592492

17. Digital Fourier microscopy for soft matter dynamics

International Nuclear Information System (INIS)

Giavazzi, Fabio; Cerbino, Roberto

2014-01-01

Soft matter is studied with a large portfolio of methods. Light scattering and video microscopy are the most employed at optical wavelengths. Light scattering provides ensemble-averaged information on soft matter in the reciprocal space. The wave-vectors probed correspond to length scales ranging from a few nanometers to fractions of millimetre. Microscopy probes the sample directly in the real space, by offering a unique access to the local properties. However, optical resolution issues limit the access to length scales smaller than approximately 200 nm. We describe recent work that bridges the gap between scattering and microscopy. Several apparently unrelated techniques are found to share a simple basic idea: the correlation properties of the sample can be characterized in the reciprocal space via spatial Fourier analysis of images collected in the real space. We describe the main features of such digital Fourier microscopy (DFM), by providing examples of several possible experimental implementations of it, some of which not yet realized in practice. We also provide an overview of experimental results obtained with DFM for the study of the dynamics of soft materials. Finally, we outline possible future developments of DFM that would ease its adoption as a standard laboratory method. (topical review)

18. Does the entorhinal cortex use the Fourier transform?

Science.gov (United States)

Orchard, Jeff; Yang, Hao; Ji, Xiang

2013-01-01

Some neurons in the entorhinal cortex (EC) fire bursts when the animal occupies locations organized in a hexagonal grid pattern in their spatial environment. Place cells have also been observed, firing bursts only when the animal occupies a particular region of the environment. Both of these types of cells exhibit theta-cycle modulation, firing bursts in the 4–12 Hz range. Grid cells fire bursts of action potentials that precess with respect to the theta cycle, a phenomenon dubbed “theta precession.” Various models have been proposed to explain these phenomena, and how they relate to navigation. Among the most promising are the oscillator interference models. The bank-of-oscillators model proposed by Welday et al. (2011) exhibits all these features. However, their simulations are based on theoretical oscillators, and not implemented entirely with spiking neurons. We extend their work in a number of ways. First, we place the oscillators in a frequency domain and reformulate the model in terms of Fourier theory. Second, this perspective suggests a division of labor for implementing spatial maps: position vs. map layout. The animal's position is encoded in the phases of the oscillators, while the spatial map shape is encoded implicitly in the weights of the connections between the oscillators and the read-out nodes. Third, it reveals that the oscillator phases all need to conform to a linear relationship across the frequency domain. Fourth, we implement a partial model of the EC using spiking leaky integrate-and-fire (LIF) neurons. Fifth, we devise new coupling mechanisms, enlightened by the global phase constraint, and show they are capable of keeping spiking neural oscillators in consistent formation. Our model demonstrates place cells, grid cells, and phase precession. The Fourier model also gives direction for future investigations, such as integrating sensory feedback to combat drift, or explaining why grid cells exist at all. PMID:24376415

19. An improved acoustic Fourier boundary element method formulation using fast Fourier transform integration

NARCIS (Netherlands)

Kuijpers, A.H.W.M.; Verbeek, G.; Verheij, J.W.

1997-01-01

Effective use of the Fourier series boundary element method (FBEM) for everyday applications is hindered by the significant numerical problems that have to be overcome for its implementation. In the FBEM formulation for acoustics, some integrals over the angle of revolution arise, which need to be

20. Fourier power spectrum characteristics of face photographs: attractiveness perception depends on low-level image properties.

Science.gov (United States)

Menzel, Claudia; Hayn-Leichsenring, Gregor U; Langner, Oliver; Wiese, Holger; Redies, Christoph

2015-01-01

We investigated whether low-level processed image properties that are shared by natural scenes and artworks - but not veridical face photographs - affect the perception of facial attractiveness and age. Specifically, we considered the slope of the radially averaged Fourier power spectrum in a log-log plot. This slope is a measure of the distribution of special frequency power in an image. Images of natural scenes and artworks possess - compared to face images - a relatively shallow slope (i.e., increased high spatial frequency power). Since aesthetic perception might be based on the efficient processing of images with natural scene statistics, we assumed that the perception of facial attractiveness might also be affected by these properties. We calculated Fourier slope and other beauty-associated measurements in face images and correlated them with ratings of attractiveness and age of the depicted persons (Study 1). We found that Fourier slope - in contrast to the other tested image properties - did not predict attractiveness ratings when we controlled for age. In Study 2A, we overlaid face images with random-phase patterns with different statistics. Patterns with a slope similar to those in natural scenes and artworks resulted in lower attractiveness and higher age ratings. In Studies 2B and 2C, we directly manipulated the Fourier slope of face images and found that images with shallower slopes were rated as more attractive. Additionally, attractiveness of unaltered faces was affected by the Fourier slope of a random-phase background (Study 3). Faces in front of backgrounds with statistics similar to natural scenes and faces were rated as more attractive. We conclude that facial attractiveness ratings are affected by specific image properties. An explanation might be the efficient coding hypothesis.

1. Application of Fractional Fourier Transform to Moving Target Indication via Along-Track Interferometry

Directory of Open Access Journals (Sweden)

Chiu Shen

2005-01-01

Full Text Available A relatively unknown yet powerful technique, the so-called fractional Fourier transform (FrFT, is applied to SAR along-track interferometry (SAR-ATI in order to estimate moving target parameters. By mapping a target's signal onto a fractional Fourier axis, the FrFT permits a constant-velocity target to be focused in the fractional Fourier domain thereby affording orders of magnitude improvement in SCR. Moving target velocity and position parameters are derived and expressed in terms of an optimum fractional angle and a measured fractional Fourier position , allowing a target to be accurately repositioned and its velocity components computed without actually forming an SAR image. The new estimation algorithm is compared with the matched filter bank approach, showing some of the advantages of the FrFT method. The proposed technique is applied to the data acquired by the two-aperture CV580 airborne radar system configured in its along-track mode. Results show that the method is effective in estimating target velocity and position parameters.

2. On the Application of the Fourier Series Solution to the Hydromagnetic Buoyant Two-Dimensional Laminar Vertical Jet

Directory of Open Access Journals (Sweden)

Marco Rosales-Vera

2012-01-01

Full Text Available The problem of a hydromagnetic hot two-dimensional laminar jet issuing vertically into an otherwise quiescent fluid of a lower temperature is studied. We propose solutions to the boundary layer equations using the classical Fourier series. The method is essentiall to transform the boundary layer equations to a coupled set of nonlinear first-order ordinary differential equations through the Fourier series. The accuracy of the results has been tested by the comparison of the velocity distributions obtained by the Fourier series with those calculated by finite difference method. The results show that the present method, based on the Fourier series, is an efficient method, suitable to solve boundary layer equations applied to plane jet flows with high accuracy.

3. Validation of measurements of Fourier phase and amplitude analysis of technetium99 gated cardiac scans using artificial hearts

International Nuclear Information System (INIS)

Yiannikas, J.; Takatani, S.; MacIntyre, W.J.; Underwood, D.A.; Cook, S.A.; Go, R.T.; Napoli, C.; Nose, Y.

1982-01-01

The use of artificial hearts, developed for total heart replacement programs, allows assessment of the accuracy of measuring the first Fourier component phase and amplitude when applied to gated cardiac technetium 99 scans. In the extreme example of asynchrony of ventricular contraction in coronary artery disease that of ventricular aneurysms, the first Fourier component measurements of amplitude were highly correlated to volume increases suggesting that the calculated amplitude accurately reflects volume changes. The calculated asynchrony using Fourier analysis of the gated technetium 99 studies of two artificial hearts was highly accurate when compared to the predetermined calculation of phase angle difference and hence degree of asynchrony. The studies suggest that measurement of phase and amplitude using the first Fourier component of time-activity waves of gated cardiac technetium 99 studies accurately measure degree of asynchrony and volume changes respectively

4. Correlation in the statistical analysis of a reverse Fourier neutron time-of-flight experiment. Pt. 2

International Nuclear Information System (INIS)

Tilli, K.J.

1982-01-01

The significance of the correlation in the statistical analysis of reverse Fourier neutron time-of-flight observations has been evaluated by applying different methods of estimation to diffraction patterns containing peaks with Gaussian line shapes. Effects of the correlation between adjacent channels of a spectrum arise both from the incorrect weighting of the experiment's independent variables and from the misinterpretation of the number of independent observations in the data. The incorrect weighting bears the greatest effects on the width parameter of a Gaussian profile, and it leads to an increase in the relative weights of the broadest peaks of the diffraction pattern. If the correlation is ignored in the analysis, the estimates obtained for the parameters of a model will not be exactly the same as those evaluated from the minimum variance estimation, in which the correlation is taken into account. However, the differences will not be statistically significant. Nevertheless, the standard deviations will then be underestimated typically by a factor of two, which will have serious consequences on every aspect of the statistical inference. (orig.)

5. Applied physics

International Nuclear Information System (INIS)

Anon.

1980-01-01

The Physics Division research program that is dedicated primarily to applied research goals involves the interaction of energetic particles with solids. This applied research is carried out in conjunction with the basic research studies from which it evolved

6. Fourier correction for spatially variant collimator blurring in SPECT

International Nuclear Information System (INIS)

Xia, W.; Lewitt, R.M.; Edholm, P.R.

1995-01-01

In single-photon emission computed tomography (SPECT), projection data are acquired by rotating the photon detector around a patient, either in a circular orbit or in a noncircular orbit. The projection data of the desired spatial distribution of emission activity is blurred by the point-response function of the collimator that is used to define the range of directions of gamma-ray photons reaching the detector. The point-response function of the collimator is not spatially stationary, but depends on the distance from the collimator to the point. Conventional methods for deblurring collimator projection data are based on approximating the actual distance-dependent point-response function by a spatially invariant blurring function, so that deconvolution methods can be applied independently to the data at each angle of view. A method is described in this paper for distance-dependent preprocessing of SPECT projection data prior to image reconstruction. Based on the special distance-dependent characteristics of the Fourier coefficients of the sinogram, a spatially variant inverse filter can be developed to process the projection data in all views simultaneously. The algorithm is first derived from fourier analysis of the projection data from the circular orbit geometry. For circular orbit projection data, experimental results from both simulated data and real phantom data indicate the potential of this method. It is shown that the spatial filtering method can be extended to the projection data from the noncircular orbit geometry. Experiments on simulated projection data from an elliptical orbit demonstrate correction of the spatially variant blurring and distortion in the reconstructed image caused by the noncircular orbit geometry

7. Subwavelength resolution Fourier ptychography with hemispherical digital condensers

Science.gov (United States)

Pan, An; Zhang, Yan; Li, Maosen; Zhou, Meiling; Lei, Ming; Yao, Baoli

2018-02-01

Fourier ptychography (FP) is a promising computational imaging technique that overcomes the physical space-bandwidth product (SBP) limit of a conventional microscope by applying angular diversity illuminations. However, to date, the effective imaging numerical aperture (NA) achievable with a commercial LED board is still limited to the range of 0.3-0.7 with a 4×/0.1NA objective due to the constraint of planar geometry with weak illumination brightness and attenuated signal-to-noise ratio (SNR). Thus the highest achievable half-pitch resolution is usually constrained between 500-1000 nm, which cannot fulfill some needs of high-resolution biomedical imaging applications. Although it is possible to improve the resolution by using a higher magnification objective with larger NA instead of enlarging the illumination NA, the SBP is suppressed to some extent, making the FP technique less appealing, since the reduction of field-of-view (FOV) is much larger than the improvement of resolution in this FP platform. Herein, in this paper, we initially present a subwavelength resolution Fourier ptychography (SRFP) platform with a hemispherical digital condenser to provide high-angle programmable plane-wave illuminations of 0.95NA, attaining a 4×/0.1NA objective with the final effective imaging performance of 1.05NA at a half-pitch resolution of 244 nm with a wavelength of 465 nm across a wide FOV of 14.60 mm2 , corresponding to an SBP of 245 megapixels. Our work provides an essential step of FP towards high-NA imaging applications without scarfing the FOV, making it more practical and appealing.

8. Fourier transform and its application to 1D and 2D NMR

International Nuclear Information System (INIS)

Canet, D.

1988-01-01

In this review article, the following points are developed: Pulsed NMR and Fourier transform; Fourier transform and two-dimensional spectroscopy; Mathematical properties of Fourier transform; Fourier transform of a sine function- one dimensional NMR; Fourier transform of a product of sine functions - two-dimensional NMR; Data manipulations in the time domain; Numerical Fourier transform [fr

9. Fourier rebinning algorithm for inverse geometry CT.

Science.gov (United States)

Mazin, Samuel R; Pele, Norbert J

2008-11-01

Inverse geometry computed tomography (IGCT) is a new type of volumetric CT geometry that employs a large array of x-ray sources opposite a smaller detector array. Volumetric coverage and high isotropic resolution produce very large data sets and therefore require a computationally efficient three-dimensional reconstruction algorithm. The purpose of this work was to adapt and evaluate a fast algorithm based on Defrise's Fourier rebinning (FORE), originally developed for positron emission tomography. The results were compared with the average of FDK reconstructions from each source row. The FORE algorithm is an order of magnitude faster than the FDK-type method for the case of 11 source rows. In the center of the field-of-view both algorithms exhibited the same resolution and noise performance. FORE exhibited some resolution loss (and less noise) in the periphery of the field-of-view. FORE appears to be a fast and reasonably accurate reconstruction method for IGCT.

10. Multicomplementary operators via finite Fourier transform

International Nuclear Information System (INIS)

Klimov, Andrei B; Sanchez-Soto, Luis L; Guise, Hubert de

2005-01-01

A complete set of d + 1 mutually unbiased bases exists in a Hilbert space of dimension d, whenever d is a power of a prime. We discuss a simple construction of d + 1 disjoint classes (each one having d - 1 commuting operators) such that the corresponding eigenstates form sets of unbiased bases. Such a construction works properly for prime dimension. We investigate an alternative construction in which the real numbers that label the classes are replaced by a finite field having d elements. One of these classes is diagonal, and can be mapped to cyclic operators by means of the finite Fourier transform, which allows one to understand complementarity in a similar way as for the position-momentum pair in standard quantum mechanics. The relevant examples of two and three qubits and two qutrits are discussed in detail

11. Fractional Fourier transform for confluent hypergeometric beams

International Nuclear Information System (INIS)

Tang, Bin; Jiang, Chun; Zhu, Haibin

2012-01-01

Based on the definition of the fractional Fourier transform (FRFT) in the cylindrical coordinate system, the propagation properties of a new family of paraxial laser beams named confluent hypergeometric (HyG) beams, of which intensity profile is similar to that for the Bessel modes, passing through FRFT optical systems have been studied in detail by some typical numerical examples. The results indicate that the normalized intensity distribution of a HyG beam in the FRFT plane is closely related to not only the fractional order p but also the beam parameters m,n, and focal length f. -- Highlights: ► We study the propagation of a HyG beam through FRFT optical systems. ► The intensity of the beam in the FRFT plane is closely related to some parameters. ► We can control the properties of HyG beams by properly choosing the parameters.

12. Rotational Fourier tracking of diffusing polygons.

Science.gov (United States)

Mayoral, Kenny; Kennair, Terry P; Zhu, Xiaoming; Milazzo, James; Ngo, Kathy; Fryd, Michael M; Mason, Thomas G

2011-11-01

We use optical microscopy to measure the rotational Brownian motion of polygonal platelets that are dispersed in a liquid and confined by depletion attractions near a wall. The depletion attraction inhibits out-of-plane translational and rotational Brownian fluctuations, thereby facilitating in-plane imaging and video analysis. By taking fast Fourier transforms (FFTs) of the images and analyzing the angular position of rays in the FFTs, we determine an isolated particle's rotational trajectory, independent of its position. The measured in-plane rotational diffusion coefficients are significantly smaller than estimates for the bulk; this difference is likely due to the close proximity of the particles to the wall arising from the depletion attraction.

13. Two-dimensional fourier transform spectrometer

Science.gov (United States)

DeFlores, Lauren; Tokmakoff, Andrei

2013-09-03

The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.

14. Regularized Laplace-Fourier-Domain Full Waveform Inversion Using a Weighted l 2 Objective Function

Science.gov (United States)

Jun, Hyunggu; Kwon, Jungmin; Shin, Changsoo; Zhou, Hongbo; Cogan, Mike

2017-03-01

Full waveform inversion (FWI) can be applied to obtain an accurate velocity model that contains important geophysical and geological information. FWI suffers from the local minimum problem when the starting model is not sufficiently close to the true model. Therefore, an accurate macroscale velocity model is essential for successful FWI, and Laplace-Fourier-domain FWI is appropriate for obtaining such a velocity model. However, conventional Laplace-Fourier-domain FWI remains an ill-posed and ill-conditioned problem, meaning that small errors in the data can result in large differences in the inverted model. This approach also suffers from certain limitations related to the logarithmic objective function. To overcome the limitations of conventional Laplace-Fourier-domain FWI, we introduce a weighted l 2 objective function, instead of the logarithmic objective function, as the data-domain objective function, and we also introduce two different model-domain regularizations: first-order Tikhonov regularization and prior model regularization. The weighting matrix for the data-domain objective function is constructed to suitably enhance the far-offset information. Tikhonov regularization smoothes the gradient, and prior model regularization allows reliable prior information to be taken into account. Two hyperparameters are obtained through trial and error and used to control the trade-off and achieve an appropriate balance between the data-domain and model-domain gradients. The application of the proposed regularizations facilitates finding a unique solution via FWI, and the weighted l 2 objective function ensures a more reasonable residual, thereby improving the stability of the gradient calculation. Numerical tests performed using the Marmousi synthetic dataset show that the use of the weighted l 2 objective function and the model-domain regularizations significantly improves the Laplace-Fourier-domain FWI. Because the Laplace-Fourier-domain FWI is improved, the

15. On a General Class of Trigonometric Functions and Fourier Series

Science.gov (United States)

Pavao, H. Germano; Capelas de Oliveira, E.

2008-01-01

We discuss a general class of trigonometric functions whose corresponding Fourier series can be used to calculate several interesting numerical series. Particular cases are presented. (Contains 4 notes.)

16. Reducing Approximation Error in the Fourier Flexible Functional Form

Directory of Open Access Journals (Sweden)

Tristan D. Skolrud

2017-12-01

Full Text Available The Fourier Flexible form provides a global approximation to an unknown data generating process. In terms of limiting function specification error, this form is preferable to functional forms based on second-order Taylor series expansions. The Fourier Flexible form is a truncated Fourier series expansion appended to a second-order expansion in logarithms. By replacing the logarithmic expansion with a Box-Cox transformation, we show that the Fourier Flexible form can reduce approximation error by 25% on average in the tails of the data distribution. The new functional form allows for nested testing of a larger set of commonly implemented functional forms.

17. Generalized Fourier slice theorem for cone-beam image reconstruction.

Science.gov (United States)

Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang

2015-01-01

The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is O(N^4), which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).

18. Applied architecture patterns on the Microsoft platform

CERN Document Server

Dovgal, Andre; Noriskin, Gregor

2014-01-01

Presented in a scenario-driven tutorial way, we lead you through fictitious example problems and present you with the best solutions. This book is intended for architects, developers, and managers who need to improve their knowledge of the Microsoft application platform. This book will appeal to anyone, especially consultants, who want to get up to speed on selecting the most appropriate platform for a particular problem. A good understanding of the general Windows platform and development technologies would be helpful.

19. The Fractional Fourier Transform and Its Application to Energy Localization Problems

Directory of Open Access Journals (Sweden)

ter Morsche Hennie G

2003-01-01

Full Text Available Applying the fractional Fourier transform (FRFT and the Wigner distribution on a signal in a cascade fashion is equivalent to a rotation of the time and frequency parameters of the Wigner distribution. We presented in ter Morsche and Oonincx, 2002, an integral representation formula that yields affine transformations on the spatial and frequency parameters of the -dimensional Wigner distribution if it is applied on a signal with the Wigner distribution as for the FRFT. In this paper, we show how this representation formula can be used to solve certain energy localization problems in phase space. Examples of such problems are given by means of some classical results. Although the results on localization problems are classical, the application of generalized Fourier transform enlarges the class of problems that can be solved with traditional techniques.

20. Multivariate Calibration and Model Integrity for Wood Chemistry Using Fourier Transform Infrared Spectroscopy

OpenAIRE

Zhou, Chengfeng; Jiang, Wei; Cheng, Qingzheng; Via, Brian K.

2015-01-01

This research addressed a rapid method to monitor hardwood chemical composition by applying Fourier transform infrared (FT-IR) spectroscopy, with particular interest in model performance for interpretation and prediction. Partial least squares (PLS) and principal components regression (PCR) were chosen as the primary models for comparison. Standard laboratory chemistry methods were employed on a mixed genus/species hardwood sample set to collect the original data. PLS was found to provide bet...

1. Scaled nonuniform Fourier transform for image reconstruction in swept source optical coherence tomography

Science.gov (United States)

Mezgebo, Biniyam; Nagib, Karim; Fernando, Namal; Kordi, Behzad; Sherif, Sherif

2018-02-01

Swept Source optical coherence tomography (SS-OCT) is an important imaging modality for both medical and industrial diagnostic applications. A cross-sectional SS-OCT image is obtained by applying an inverse discrete Fourier transform (DFT) to axial interferograms measured in the frequency domain (k-space). This inverse DFT is typically implemented as a fast Fourier transform (FFT) that requires the data samples to be equidistant in k-space. As the frequency of light produced by a typical wavelength-swept laser is nonlinear in time, the recorded interferogram samples will not be uniformly spaced in k-space. Many image reconstruction methods have been proposed to overcome this problem. Most such methods rely on oversampling the measured interferogram then use either hardware, e.g., Mach-Zhender interferometer as a frequency clock module, or software, e.g., interpolation in k-space, to obtain equally spaced samples that are suitable for the FFT. To overcome the problem of nonuniform sampling in k-space without any need for interferogram oversampling, an earlier method demonstrated the use of the nonuniform discrete Fourier transform (NDFT) for image reconstruction in SS-OCT. In this paper, we present a more accurate method for SS-OCT image reconstruction from nonuniform samples in k-space using a scaled nonuniform Fourier transform. The result is demonstrated using SS-OCT images of Axolotl salamander eggs.

2. Modeling open nanophotonic systems using the Fourier modal method: generalization to 3D Cartesian coordinates.

Science.gov (United States)

Häyrynen, Teppo; Osterkryger, Andreas Dyhl; de Lasson, Jakob Rosenkrantz; Gregersen, Niels

2017-09-01

Recently, an open geometry Fourier modal method based on a new combination of an open boundary condition and a non-uniform k-space discretization was introduced for rotationally symmetric structures, providing a more efficient approach for modeling nanowires and micropillar cavities [J. Opt. Soc. Am. A33, 1298 (2016)JOAOD61084-752910.1364/JOSAA.33.001298]. Here, we generalize the approach to three-dimensional (3D) Cartesian coordinates, allowing for the modeling of rectangular geometries in open space. The open boundary condition is a consequence of having an infinite computational domain described using basis functions that expand the whole space. The strength of the method lies in discretizing the Fourier integrals using a non-uniform circular "dartboard" sampling of the Fourier k space. We show that our sampling technique leads to a more accurate description of the continuum of the radiation modes that leak out from the structure. We also compare our approach to conventional discretization with direct and inverse factorization rules commonly used in established Fourier modal methods. We apply our method to a variety of optical waveguide structures and demonstrate that the method leads to a significantly improved convergence, enabling more accurate and efficient modeling of open 3D nanophotonic structures.

3. Image/patient registration from (partial) projection data by the Fourier phase matching method

International Nuclear Information System (INIS)

Weiguo Lu; You, J.

1999-01-01

A technique for 2D or 3D image/patient registration, PFPM (projection based Fourier phase matching method), is proposed. This technique provides image/patient registration directly from sequential tomographic projection data. The method can also deal with image files by generating 2D Radon transforms slice by slice. The registration in projection space is done by calculating a Fourier invariant (FI) descriptor for each one-dimensional projection datum, and then registering the FI descriptor by the Fourier phase matching (FPM) method. The algorithm has been tested on both synthetic and experimental data. When dealing with translated, rotated and uniformly scaled 2D image registration, the performance of the PFPM method is comparable to that of the IFPM (image based Fourier phase matching) method in robustness, efficiency, insensitivity to the offset between images, and registration time. The advantages of the former are that subpixel resolution is feasible, and it is more insensitive to image noise due to the averaging effect of the projection acquisition. Furthermore, the PFPM method offers the ability to generalize to 3D image/patient registration and to register partial projection data. By applying patient registration directly from tomographic projection data, image reconstruction is not needed in the therapy set-up verification, thus reducing computational time and artefacts. In addition, real time registration is feasible. Registration from partial projection data meets the geometry and dose requirements in many application cases and makes dynamic set-up verification possible in tomotherapy. (author)

4. Transient Fourier holography with bacteriorhodopsin films for breast cancer diagnostics

Science.gov (United States)

Rao, Devulapalli; Kothapalli, Sri-Rajasekar; Wu, Pengfei; Yelleswarapu, Chandra

X-ray mammography is the current gold standard for breast cancer screening. Microcalcifications and other features which are helpful to the radiologist for early diagnostics are often buried in the noise generated by the surrounding dense tissue. So image processing techniques are required to enhance these important features to improve the sensitivity of detection. An innovative technique is demonstrated for recording a hologram of the mammogram. It is recorded on a thin polymer film of Bacteriorhodopsin (bR) as photo induced isomerization grating containing the interference pattern between the object beam containing the Fourier spatial frequency components of the mammogram and a reference beam. The hologram contains all the enhanced features of the mammogram. A significant innovation of the technique is that the enhanced components in the processed image can be viewed by the radiologist in time scale. A technician can record the movie and when the radiologist looks at the movie at his convenience, freezing the frame as and when desired, he would see the microcalcifications as the brightest and last long in time. He would also observe lesions with intensity decreasing as their size increases. The same bR film can be used repeatedly for recording holograms with different mammograms. The technique is versatile and a different frequency band can be chosen to be optimized by changing the reference beam intensity. The experimental arrangement can be used for mammograms in screen film or digital format.

5. Large Molecule Structures by Broadband Fourier Transform Molecular Rotational Spectroscopy

Science.gov (United States)

Evangelisti, Luca; Seifert, Nathan A.; Spada, Lorenzo; Pate, Brooks

2016-06-01

Fourier transform molecular rotational resonance spectroscopy (FT-MRR) using pulsed jet molecular beam sources is a high-resolution spectroscopy technique that can be used for chiral analysis of molecules with multiple chiral centers. The sensitivity of the molecular rotational spectrum pattern to small changes in the three dimensional structure makes it possible to identify diastereomers without prior chemical separation. For larger molecules, there is the additional challenge that different conformations of each diastereomer may be present and these need to be differentiated from the diastereomers in the spectral analysis. Broadband rotational spectra of several larger molecules have been measured using a chirped-pulse FT-MRR spectrometer. Measurements of nootkatone (C15H22O), cedrol (C15H26O), ambroxide (C16H28O) and sclareolide (C16H26O2) are presented. These spectra are measured with high sensitivity (signal-to-noise ratio near 1,000:1) and permit structure determination of the most populated isomers using isotopic analysis of the 13C and 18O isotopologues in natural abundance. The accuracy of quantum chemistry calculations to identify diastereomers and conformers and to predict the dipole moment properties needed for three wave mixing measurements is examined.

6. Introduction to the discrete Fourier series considering both mathematical and engineering aspects - A linear-algebra approach

Directory of Open Access Journals (Sweden)

Ludwig Kohaupt

2015-12-01

Full Text Available The discrete Fourier series is a valuable tool developed and used by mathematicians and engineers alike. One of the most prominent applications is signal processing. Usually, it is important that the signals be transmitted fast, for example, when transmitting images over large distances such as between the moon and the earth or when generating images in computer tomography. In order to achieve this, appropriate algorithms are necessary. In this context, the fast Fourier transform (FFT plays a key role which is an algorithm for calculating the discrete Fourier transform (DFT; this, in turn, is tightly connected with the discrete Fourier series. The last one itself is the discrete analog of the common (continuous-time Fourier series and is usually learned by mathematics students from a theoretical point of view. The aim of this expository/pedagogical paper is to give an introduction to the discrete Fourier series for both mathematics and engineering students. It is intended to expand the purely mathematical view; the engineering aspect is taken into account by applying the FFT to an example from signal processing that is small enough to be used in class-room teaching and elementary enough to be understood also by mathematics students. The MATLAB program is employed to do the computations.

7. Applied Electromagnetics

Energy Technology Data Exchange (ETDEWEB)

Yamashita, H; Marinova, I; Cingoski, V [eds.

2002-07-01

These proceedings contain papers relating to the 3rd Japanese-Bulgarian-Macedonian Joint Seminar on Applied Electromagnetics. Included are the following groups: Numerical Methods I; Electrical and Mechanical System Analysis and Simulations; Inverse Problems and Optimizations; Software Methodology; Numerical Methods II; Applied Electromagnetics.

8. Applied Electromagnetics

International Nuclear Information System (INIS)

Yamashita, H.; Marinova, I.; Cingoski, V.

2002-01-01

These proceedings contain papers relating to the 3rd Japanese-Bulgarian-Macedonian Joint Seminar on Applied Electromagnetics. Included are the following groups: Numerical Methods I; Electrical and Mechanical System Analysis and Simulations; Inverse Problems and Optimizations; Software Methodology; Numerical Methods II; Applied Electromagnetics

9. A method to identify differential expression profiles of time-course gene data with Fourier transformation.

Science.gov (United States)

Kim, Jaehee; Ogden, Robert Todd; Kim, Haseong

2013-10-18

Time course gene expression experiments are an increasingly popular method for exploring biological processes. Temporal gene expression profiles provide an important characterization of gene function, as biological systems are both developmental and dynamic. With such data it is possible to study gene expression changes over time and thereby to detect differential genes. Much of the early work on analyzing time series expression data relied on methods developed originally for static data and thus there is a need for improved methodology. Since time series expression is a temporal process, its unique features such as autocorrelation between successive points should be incorporated into the analysis. This work aims to identify genes that show different gene expression profiles across time. We propose a statistical procedure to discover gene groups with similar profiles using a nonparametric representation that accounts for the autocorrelation in the data. In particular, we first represent each profile in terms of a Fourier basis, and then we screen out genes that are not differentially expressed based on the Fourier coefficients. Finally, we cluster the remaining gene profiles using a model-based approach in the Fourier domain. We evaluate the screening results in terms of sensitivity, specificity, FDR and FNR, compare with the Gaussian process regression screening in a simulation study and illustrate the results by application to yeast cell-cycle microarray expression data with alpha-factor synchronization.The key elements of the proposed methodology: (i) representation of gene profiles in the Fourier domain; (ii) automatic screening of genes based on the Fourier coefficients and taking into account autocorrelation in the data, while controlling the false discovery rate (FDR); (iii) model-based clustering of the remaining gene profiles. Using this method, we identified a set of cell-cycle-regulated time-course yeast genes. The proposed method is general and can be

10. Real-time quantitative Schlieren imaging by fast Fourier demodulation of a checkered backdrop

Science.gov (United States)

Wildeman, Sander

2018-06-01

A quantitative synthetic Schlieren imaging (SSI) method based on fast Fourier demodulation is presented. Instead of a random dot pattern (as usually employed in SSI), a 2D periodic pattern (such as a checkerboard) is used as a backdrop to the refractive object of interest. The range of validity and accuracy of this "Fast Checkerboard Demodulation" (FCD) method are assessed using both synthetic data and experimental recordings of patterns optically distorted by small waves on a water surface. It is found that the FCD method is at least as accurate as sophisticated, multi-stage, digital image correlation (DIC) or optical flow (OF) techniques used with random dot patterns, and it is significantly faster. Efficient, fully vectorized, implementations of both the FCD and DIC/OF schemes developed for this study are made available as open source Matlab scripts.

11. Lacunary Fourier Series and a Qualitative Uncertainty Principle for ...

We define lacunary Fourier series on a compact connected semisimple Lie group . If f ∈ L 1 ( G ) has lacunary Fourier series and vanishes on a non empty open subset of , then we prove that vanishes identically. This result can be viewed as a qualitative uncertainty principle.

12. Bilaterally symmetric Fourier approximations of the skull outlines of ...

Present work illustrates a scheme of quantitative description of the shape of the skull outlines of temnospondyl amphibians using bilaterally symmetric closed Fourier curves. Some special points have been identified on the Fourier fits of the skull outlines, which are the local maxima, or minima of the distances from the ...

13. Fourier transformations for difference analogs of the harmonic oscillator

International Nuclear Information System (INIS)

1995-01-01

The relation between the Mehler bilinear generating function for the Hermite polynomials and the kernel of the Fourier transformation that connect the spaces of coordinate and momentum is discussed. On the base of the relation the discrete analogs of the Fourier transformation for the Kravchuk and Charlier functions are considered. 6 refs

14. The Fourier Transform for Certain HyperKähler Fourfolds

NARCIS (Netherlands)

Shen, M.; Vial, C.

2016-01-01

Using a codimension-1 algebraic cycle obtained from the Poincaré line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety A and showed that the Fourier transform induces a decomposition of the Chow ring CH∗(A). By using a codimension-2 algebraic cycle

15. Infrared Fourier spectres of pectin obtained from pumpkin

International Nuclear Information System (INIS)

Usmanova, S.R.; Dzhonmurodov, A.S.; Nazirova, Kh.I.; Mukhidinov, Z.K.

2015-01-01

Present article is devoted to infrared Fourier spectres of pectin obtained from pumpkin. The analysis of pectin obtained from pumpkin was conducted by means of infrared spectrophotometer with Fourier transformation. The infrared spectroscopic study of pectin polysaccharide fraction of pectin matter, as well as pectin helium and micro helium obtained by means of fast extraction was conducted.

16. Time-of-flight Fourier spectrometry of UCN

International Nuclear Information System (INIS)

Kulin, G.V.; Frank, A.I.; Goryunov, S.V.; Kustov, D.V.; Geltenbort, P.; Jentshel, M.; Strepetov, A.N.; Bushuev, V.A.

2014-01-01

The results of preliminary experiments on TOF Fourier UCN spectrometry are presented. The description of the new Fourier spectrometer that may be used for the measurement of the UCN spectra arising from diffraction by a moving grating is given. The results of preliminary experiments and Monte Carlo calculations give reason to hope for the success of the planned experiment.

17. Fourier path-integral Monte Carlo methods: Partial averaging

International Nuclear Information System (INIS)

Doll, J.D.; Coalson, R.D.; Freeman, D.L.

1985-01-01

Monte Carlo Fourier path-integral techniques are explored. It is shown that fluctuation renormalization techniques provide an effective means for treating the effects of high-order Fourier contributions. The resulting formalism is rapidly convergent, is computationally convenient, and has potentially useful variational aspects

18. Exploring Fourier Series and Gibbs Phenomenon Using Mathematica

Science.gov (United States)

Ghosh, Jonaki B.

2011-01-01

This article describes a laboratory module on Fourier series and Gibbs phenomenon which was undertaken by 32 Year 12 students. It shows how the use of CAS played the role of an "amplifier" by making higher level mathematical concepts accessible to students of year 12. Using Mathematica students were able to visualise Fourier series of…

19. Fourier transform in multimode systems in the Bargmann representation

International Nuclear Information System (INIS)

Lei, C; Vourdas, A

2007-01-01

A Fourier transform in a multimode system is studied, using the Bargmann representation. The growth of a Bargmann function is shown to be related to the second-order correlation of the corresponding state. Both the total growth and the total second-order correlation remain unchanged under the Fourier transform. Examples with coherent states, squeezed states and Mittag-Leffler states are discussed

20. Revisiting the quantum harmonic oscillator via unilateral Fourier transforms

International Nuclear Information System (INIS)

Nogueira, Pedro H F; Castro, Antonio S de

2016-01-01

The literature on the exponential Fourier approach to the one-dimensional quantum harmonic oscillator problem is revised and criticized. It is shown that the solution of this problem has been built on faulty premises. The problem is revisited via the Fourier sine and cosine transform method and the stationary states are properly determined by requiring definite parity and square-integrable eigenfunctions. (paper)

1. Fast algorithm of adaptive Fourier series

Science.gov (United States)

Gao, You; Ku, Min; Qian, Tao

2018-05-01

Adaptive Fourier decomposition (AFD, precisely 1-D AFD or Core-AFD) was originated for the goal of positive frequency representations of signals. It achieved the goal and at the same time offered fast decompositions of signals. There then arose several types of AFDs. AFD merged with the greedy algorithm idea, and in particular, motivated the so-called pre-orthogonal greedy algorithm (Pre-OGA) that was proven to be the most efficient greedy algorithm. The cost of the advantages of the AFD type decompositions is, however, the high computational complexity due to the involvement of maximal selections of the dictionary parameters. The present paper offers one formulation of the 1-D AFD algorithm by building the FFT algorithm into it. Accordingly, the algorithm complexity is reduced, from the original $\\mathcal{O}(M N^2)$ to $\\mathcal{O}(M N\\log_2 N)$, where $N$ denotes the number of the discretization points on the unit circle and $M$ denotes the number of points in $[0,1)$. This greatly enhances the applicability of AFD. Experiments are carried out to show the high efficiency of the proposed algorithm.

2. Realization of quantum Fourier transform over ZN

International Nuclear Information System (INIS)

Fu Xiang-Qun; Bao Wan-Su; Li Fa-Da; Zhang Yu-Chao

2014-01-01

Since the difficulty in preparing the equal superposition state of amplitude is 1/√N, we construct a quantile transform of quantum Fourier transform (QFT) over Z N based on the elementary transforms, such as Hadamard transform and Pauli transform. The QFT over Z N can then be realized by the quantile transform, and used to further design its quantum circuit and analyze the requirements for the quantum register and quantum gates. However, the transform needs considerable quantum computational resources and it is difficult to construct a high-dimensional quantum register. Hence, we investigate the design of t-bit quantile transform, and introduce the definition of t-bit semiclassical QFT over Z N . According to probability amplitude, we prove that the transform can be used to realize QFT over Z N and further design its quantum circuit. For this transform, the requirements for the quantum register, the one-qubit gate, and two-qubit gate reduce obviously when compared with those for the QFT over Z N . (general)

3. First order deformations of the Fourier matrix

Energy Technology Data Exchange (ETDEWEB)

Banica, Teodor, E-mail: teo.banica@gmail.com [Department of Mathematics, Cergy-Pontoise University, 95000 Cergy-Pontoise (France)

2014-01-15

The N × N complex Hadamard matrices form a real algebraic manifold C{sub N}. The singularity at a point H ∈ C{sub N} is described by a filtration of cones T{sub H}{sup ×}C{sub N}⊂T{sub H}{sup ∘}C{sub N}⊂T{sub H}C{sub N}⊂T{sup ~}{sub H}C{sub N}, coming from the trivial, affine, smooth, and first order deformations. We study here these cones in the case where H = F{sub N} is the Fourier matrix, (w{sup ij}) with w = e{sup 2πi/N}, our main result being a simple description of T{sup ~}{sub H}C{sub N}. As a consequence, the rationality conjecture dim{sub R}(T{sup ~}{sub H}C{sub N})=dim{sub Q}(T{sup ~}{sub H}C{sub N}∩M{sub N}(Q)) holds at H = F{sub N}.

4. The smoothing and fast Fourier transformation of experimental X-ray and neutron data from amorphous materials

International Nuclear Information System (INIS)

Dixon, M.; Wright, A.C.; Hutchinson, P.

1977-01-01

The application of fast Fourier transformation techniques to the analysis of experimental X-ray and neutron diffraction patterns from amorphous materials is discussed and compared with conventional techniques using Filon's quadrature. The fast Fourier transform package described also includes cubic spline smoothing and has been extensively tested, using model data to which statistical errors have been added by means of a pseudo-random number generator with Gaussian shaper. Neither cubic spline nor hand smoothing has much effect on the resulting transform since the noise removed is of too high a frequency. (Auth.)

5. Three dimensional image reconstruction in the Fourier domain

International Nuclear Information System (INIS)

Stearns, C.W.; Chesler, D.A.; Brownell, G.L.

1987-01-01

Filtered backprojection reconstruction algorithms are based upon the relationship between the Fourier transform of the imaged object and the Fourier transforms of its projections. A new reconstruction algorithm has been developed which performs the image assembly operation in Fourier space, rather than in image space by backprojection. This represents a significant decrease in the number of operations required to assemble the image. The new Fourier domain algorithm has resolution comparable to the filtered backprojection algorithm, and, after correction by a pointwise multiplication, demonstrates proper recovery throughout image space. Although originally intended for three-dimensional imaging applications, the Fourier domain algorithm can also be developed for two-dimensional imaging applications such as planar positron imaging systems

6. The relationship between shock response spectrum and fast Fourier transform

International Nuclear Information System (INIS)

Zola, Maurizio

2001-01-01

In this paper the basic relationship between response spectrum and fast Fourier transform is laid down. Since a long time the response spectrum has been used by structural engineers in the seismic domain and nowadays it is going to be used to define transient motions. This way to define the excitation is more general and more real than the use of classical shape pulses for the reproduction of real environment. Nevertheless the response spectrum of a real excitation represents a loss of some information with respect to the Fourier transform. A useful discussion could arise from these observations. Appendix A gives the relationship between the mathematic Fourier transform and the digital Fourier transform given by computers, while Appendix B gives some examples of response spectra and Fourier transforms of simple functions. (author)

7. The morphing of geographical features by Fourier transformation.

Science.gov (United States)

Li, Jingzhong; Liu, Pengcheng; Yu, Wenhao; Cheng, Xiaoqiang

2018-01-01

This paper presents a morphing model of vector geographical data based on Fourier transformation. This model involves three main steps. They are conversion from vector data to Fourier series, generation of intermediate function by combination of the two Fourier series concerning a large scale and a small scale, and reverse conversion from combination function to vector data. By mirror processing, the model can also be used for morphing of linear features. Experimental results show that this method is sensitive to scale variations and it can be used for vector map features' continuous scale transformation. The efficiency of this model is linearly related to the point number of shape boundary and the interceptive value n of Fourier expansion. The effect of morphing by Fourier transformation is plausible and the efficiency of the algorithm is acceptable.

8. Double Fourier analysis for Emotion Identification in Voiced Speech

International Nuclear Information System (INIS)

Sierra-Sosa, D.; Bastidas, M.; Ortiz P, D.; Quintero, O.L.

2016-01-01

We propose a novel analysis alternative, based on two Fourier Transforms for emotion recognition from speech. Fourier analysis allows for display and synthesizes different signals, in terms of power spectral density distributions. A spectrogram of the voice signal is obtained performing a short time Fourier Transform with Gaussian windows, this spectrogram portraits frequency related features, such as vocal tract resonances and quasi-periodic excitations during voiced sounds. Emotions induce such characteristics in speech, which become apparent in spectrogram time-frequency distributions. Later, the signal time-frequency representation from spectrogram is considered an image, and processed through a 2-dimensional Fourier Transform in order to perform the spatial Fourier analysis from it. Finally features related with emotions in voiced speech are extracted and presented. (paper)

9. Analysis of moiré fringes by Wiener filtering: An extension to the Fourier method

International Nuclear Information System (INIS)

Harasse, Sébastien; Yashiro, Wataru; Momose, Atsushi

2012-01-01

In X-ray Talbot interferometry, tilting the phase grating with respect to the absorption grating results in the formation of spatial fringes. The analysis of this moiré pattern, classically performed by the Fourier method, allows the extraction of the sample phase shift information from a single image. In this context, an extension to the Fourier method is proposed. The filter used to extract the fringe information is chosen optimally in the least-squares sense, given models for the zeroth and first order modes, noise and the modulation transfer function. The latter is obtained by measuring the detector response to moiré fringes with increasing frequencies. The obtained Wiener filter allows a better reconstruction of the phase information at all fringe frequencies, compared to the usual box or gaussian filters. This is demonstrated quantitatively by experiments using synchrotron radiation.

10. Essays in applied microeconometrics

NARCIS (Netherlands)

Cervený, Jakub

2017-01-01

Duration analysis has been widely used in the applied economic research since the late 1970s. The framework allows to examine the duration of time intervals and the rate of transition across a set of states over time. Many economic behaviors follow a similar pattern, such as transition from the

11. Fourier transform and controlling of flux in scalar hysteresis measurement

International Nuclear Information System (INIS)

Kuczmann, Miklos

2008-01-01

The paper deals with a possible realization of eliminating the effect of noise in scalar hysteresis measurements. The measured signals have been transformed into the frequency domain, and, after applying digital filter, the spectrums of the filtered signals have been transformed back to the time domain. The proposed technique results in an accurate noise-removal algorithm. The paper illustrates a fast controlling algorithm applying the inverse of the actually measured hysteresis loop, and another proportional one to measure distorted flux pattern. By developing the mentioned algorithms, it aims at the controlling of a more complicated phenomena, i.e. measuring the vector hysteresis characteristics

12. Caching Patterns and Implementation

Directory of Open Access Journals (Sweden)

Octavian Paul ROTARU

2006-01-01

Full Text Available Repetitious access to remote resources, usually data, constitutes a bottleneck for many software systems. Caching is a technique that can drastically improve the performance of any database application, by avoiding multiple read operations for the same data. This paper addresses the caching problems from a pattern perspective. Both Caching and caching strategies, like primed and on demand, are presented as patterns and a pattern-based flexible caching implementation is proposed.The Caching pattern provides method of expensive resources reacquisition circumvention. Primed Cache pattern is applied in situations in which the set of required resources, or at least a part of it, can be predicted, while Demand Cache pattern is applied whenever the resources set required cannot be predicted or is unfeasible to be buffered.The advantages and disadvantages of all the caching patterns presented are also discussed, and the lessons learned are applied in the implementation of the pattern-based flexible caching solution proposed.

13. Applied superconductivity

CERN Document Server

Newhouse, Vernon L

1975-01-01

Applied Superconductivity, Volume II, is part of a two-volume series on applied superconductivity. The first volume dealt with electronic applications and radiation detection, and contains a chapter on liquid helium refrigeration. The present volume discusses magnets, electromechanical applications, accelerators, and microwave and rf devices. The book opens with a chapter on high-field superconducting magnets, covering applications and magnet design. Subsequent chapters discuss superconductive machinery such as superconductive bearings and motors; rf superconducting devices; and future prospec

14. The Scope Of Fourier Transform Infrared (FTIR)

Science.gov (United States)

Hirschfeld, T.

1981-10-01

15. Fourier transform based scalable image quality measure.

Science.gov (United States)

Narwaria, Manish; Lin, Weisi; McLoughlin, Ian; Emmanuel, Sabu; Chia, Liang-Tien

2012-08-01

We present a new image quality assessment (IQA) algorithm based on the phase and magnitude of the 2D (twodimensional) Discrete Fourier Transform (DFT). The basic idea is to compare the phase and magnitude of the reference and distorted images to compute the quality score. However, it is well known that the Human Visual Systems (HVSs) sensitivity to different frequency components is not the same. We accommodate this fact via a simple yet effective strategy of nonuniform binning of the frequency components. This process also leads to reduced space representation of the image thereby enabling the reduced-reference (RR) prospects of the proposed scheme. We employ linear regression to integrate the effects of the changes in phase and magnitude. In this way, the required weights are determined via proper training and hence more convincing and effective. Lastly, using the fact that phase usually conveys more information than magnitude, we use only the phase for RR quality assessment. This provides the crucial advantage of further reduction in the required amount of reference image information. The proposed method is therefore further scalable for RR scenarios. We report extensive experimental results using a total of 9 publicly available databases: 7 image (with a total of 3832 distorted images with diverse distortions) and 2 video databases (totally 228 distorted videos). These show that the proposed method is overall better than several of the existing fullreference (FR) algorithms and two RR algorithms. Additionally, there is a graceful degradation in prediction performance as the amount of reference image information is reduced thereby confirming its scalability prospects. To enable comparisons and future study, a Matlab implementation of the proposed algorithm is available at http://www.ntu.edu.sg/home/wslin/reduced_phase.rar.

16. Cryogenic Scan Mechanism for Fourier Transform Spectrometer

Science.gov (United States)

Brasunas, John C.; Francis, John L.

2011-01-01

A compact and lightweight mechanism has been developed to accurately move a Fourier transform spectrometer (FTS) scan mirror (a cube corner) in a near-linear fashion with near constant speed at cryogenic temperatures. This innovation includes a slide mechanism to restrict motion to one dimension, an actuator to drive the motion, and a linear velocity transducer (LVT) to measure the speed. The cube corner mirror is double-passed in one arm of the FTS; double-passing is required to compensate for optical beam shear resulting from tilting of the moving cube corner. The slide, actuator, and LVT are off-the-shelf components that are capable of cryogenic vacuum operation. The actuator drives the slide for the required travel of 2.5 cm. The LVT measures translation speed. A proportional feedback loop compares the LVT voltage with the set voltage (speed) to derive an error signal to drive the actuator and achieve near constant speed. When the end of the scan is reached, a personal computer reverses the set voltage. The actuator and LVT have no moving parts in contact, and have magnetic properties consistent with cryogenic operation. The unlubricated slide restricts motion to linear travel, using crossed roller bearings consistent with 100-million- stroke operation. The mechanism tilts several arc seconds during transport of the FTS mirror, which would compromise optical fringe efficiency when using a flat mirror. Consequently, a cube corner mirror is used, which converts a tilt into a shear. The sheared beam strikes (at normal incidence) a flat mirror at the end of the FTS arm with the moving mechanism, thereby returning upon itself and compensating for the shear

17. A transformada de Fourier em basic The Fourier transform (FFT in basic

Directory of Open Access Journals (Sweden)

Mauricio Gomes Constantino

2000-06-01

Full Text Available In this paper we describe three computer programs in Basic language about the Fourier transform (FFT which are available in the Internet site http://artemis.ffclrp.usp.br/SoftwareE.htm (in English or http://artemis.ffclrp.usp.br/softwareP.htm (in Portuguese since October 1998. Those are addresses to the Web Page of our Laboratory of Organic Synthesis. The programs can be downloaded and used by anyone who is interested on the subject. The texts, menus and captions in the programs are written in English.

18. Research studies performed using the Cairo Fourier Diffractometer Facility

International Nuclear Information System (INIS)

Maayouf, R.M.A.; Ridikas, D.

2009-12-01

This report represents the results of the research studies performed using the Cairo Fourier Diffractometer Facility (CFDF), within 10 years after it was installed and put into operation at the beginning of 1996. The main components of the CFDF were supplied by the IAEA according to the technical assistance project EGY/1/022 'Upgrading of Research Reactor Utilization'. The present report is the second published INDC report, while the first one, published at the beginning of 1997, was about the performance of the CFDF and its main characteristic parameters. Plenty of measurements were performed since then, yielding several publications both in local and international scientific periodicals and resulting in 8 M.Sc. and Ph.D. degrees from Egyptian Universities. In addition, a new approach for the analysis of the neutron spectra was implemented using the CFDF. Specially designed interface card with proper software program was applied instead of the reverse time of flight (RTOF) and Finnish made analyzer originally attached to the facility. It has been verified that the new approach can successfully replace the RTOF analyzer, significantly decreasing the time of measurement and saving the reactor's operation time. Besides, a special fault diagnostic system program was developed and tested for caring and handling the possible failures of the CFDF. Moreover, measurements were carried out for the diffraction spectra emitted at different points of one of the samples. The latter was scanned across the neutron beam of the CFDF, for studying the stress after welding; used in industrial applications. (author)

19. Exploring chemical reaction mechanisms through harmonic Fourier beads path optimization.

Science.gov (United States)

Khavrutskii, Ilja V; Smith, Jason B; Wallqvist, Anders

2013-10-28

Here, we apply the harmonic Fourier beads (HFB) path optimization method to study chemical reactions involving covalent bond breaking and forming on quantum mechanical (QM) and hybrid QM∕molecular mechanical (QM∕MM) potential energy surfaces. To improve efficiency of the path optimization on such computationally demanding potentials, we combined HFB with conjugate gradient (CG) optimization. The combined CG-HFB method was used to study two biologically relevant reactions, namely, L- to D-alanine amino acid inversion and alcohol acylation by amides. The optimized paths revealed several unexpected reaction steps in the gas phase. For example, on the B3LYP∕6-31G(d,p) potential, we found that alanine inversion proceeded via previously unknown intermediates, 2-iminopropane-1,1-diol and 3-amino-3-methyloxiran-2-ol. The CG-HFB method accurately located transition states, aiding in the interpretation of complex reaction mechanisms. Thus, on the B3LYP∕6-31G(d,p) potential, the gas phase activation barriers for the inversion and acylation reactions were 50.5 and 39.9 kcal∕mol, respectively. These barriers determine the spontaneous loss of amino acid chirality and cleavage of peptide bonds in proteins. We conclude that the combined CG-HFB method further advances QM and QM∕MM studies of reaction mechanisms.

20. Non-rigid registration of tomographic images with Fourier transforms

International Nuclear Information System (INIS)

Osorio, Ar; Isoardi, Ra; Mato, G

2007-01-01

Spatial image registration of deformable body parts such as thorax and abdomen has important medical applications, but at the same time, it represents an important computational challenge. In this work we propose an automatic algorithm to perform non-rigid registration of tomographic images using a non-rigid model based on Fourier transforms. As a measure of similarity, we use the correlation coefficient, finding that the optimal order of the transformation is n = 3 (36 parameters). We apply this method to a digital phantom and to 7 pairs of patient images corresponding to clinical CT scans. The preliminary results indicate a fairly good agreement according to medical experts, with an average registration error of 2 mm for the case of clinical images. For 2D images (dimensions 512x512), the average running time for the algorithm is 15 seconds using a standard personal computer. Summarizing, we find that intra-modality registration of the abdomen can be achieved with acceptable accuracy for slight deformations and can be extended to 3D with a reasonable execution time

1. Fourier Transform Infrared Spectroscopy and Photoacoustic Spectroscopy for Saliva Analysis.

Science.gov (United States)

Mikkonen, Jopi J W; Raittila, Jussi; Rieppo, Lassi; Lappalainen, Reijo; Kullaa, Arja M; Myllymaa, Sami

2016-09-01

Saliva provides a valuable tool for assessing oral and systemic diseases, but concentrations of salivary components are very small, calling the need for precise analysis methods. In this work, Fourier transform infrared (FT-IR) spectroscopy using transmission and photoacoustic (PA) modes were compared for quantitative analysis of saliva. The performance of these techniques was compared with a calibration series. The linearity of spectrum output was verified by using albumin-thiocyanate (SCN(-)) solution at different SCN(-) concentrations. Saliva samples used as a comparison were obtained from healthy subjects. Saliva droplets of 15 µL were applied on the silicon sample substrate, 6 drops for each specimen, and dried at 37 ℃ overnight. The measurements were carried out using an FT-IR spectrometer in conjunction with an accessory unit for PA measurements. The findings with both transmission and PA modes mirror each other. The major bands presented were 1500-1750 cm(-1) for proteins and 1050-1200 cm(-1) for carbohydrates. In addition, the distinct spectral band at 2050 cm(-1) derives from SCN(-) anions, which is converted by salivary peroxidases to hypothiocyanate (OSCN(-)). The correlation between the spectroscopic data with SCN(-) concentration (r > 0.990 for transmission and r = 0.967 for PA mode) was found to be significant (P < 0.01), thus promising to be utilized in future applications. © The Author(s) 2016.

2. Toward a soft x-ray Fourier-transform spectrometer

International Nuclear Information System (INIS)

Howells, M.R.; Frank, K.; Hussain, Z.; Moler, E.J.; Reich, T.; Moeller, D.

1993-01-01

The use of Fourier transform spectroscopy (FTS) in the soft x-ray region is advocated as a possible route to spectral resolution superior to that attainable with a grating system. A technical plan is described for applying FTS to the study of the absorption spectrum of helium in the region of double ionization around 60--80 eV. The proposed scheme includes a Mach-Zehnder interferometer deformed into a rhombus shape to provide grazing incidence reflections. The path difference between the interfering beams is to be tuned by translation of a table carrying four mirrors over a range ±1 cm which, in the absence of errors generating relative tilts of the wave fronts, would provide a resolving power equal to the number of waves of path difference: half a million at 65 eV, for example. The signal-to-noise ratio of the spectrum is analyzed and for operation on an Advanced Light Source bending magnet beam line should be about 330

3. Effects of illumination on image reconstruction via Fourier ptychography

Science.gov (United States)

Cao, Xinrui; Sinzinger, Stefan

2017-12-01

The Fourier ptychographic microscopy (FPM) technique provides high-resolution images by combining a traditional imaging system, e.g. a microscope or a 4f-imaging system, with a multiplexing illumination system, e.g. an LED array and numerical image processing for enhanced image reconstruction. In order to numerically combine images that are captured under varying illumination angles, an iterative phase-retrieval algorithm is often applied. However, in practice, the performance of the FPM algorithm degrades due to the imperfections of the optical system, the image noise caused by the camera, etc. To eliminate the influence of the aberrations of the imaging system, an embedded pupil function recovery (EPRY)-FPM algorithm has been proposed [Opt. Express 22, 4960-4972 (2014)]. In this paper, we study how the performance of FPM and EPRY-FPM algorithms are affected by imperfections of the illumination system using both numerical simulations and experiments. The investigated imperfections include varying and non-uniform intensities, and wavefront aberrations. Our study shows that the aberrations of the illumination system significantly affect the performance of both FPM and EPRY-FPM algorithms. Hence, in practice, aberrations in the illumination system gain significant influence on the resulting image quality.

4. Analysis of phthalate ester content in poly(vinyl chloride) plastics by means of Fourier transform Raman spectroscopy

DEFF Research Database (Denmark)

Nørbygaard, Thomas; Berg, Rolf W.

2004-01-01

Fourier transform (FT) Raman spectroscopy is applied to a range of phthalate ester plasticizers in pure form as well as in poly(vinyl chloride) (PVC) samples. It is found that phthalate esters as a group can be identified by a set of six characteristic Raman bands. FT-Raman spectra of 22 phthalate...

5. Automatic picking of the first arrival event using the unwrapped-phase of the Fourier transformed wavefield

KAUST Repository

Choi, Yun Seok; Alkhalifah, Tariq Ali; Saragiotis, Christos

2011-01-01

an approach based on unwrapping the phase. We unwrap the phase by taking the derivative of the Fourier-transformed wavefield with respect to the angular frequency and isolate its amplitude component. To do so, we first apply a damping function to the seismic

6. Applied mathematics

CERN Document Server

Logan, J David

2013-01-01

Praise for the Third Edition"Future mathematicians, scientists, and engineers should find the book to be an excellent introductory text for coursework or self-study as well as worth its shelf space for reference." -MAA Reviews Applied Mathematics, Fourth Edition is a thoroughly updated and revised edition on the applications of modeling and analyzing natural, social, and technological processes. The book covers a wide range of key topics in mathematical methods and modeling and highlights the connections between mathematics and the applied and nat

7. Robust alignment of chromatograms by statistically analyzing the shifts matrix generated by moving window fast Fourier transform cross-correlation.

Science.gov (United States)

Zhang, Mingjing; Wen, Ming; Zhang, Zhi-Min; Lu, Hongmei; Liang, Yizeng; Zhan, Dejian

2015-03-01

Retention time shift is one of the most challenging problems during the preprocessing of massive chromatographic datasets. Here, an improved version of the moving window fast Fourier transform cross-correlation algorithm is presented to perform nonlinear and robust alignment of chromatograms by analyzing the shifts matrix generated by moving window procedure. The shifts matrix in retention time can be estimated by fast Fourier transform cross-correlation with a moving window procedure. The refined shift of each scan point can be obtained by calculating the mode of corresponding column of the shifts matrix. This version is simple, but more effective and robust than the previously published moving window fast Fourier transform cross-correlation method. It can handle nonlinear retention time shift robustly if proper window size has been selected. The window size is the only one parameter needed to adjust and optimize. The properties of the proposed method are investigated by comparison with the previous moving window fast Fourier transform cross-correlation and recursive alignment by fast Fourier transform using chromatographic datasets. The pattern recognition results of a gas chromatography mass spectrometry dataset of metabolic syndrome can be improved significantly after preprocessing by this method. Furthermore, the proposed method is available as an open source package at https://github.com/zmzhang/MWFFT2. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

8. From Fourier Transforms to Singular Eigenfunctions for Multigroup Transport

International Nuclear Information System (INIS)

Ganapol, B.D.

2001-01-01

A new Fourier transform approach to the solution of the multigroup transport equation with anisotropic scattering and isotropic source is presented. Through routine analytical continuation, the inversion contour is shifted from the real line to produce contributions from the poles and cuts in the complex plane. The integrand along the branch cut is then recast in terms of matrix continuum singular eigenfunctions, demonstrating equivalence of Fourier transform inversion and the singular eigenfunction expansion. The significance of this paper is that it represents the initial step in revealing the intimate connection between the Fourier transform and singular eigenfunction approaches as well as serves as a basis for a numerical algorithm

9. The application and improvement of Fourier transform spectrometer experiment

Science.gov (United States)

Liu, Zhi-min; Gao, En-duo; Zhou, Feng-qi; Wang, Lan-lan; Feng, Xiao-hua; Qi, Jin-quan; Ji, Cheng; Wang, Luning

2017-08-01

According to teaching and experimental requirements of Optoelectronic information science and Engineering, in order to consolidate theoretical knowledge and improve the students practical ability, the Fourier transform spectrometer ( FTS) experiment, its design, application and improvement are discussed in this paper. The measurement principle and instrument structure of Fourier transform spectrometer are introduced, and the spectrums of several common Laser devices are measured. Based on the analysis of spectrum and test, several possible improvement methods are proposed. It also helps students to understand the application of Fourier transform in physics.

10. Image reconstruction from pairs of Fourier-transform magnitude

International Nuclear Information System (INIS)

Hunt, B.R.; Overman, T.L.; Gough, P.

1998-01-01

The retrieval of phase information from only the magnitude of the Fourier transform of a signal remains an important problem for many applications. We present an algorithm for phase retrieval when there exist two related sets of Fourier-transform magnitude data. The data are assumed to come from a single object observed in two different polarizations through a distorting medium, so the phase component of the Fourier transform of the object is corrupted. Phase retrieval is accomplished by minimization of a suitable criterion function, which can take three different forms. copyright 1998 Optical Society of America

11. Applying Fingerprint Fourier Transformed Infrared Spectroscopy and Chemometrics to Assess Soil Ecosystem Disturbance and Recovery

Science.gov (United States)

The assessment and monitoring of soil ecosystem function has been hindered due to the shortcomings of many traditional analytical techniques (e.g., soil enzyme activities, microbial incubations), including: high cost, long time investment and difficulties with data interpretation. Consequently, ther...

12. Simplification of gamma-ray spectral data by using Fourier transform

International Nuclear Information System (INIS)

Tominaga, Shoji; Nagata, Shojiro; Nayatani, Yoshinobu; Ueda, Isamu; Sasaki, Satoshi.

1977-01-01

A method is proposed to represent γ-ray response spectra by Fourier series for the purpose of compressing spectral data. The usefulness of the method was confirmed by applying it to a spectral library of a NaI detector. In the method, a response spectrum as a wave is described by superposition of sine (cosine) waves with low frequencies, whose coefficient parameters can be obtained by a Fast Fourier Transform program. The relation between the number of parameters and the fitting error is discussed, and as the result, it is shown that the number of parameters can be reduced to about a half. The merits and features are presented in practical application of the method to the analysis of γ-ray spectra. (auth.)

13. Application of Fourier transform to MHD flow over an accelerated plate with partial-slippage

Directory of Open Access Journals (Sweden)

2014-06-01

Full Text Available Magneto-Hydrodynamic (MHD flow over an accelerated plate is investigated with partial slip conditions. Generalized Fourier Transform is used to get the exact solution not only for uniform acceleration but also for variable acceleration. The numerical solution is obtained by using linear finite element method in space and One-Step-θ-scheme in time. The resulting discretized algebraic systems are solved by applying geometric-multigrid approach. Numerical solutions are compared with the obtained Fourier transform results. Many interesting results related with slippage and MHD effects are discussed in detail through graphical sketches and tables. Application of Dirac-Delta function is one of the main features of present work.

14. A New approach for the data acquisition system of the cairo fourier diffractometer

International Nuclear Information System (INIS)

Maayouf, R.M.A.; Khalil, M.I.

2000-01-01

The present work deals with a new approach for the reverse time of flight (RTOF) analysis of the diffraction spectra. The approach is based on the same RTOF concept used for the design of a separate RTOF analyzer and applies, for data acquisition, a special interface card and software program installed in a PC computer, to perform the cross-correlation functions between the three signals received from the chopper decoder, detector and the pulsed neutron source respectively. The new approach have been realized for use with a Fourier diffractometer facility based on the RTOF concept. It has been found from test measurements performed with the high resolution Fourier diffractometer (HRFD) at the IBR-2 reactor (JINR, Dubna) that the new approach can successfully replace the RTOF analyzer

15. Rapid Fourier space solution of linear partial integro-differential equations in toroidal magnetic confinement geometries

International Nuclear Information System (INIS)

McMillan, B.F.; Jolliet, S.; Tran, T.M.; Villard, L.; Bottino, A.; Angelino, P.

2010-01-01

Fluctuating quantities in magnetic confinement geometries often inherit a strong anisotropy along the field lines. One technique for describing these structures is the use of a certain set of Fourier components on the tori of nested flux surfaces. We describe an implementation of this approach for solving partial differential equations, like Poisson's equation, where a different set of Fourier components may be chosen on each surface according to the changing safety factor profile. Allowing the resolved components to change to follow the anisotropy significantly reduces the total number of degrees of freedom in the description. This can permit large gains in computational performance. We describe, in particular, how this approach can be applied to rapidly solve the gyrokinetic Poisson equation in a particle code, ORB5 (Jolliet et al. (2007) [5]), with a regular (non-field-aligned) mesh. (authors)

16. Fast data reconstructed method of Fourier transform imaging spectrometer based on multi-core CPU

Science.gov (United States)

Yu, Chunchao; Du, Debiao; Xia, Zongze; Song, Li; Zheng, Weijian; Yan, Min; Lei, Zhenggang

2017-10-01

Imaging spectrometer can gain two-dimensional space image and one-dimensional spectrum at the same time, which shows high utility in color and spectral measurements, the true color image synthesis, military reconnaissance and so on. In order to realize the fast reconstructed processing of the Fourier transform imaging spectrometer data, the paper designed the optimization reconstructed algorithm with OpenMP parallel calculating technology, which was further used for the optimization process for the HyperSpectral Imager of `HJ-1' Chinese satellite. The results show that the method based on multi-core parallel computing technology can control the multi-core CPU hardware resources competently and significantly enhance the calculation of the spectrum reconstruction processing efficiency. If the technology is applied to more cores workstation in parallel computing, it will be possible to complete Fourier transform imaging spectrometer real-time data processing with a single computer.

17. The feasibility of using a Fourier RTOF spectrometer at a low-power research reactor

International Nuclear Information System (INIS)

Maayouf, R.M.A.; Priesmeyer, H.G.; Kudryashev, V.A.

1991-01-01

The present situation of Fourier time-of-flight (TOF) spectrometry is discussed using the FSS spectrometer as example. The use of the Fourier reverse TOF spectrometry, as an efficient tool for studying condensed matter, at a 2 MW (WWR-S type) reactor is also assessed. The arrangement of the RTOF spectrometer, which could be successfully used at such type of reactor, is introduced. The suggested arrangement applies a neutron guide tube of 24 m length and allows for effective luminosity 2.4.10 6 at a flight path distance of 3.6 m. The number of neutrons scattered from a sample (5 cm 3 in volume) and incident on the detector system, as estimated for the suggested arrangement, is ∝1.6.10 3 n/sec. Such high counting rate allows to measure a diffraction spectrum within less than an hour. (orig.) With 12 figs [de

18. Mix ratio measurements of pozzolanic blends by Fourier transform infrared-attenuated total reflectance method

International Nuclear Information System (INIS)

Rebagay, T.V.; Dodd, D.A.

1992-07-01

The disposal of low-level radioactive liquid wastes at the Hanford Site near Richland, Washington, involves mixing the wastes with pozzolanic grout-forming solid blends. Checking the quality of each blend component and its mix ratio will ensure processibility of the blend and the long-term performance of the resulting waste grout. In earlier work at Hanford laboratories, Fourier transform infrared-transmission method (FTIR-TR) using KBr pellet was applied successfully in the analysis of blends consisting of cement, fly ash, and clays. This method involves time-consuming sample preparation resulting in slow turnaround for repetitive sampling. Because reflection methods do not require elaborate sample preparation, they have the potential to reduce turnaround analysis time. Neat samples may be examined making these methods attractive for quality control. This study investigates the capability of Fourier transform infrared-attenuated total reflectance method (FTIR-ATR) to analyze pozzolanic blends

19. Fourier transform spectroscopy of semiconductor materials

International Nuclear Information System (INIS)

Jonak-Auer, I.

1996-11-01

In order to determine the type of charge carriers, i.e. electrons or holes, participating in optical transitions, cyclotron resonance experiments using circularly polarized radiation were performed on strained-layer [111]-oriented InGaAs/(Al)GaAs multiple quantum wells and on a [100]-oriented InAs/GaSb double-heterostructure. Because of the rather complicated band-structures of these samples it is a priori unknown which carriers take part in transitions. The measurements yield the surprising result, that for the InGaAs/GaAs multiple quantum well the experimentally observed cyclotron resonance appears in the electron-active polarization in the frequency-regime of the Far Infrared (FIR), but in the hole-active polarization in the range of millimeter waves, whereas for the InGaAs/AlGaAs sample the resonance is caused by holes also in the FIR. Since by theoretical considerations the possibility of electrons causing the FIR cyclotron resonance could be excluded, the measurements are interpreted as being caused by holes due to broken selection rules. In the InAs/GaSb sample hole cyclotron resonance could for the first time be measured on a double-heterostructure. As for the application oriented measurements, they comprised a study of the hydrogen content of amorphous silicon nitride layers, and were performed in collaboration with Austria Mikro Systeme International AG. Fourier spectroscopy is a fast and non-destructive means for determining impurity concentrations. Radiation in the Mid Infrared regime stimulates N-H and Si-H stretching vibrations which lead to absorption peaks and can directly be attributed to the hydrogen concentration via calibration factors taken from the literature. In comparison with recommended procedures in the literature, a much higher accuracy in determining the areas of the absorption peaks could be gained in the course of this thesis by a proper polynomial fit of the background spectrum outside the absorption lines. The hydrogen content of

20. Applied Enzymology.

Science.gov (United States)

Manoharan, Asha; Dreisbach, Joseph H.

1988-01-01

Describes some examples of chemical and industrial applications of enzymes. Includes a background, a discussion of structure and reactivity, enzymes as therapeutic agents, enzyme replacement, enzymes used in diagnosis, industrial applications of enzymes, and immobilizing enzymes. Concludes that applied enzymology is an important factor in…

1. Fourier phase retrieval with a single mask by Douglas-Rachford algorithms.

Science.gov (United States)

Chen, Pengwen; Fannjiang, Albert

2018-05-01

The Fourier-domain Douglas-Rachford (FDR) algorithm is analyzed for phase retrieval with a single random mask. Since the uniqueness of phase retrieval solution requires more than a single oversampled coded diffraction pattern, the extra information is imposed in either of the following forms: 1) the sector condition on the object; 2) another oversampled diffraction pattern, coded or uncoded. For both settings, the uniqueness of projected fixed point is proved and for setting 2) the local, geometric convergence is derived with a rate given by a spectral gap condition. Numerical experiments demonstrate global, power-law convergence of FDR from arbitrary initialization for both settings as well as for 3 or more coded diffraction patterns without oversampling. In practice, the geometric convergence can be recovered from the power-law regime by a simple projection trick, resulting in highly accurate reconstruction from generic initialization.

2. Glaucoma diagnosis by mapping macula with Fourier domain optical coherence tomography

Science.gov (United States)

Tan, Ou; Lu, Ake; Chopra, Vik; Varma, Rohit; Hiroshi, Ishikawa; Schuman, Joel; Huang, David

2008-03-01

A new image segmentation method was developed to detect macular retinal sub-layers boundary on newly-developed Fourier-Domain Optical Coherence Tomography (FD-OCT) with macular grid scan pattern. The segmentation results were used to create thickness map of macular ganglion cell complex (GCC), which contains the ganglion cell dendrites, cell bodies and axons. Overall average and several pattern analysis parameters were defined on the GCC thickness map and compared for the diagnosis of glaucoma. Intraclass correlation (ICC) is used to compare the reproducibility of the parameters. Area under receiving operative characteristic curve (AROC) was calculated to compare the diagnostic power. The result is also compared to the output of clinical time-domain OCT (TD-OCT). We found that GCC based parameters had good repeatability and comparable diagnostic power with circumpapillary nerve fiber layer (cpNFL) thickness. Parameters based on pattern analysis can increase the diagnostic power of GCC macular mapping.

3. Representación paramétrica de la transformada de Fourier de tejidos textiles Implementation of the parametric representation of the Fourier transform in fabrics

Directory of Open Access Journals (Sweden)

Yezid Torres Moreno

2007-06-01

Full Text Available La naturaleza periódica de las imágenes de tejido textil permite el uso de las técnicas de la transformación de Fourier rápida para su clasificación. Debido a los patrones de repetición dentro de las imágenes del tejido textil, es posible encontrar una forma relativamente fácil de descripción para su densidad espectral de energía. Un trabajo previamente publicado permite mostrar el uso de descriptores para el espectro de Fourier de las imágenes, en particular su eficiencia a la invarianza a la rotación, traslación y cambio de escala [1].Dichos descriptores mostraron ser muy efectivos para representar un tejido textil y pueden ser utilizados para caracterizar texturas cuasi¿periódicas mediante técnicas no destructivas en tiempo real e in situ. Muestras de texturas textiles son evaluadas con esta técnica de representación paramétrica con el propósito de analizar su robustez y reproducibilidad. Finalmente, un conjunto de tejidos textiles es sometido a este modelo con el objetivo de evaluar la posibilidad de utilizarlo para la clasificación, verificación y reconocimiento de formas.The periodic nature of the fabric images allows using fast Fourier transform techniques in image processing for its characterization. Due to the repetition of patterns inside the images of textile, is possible to ﬁnd a form relatively easy of description in their energy spectrum. A recent work outlines a group of geometric descriptors for the Fourier spectrum of the images; looking for this eﬃciency to rotation, translation and scale change invariance [1]. These descriptors showed to be very eﬀective to represent a textile fabric and can be used to characterize the quasi periodic textures in real time and in situ non destructive techniques. Samples of textile textures are tested to this technique of parametric representation with the purpose of analyzing their robustness and reproducibility. Finally, a set of textile fabrics is subjected to

4. The convection patterns in microemulsions

International Nuclear Information System (INIS)

Korneta, W.; Lopez Quintela, M.A.; Fernandez Novoa, A.

1991-07-01

The Rayleigh-Benard convection in the microemulsion consisting of water (7.5%), cyclohexan (oil-61.7%) and diethylenglycolmonobutylether (surfactant-30.8%) is studied from the onset of convection to the phase separation. The five classes of convection patterns are observed and recorded on the video: localized travelling waves, travelling waves, travelling waves and localized steady rolls, steady rolls and steady polygons. The Fourier transforms and histograms of these patterns are presented. The origin of any pattern is discussed. The intermittent behaviour close to the phase separation was observed. Possible applications of the obtained results are suggested. (author). 6 refs, 4 figs

5. Combined Helmholtz Integral Equation - Fourier series formulation of acoustical radiation and scattering problems

CSIR Research Space (South Africa)

Fedotov, I

2006-07-01

Full Text Available The Combined Helmholtz Integral Equation – Fourier series Formulation (CHIEFF) is based on representation of a velocity potential in terms of Fourier series and finding the Fourier coefficients of this expansion. The solution could be substantially...

6. Almost everywhere convergence over cubes of multiple trigonometric Fourier series

International Nuclear Information System (INIS)

Antonov, N Yu

2004-01-01

Under certain conditions on a function φ:[0,+∞)→[0,+∞) we prove a theorem asserting that the convergence almost everywhere of trigonometric Fourier series for all functions of class φ(L) [-π,π) implies the convergence over cubes of the multiple Fourier series and all its conjugates for an arbitrary function f element of φ(L)(log + L) d-1 ) [-π,π) d , d element of N. It follows from this and an earlier result of the author on the convergence almost everywhere of Fourier series of functions of one variable and class L(log + L)(log + log + log + L)) [-π,π) that if f element of L(log + L) d (log + log + log + L)) [-π,π) d , d element of N, then the Fourier series of f and all its conjugates converge over cubes almost everywhere

7. On the Equisummability of Hermite and Fourier Expansions

We prove an equisummability result for the Fourier expansions and Hermite expansions as well as special Hermite expansions. We also prove the uniform boundedness of the Bochner-Riesz means associated to the Hermite expansions for polyradial functions.

8. q-Generalization of the inverse Fourier transform

International Nuclear Information System (INIS)

Jauregui, M.; Tsallis, C.

2011-01-01

A wide class of physical distributions appears to follow the q-Gaussian form, which plays the role of attractor according to a q-generalized Central Limit Theorem, where a q-generalized Fourier transform plays an important role. We introduce here a method which determines a distribution from the knowledge of its q-Fourier transform and some supplementary information. This procedure involves a recently q-generalized representation of the Dirac delta and the class of functions on which it acts. The present method conveniently extends the inverse of the standard Fourier transform, and is therefore expected to be very useful in the study of many complex systems. - Highlights: → We present a method to invert the q-Fourier transform of a distribution. → We illustrate when Dirac delta can be represented using q-exponentials. → We describe a family of functions for which this new representation works.

9. On Sums of Numerical Series and Fourier Series

Science.gov (United States)

Pavao, H. Germano; de Oliveira, E. Capelas

2008-01-01

We discuss a class of trigonometric functions whose corresponding Fourier series, on a conveniently chosen interval, can be used to calculate several numerical series. Particular cases are presented and two recent results involving numerical series are recovered. (Contains 1 note.)

10. On the physical relevance of the discrete Fourier transform

CSIR Research Space (South Africa)

Greben, JM

1991-11-01

Full Text Available This paper originated from the author's dissatisfaction with the way the discrete Fourier transform is usually presented in the literature. Although mathematically correct, the physical meaning of the common representation is unsatisfactory...

11. Fourier-Accelerated Nodal Solvers (FANS) for homogenization problems

Science.gov (United States)

Leuschner, Matthias; Fritzen, Felix

2017-11-01

Fourier-based homogenization schemes are useful to analyze heterogeneous microstructures represented by 2D or 3D image data. These iterative schemes involve discrete periodic convolutions with global ansatz functions (mostly fundamental solutions). The convolutions are efficiently computed using the fast Fourier transform. FANS operates on nodal variables on regular grids and converges to finite element solutions. Compared to established Fourier-based methods, the number of convolutions is reduced by FANS. Additionally, fast iterations are possible by assembling the stiffness matrix. Due to the related memory requirement, the method is best suited for medium-sized problems. A comparative study involving established Fourier-based homogenization schemes is conducted for a thermal benchmark problem with a closed-form solution. Detailed technical and algorithmic descriptions are given for all methods considered in the comparison. Furthermore, many numerical examples focusing on convergence properties for both thermal and mechanical problems, including also plasticity, are presented.

12. Decay properties of linear thermoelastic plates: Cattaneo versus Fourier law

KAUST Repository

Said-Houari, Belkacem

2013-02-01

In this article, we investigate the decay properties of the linear thermoelastic plate equations in the whole space for both Fourier and Cattaneo\\'s laws of heat conduction. We point out that while the paradox of infinite propagation speed inherent in Fourier\\'s law is removed by changing to the Cattaneo law, the latter always leads to a loss of regularity of the solution. The main tool used to prove our results is the energy method in the Fourier space together with some integral estimates. We prove the decay estimates for initial data U0 ∈ Hs(ℝ) ∩ L1(ℝ). In addition, by restricting the initial data to U0 ∈ Hs(ℝ) ∩ L1,γ(ℝ) and γ ∈ [0, 1], we can derive faster decay estimates with the decay rate improvement by a factor of t-γ/2. © 2013 Copyright Taylor and Francis Group, LLC.

13. Extending Single-Molecule Microscopy Using Optical Fourier Processing

Science.gov (United States)

2015-01-01

This article surveys the recent application of optical Fourier processing to the long-established but still expanding field of single-molecule imaging and microscopy. A variety of single-molecule studies can benefit from the additional image information that can be obtained by modulating the Fourier, or pupil, plane of a widefield microscope. After briefly reviewing several current applications, we present a comprehensive and computationally efficient theoretical model for simulating single-molecule fluorescence as it propagates through an imaging system. Furthermore, we describe how phase/amplitude-modulating optics inserted in the imaging pathway may be modeled, especially at the Fourier plane. Finally, we discuss selected recent applications of Fourier processing methods to measure the orientation, depth, and rotational mobility of single fluorescent molecules. PMID:24745862

14. Decay properties of linear thermoelastic plates: Cattaneo versus Fourier law

KAUST Repository

Said-Houari, Belkacem

2013-01-01

In this article, we investigate the decay properties of the linear thermoelastic plate equations in the whole space for both Fourier and Cattaneo's laws of heat conduction. We point out that while the paradox of infinite propagation speed inherent

15. A fourier transform quality measure for iris images

CSIR Research Space (South Africa)

Makinana, S

2014-08-01

Full Text Available to ensure that good quality images are selected for feature extraction, in order to improve iris recognition system. In addition, this research proposes a measure of iris image quality using a Fourier Transform. The experimental results demonstrate...

16. Error Analysis for Fourier Methods for Option Pricing

KAUST Repository

Hä ppö lä , Juho

2016-01-01

We provide a bound for the error committed when using a Fourier method to price European options when the underlying follows an exponential Levy dynamic. The price of the option is described by a partial integro-differential equation (PIDE

17. Surface Fourier-transform lens using a metasurface

International Nuclear Information System (INIS)

Li, Yun Bo; Cai, Ben Geng; Cheng, Qiang; Cui, Tie Jun

2015-01-01

We propose a surface (or 2D) Fourier-transform lens using a gradient refractive index (GRIN) metasurface in the microwave band, which is composed of sub-wavelength quasi-periodical metallic patches on a grounded dielectric substrate. Such a metasurface supports the transverse magnetic (TM) modes of surface waves. To gradually change the size of textures, we obtain different surface refractive indices, which can be tailored to fit the required refractive-index profile of a surface Fourier-transform lens. According to the theory of spatial Fourier transformation, we make use of the proposed lens to realize surface plane-wave scanning under different feeding locations. The simulation and experimental results jointly confirm the validity of the surface Fourier-transform lens. The proposed method can also be extended to the terahertz frequency. (paper)

18. Fourier-Based Transmit Beampattern Design Using MIMO Radar

KAUST Repository

Lipor, John; Ahmed, Sajid; Alouini, Mohamed-Slim

2014-01-01

a constant-envelope or drawing from a finite alphabet. In this paper, a closed-form method to design for a uniform linear array is proposed that utilizes the discrete Fourier transform (DFT) coefficients and Toeplitz matrices. The resulting

19. The Fourier law in a momentum-conserving chain

NARCIS (Netherlands)

Giardinà, C.; Kurchan, J.

2005-01-01

We introduce a family of models for heat conduction with and without momentum conservation. They are analytically solvable in the high temperature limit and can also be efficiently simulated. In all cases the Fourier law is verified in one dimension.

20. Innovative design method of automobile profile based on Fourier descriptor

Science.gov (United States)

Gao, Shuyong; Fu, Chaoxing; Xia, Fan; Shen, Wei

2017-10-01

Aiming at the innovation of the contours of automobile side, this paper presents an innovative design method of vehicle side profile based on Fourier descriptor. The design flow of this design method is: pre-processing, coordinate extraction, standardization, discrete Fourier transform, simplified Fourier descriptor, exchange descriptor innovation, inverse Fourier transform to get the outline of innovative design. Innovative concepts of the innovative methods of gene exchange among species and the innovative methods of gene exchange among different species are presented, and the contours of the innovative design are obtained separately. A three-dimensional model of a car is obtained by referring to the profile curve which is obtained by exchanging xenogeneic genes. The feasibility of the method proposed in this paper is verified by various aspects.

1. Fourier transform wavefront control with adaptive prediction of the atmosphere.

Science.gov (United States)

Poyneer, Lisa A; Macintosh, Bruce A; Véran, Jean-Pierre

2007-09-01

Predictive Fourier control is a temporal power spectral density-based adaptive method for adaptive optics that predicts the atmosphere under the assumption of frozen flow. The predictive controller is based on Kalman filtering and a Fourier decomposition of atmospheric turbulence using the Fourier transform reconstructor. It provides a stable way to compensate for arbitrary numbers of atmospheric layers. For each Fourier mode, efficient and accurate algorithms estimate the necessary atmospheric parameters from closed-loop telemetry and determine the predictive filter, adjusting as conditions change. This prediction improves atmospheric rejection, leading to significant improvements in system performance. For a 48x48 actuator system operating at 2 kHz, five-layer prediction for all modes is achievable in under 2x10(9) floating-point operations/s.

2. Subwavelength Fourier-transform imaging without a lens or a beamsplitter

International Nuclear Information System (INIS)

Liu Rui-Feng; Yuan Xin-Xing; Fang Yi-Zhen; Zhang Pei; Zhou Yu; Gao Hong; Li Fu-Li

2014-01-01

The fourier-transform patterns of an object are usually observed in the far-field region or obtained in the near-field region with the help of lenses. Here we propose and experimentally demonstrate a scheme of Fourier-transform patterns in the Fresnel diffraction region with thermal light. In this scheme, neither a lens nor a beamsplitter is used, and only one single charge coupled device (CCD) is employed. It means that dividing one beam out of a light source into signal and reference beams is not as necessary as the one done by the use of a beamsplitter in usual ghost interference experiments. Moreover, the coincidence measurement of two point detectors is not necessary and data recorded on a single CCD are sufficient for reconstructing the ghost diffraction patterns. The feature of the scheme promises a great potential application in the fields of X-ray and neutron diffraction imaging processes. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

3. Applied dynamics

CERN Document Server

Schiehlen, Werner

2014-01-01

Applied Dynamics is an important branch of engineering mechanics widely applied to mechanical and automotive engineering, aerospace and biomechanics as well as control engineering and mechatronics. The computational methods presented are based on common fundamentals. For this purpose analytical mechanics turns out to be very useful where D’Alembert’s principle in the Lagrangian formulation proves to be most efficient. The method of multibody systems, finite element systems and continuous systems are treated consistently. Thus, students get a much better understanding of dynamical phenomena, and engineers in design and development departments using computer codes may check the results more easily by choosing models of different complexity for vibration and stress analysis.

4. Applied optics

International Nuclear Information System (INIS)

Orszag, A.; Antonetti, A.

1988-01-01

The 1988 progress report, of the Applied Optics laboratory, of the (Polytechnic School, France), is presented. The optical fiber activities are focused on the development of an optical gyrometer, containing a resonance cavity. The following domains are included, in the research program: the infrared laser physics, the laser sources, the semiconductor physics, the multiple-photon ionization and the nonlinear optics. Investigations on the biomedical, the biological and biophysical domains are carried out. The published papers and the congress communications are listed [fr

5. Simple optical setup implementation for digital Fourier transform holography

Energy Technology Data Exchange (ETDEWEB)

De Oliveira, G N [Pos-graduacao em Engenharia Mecanica, TEM/PGMEC, Universidade Federal Fluminense, Rua Passo da Patria, 156, Niteroi, R.J., Cep.: 24.210-240 (Brazil); Rodrigues, D M C; Dos Santos, P A M, E-mail: pams@if.uff.br [Instituto de Fisica, Laboratorio de Optica Nao-linear e Aplicada, Universidade Federal Fluminense, Av. Gal. Nilton Tavares de Souza, s/n, Gragoata, Niteroi, R.J., Cep.:24.210-346 (Brazil)

2011-01-01

In the present work a simple implementation of Digital Fourier Transform Holography (DFTH) setup is discussed. This is obtained making a very simple modification in the classical setup arquiteture of the Fourier Transform holography. It is also demonstrated the easy and practical viability of the setup in an interferometric application for mechanical parameters determination. The work is also proposed as an interesting advanced introductory training for graduated students in digital holography.

6. A New Nonlinear Unit Root Test with Fourier Function

OpenAIRE

Güriş, Burak

2017-01-01

Traditional unit root tests display a tendency to be nonstationary in the case of structural breaks and nonlinearity. To eliminate this problem this paper proposes a new flexible Fourier form nonlinear unit root test. This test eliminates this problem to add structural breaks and nonlinearity together to the test procedure. In this test procedure, structural breaks are modeled by means of a Fourier function and nonlinear adjustment is modeled by means of an Exponential Smooth Threshold Autore...

7. A discrete Fourier transform for virtual memory machines

Science.gov (United States)

Galant, David C.

1992-01-01

An algebraic theory of the Discrete Fourier Transform is developed in great detail. Examination of the details of the theory leads to a computationally efficient fast Fourier transform for the use on computers with virtual memory. Such an algorithm is of great use on modern desktop machines. A FORTRAN coded version of the algorithm is given for the case when the sequence of numbers to be transformed is a power of two.

8. Image registration under translation and rotation in two-dimensional planes using Fourier slice theorem.

Science.gov (United States)

Pohit, M; Sharma, J

2015-05-10

Image recognition in the presence of both rotation and translation is a longstanding problem in correlation pattern recognition. Use of log polar transform gives a solution to this problem, but at a cost of losing the vital phase information from the image. The main objective of this paper is to develop an algorithm based on Fourier slice theorem for measuring the simultaneous rotation and translation of an object in a 2D plane. The algorithm is applicable for any arbitrary object shift for full 180° rotation.

9. In vivo measurement of lower back deformations with Fourier-transform profilometry

International Nuclear Information System (INIS)

Hanafi, Abdelmalek; Gharbi, Tijani; Cornu, Jean-Yves

2005-01-01

Through the variation of their cross sections, the in vivo response of lower back muscles to low loading in an upright seated posture is explored by the Fourier-transform profilometry technique. The maximization of its sensitivity allows us to reach an adequate resolution for the evaluation of low-back displacements. Refinements of the fringe pattern analysis permit the minimization of errors. The experiments show an asymmetric distribution of the displacement during head rotation movements. Significant contribution of the lower back to grasping exertions is also observed. These results are thought to be useful for early defect detection in the lower back

10. Radiation dose reduction in medical x-ray CT via Fourier-based iterative reconstruction.

Science.gov (United States)

Fahimian, Benjamin P; Zhao, Yunzhe; Huang, Zhifeng; Fung, Russell; Mao, Yu; Zhu, Chun; Khatonabadi, Maryam; DeMarco, John J; Osher, Stanley J; McNitt-Gray, Michael F; Miao, Jianwei

2013-03-01

A Fourier-based iterative reconstruction technique, termed Equally Sloped Tomography (EST), is developed in conjunction with advanced mathematical regularization to investigate radiation dose reduction in x-ray CT. The method is experimentally implemented on fan-beam CT and evaluated as a function of imaging dose on a series of image quality phantoms and anonymous pediatric patient data sets. Numerical simulation experiments are also performed to explore the extension of EST to helical cone-beam geometry. EST is a Fourier based iterative algorithm, which iterates back and forth between real and Fourier space utilizing the algebraically exact pseudopolar fast Fourier transform (PPFFT). In each iteration, physical constraints and mathematical regularization are applied in real space, while the measured data are enforced in Fourier space. The algorithm is automatically terminated when a proposed termination criterion is met. Experimentally, fan-beam projections were acquired by the Siemens z-flying focal spot technology, and subsequently interleaved and rebinned to a pseudopolar grid. Image quality phantoms were scanned at systematically varied mAs settings, reconstructed by EST and conventional reconstruction methods such as filtered back projection (FBP), and quantified using metrics including resolution, signal-to-noise ratios (SNRs), and contrast-to-noise ratios (CNRs). Pediatric data sets were reconstructed at their original acquisition settings and additionally simulated to lower dose settings for comparison and evaluation of the potential for radiation dose reduction. Numerical experiments were conducted to quantify EST and other iterative methods in terms of image quality and computation time. The extension of EST to helical cone-beam CT was implemented by using the advanced single-slice rebinning (ASSR) method. Based on the phantom and pediatric patient fan-beam CT data, it is demonstrated that EST reconstructions with the lowest scanner flux setting of 39 m

11. Radiation dose reduction in medical x-ray CT via Fourier-based iterative reconstruction

International Nuclear Information System (INIS)

Fahimian, Benjamin P.; Zhao Yunzhe; Huang Zhifeng; Fung, Russell; Zhu Chun; Miao Jianwei; Mao Yu; Khatonabadi, Maryam; DeMarco, John J.; McNitt-Gray, Michael F.; Osher, Stanley J.

2013-01-01

Purpose: A Fourier-based iterative reconstruction technique, termed Equally Sloped Tomography (EST), is developed in conjunction with advanced mathematical regularization to investigate radiation dose reduction in x-ray CT. The method is experimentally implemented on fan-beam CT and evaluated as a function of imaging dose on a series of image quality phantoms and anonymous pediatric patient data sets. Numerical simulation experiments are also performed to explore the extension of EST to helical cone-beam geometry. Methods: EST is a Fourier based iterative algorithm, which iterates back and forth between real and Fourier space utilizing the algebraically exact pseudopolar fast Fourier transform (PPFFT). In each iteration, physical constraints and mathematical regularization are applied in real space, while the measured data are enforced in Fourier space. The algorithm is automatically terminated when a proposed termination criterion is met. Experimentally, fan-beam projections were acquired by the Siemens z-flying focal spot technology, and subsequently interleaved and rebinned to a pseudopolar grid. Image quality phantoms were scanned at systematically varied mAs settings, reconstructed by EST and conventional reconstruction methods such as filtered back projection (FBP), and quantified using metrics including resolution, signal-to-noise ratios (SNRs), and contrast-to-noise ratios (CNRs). Pediatric data sets were reconstructed at their original acquisition settings and additionally simulated to lower dose settings for comparison and evaluation of the potential for radiation dose reduction. Numerical experiments were conducted to quantify EST and other iterative methods in terms of image quality and computation time. The extension of EST to helical cone-beam CT was implemented by using the advanced single-slice rebinning (ASSR) method. Results: Based on the phantom and pediatric patient fan-beam CT data, it is demonstrated that EST reconstructions with the lowest

12. Application of Fourier elastodynamics to direct and inverse problems for the scattering of elastic waves from flaws near surfaces

International Nuclear Information System (INIS)

Richardson, J.M.; Fertig, K.W. Jr.

1983-01-01

In order to inspect flaws which lie too close to the surface a Fourier elastodynamic formalism is proposed which enables one to decompose the elastodynamic system into separately charterizable parts by means of planes perpendicular to the z-axis. The process can be represented by a generalized transfer function relating the near-field scattered waves to the waves incident on a slab of material containing the flaw. The Fourier elastodynamics are applied to the characterization of the total scattering process involving a flaw at various distances from a plastic-water interface. An abbreviated discussion of Fourier elastodynamics is presented, and the results specialized to the case of spherical voids and inclusions bear an interface. Finally, the computational results for several ranges of temporal frequency and for a sequence of values of the distance from the flaw center to the interface are discussed

13. Self-Fourier functions and coherent laser combination

International Nuclear Information System (INIS)

Corcoran, C J; Pasch, K A

2004-01-01

The Gaussian and Comb functions are generally quoted as being the two basic functions that are their own Fourier transforms. In 1991, Caola presented a recipe for generating functions that are their own Fourier transforms by symmetrizing any transformable function and then adding its own Fourier transform to it. In this letter, we present a new method for generating a set of functions that are exactly their own Fourier transforms, and which have direct application to laser cavity design for a wide variety of applications. The generated set includes the Gaussian and Comb functions as special cases and forms a continuous bridge of functions between them. The new generating method uses the Gaussian and Comb functions as bases and does not rely on the Fourier operator itself. This self-Fourier function promises to be particularly useful in high-power laser design through coherent laser beam combination. Although these results are presented in a single dimension as with a linear array, the results are equally valid in two dimensions. (letter to the editor)

14. Mathematical and information-geometrical entropy for phenomenological Fourier and non-Fourier heat conduction

Science.gov (United States)

Li, Shu-Nan; Cao, Bing-Yang

2017-09-01

The second law of thermodynamics governs the direction of heat transport, which provides the foundational definition of thermodynamic Clausius entropy. The definitions of entropy are further generalized for the phenomenological heat transport models in the frameworks of classical irreversible thermodynamics and extended irreversible thermodynamics (EIT). In this work, entropic functions from mathematics are combined with phenomenological heat conduction models and connected to several information-geometrical conceptions. The long-time behaviors of these mathematical entropies exhibit a wide diversity and physical pictures in phenomenological heat conductions, including the tendency to thermal equilibrium, and exponential decay of nonequilibrium and asymptotics, which build a bridge between the macroscopic and microscopic modelings. In contrast with the EIT entropies, the mathematical entropies expressed in terms of the internal energy function can avoid singularity paired with nonpositive local absolute temperature caused by non-Fourier heat conduction models.

15. Fourier-based linear systems description of free-breathing pulmonary magnetic resonance imaging

Science.gov (United States)

Capaldi, D. P. I.; Svenningsen, S.; Cunningham, I. A.; Parraga, G.

2015-03-01

Fourier-decomposition of free-breathing pulmonary magnetic resonance imaging (FDMRI) was recently piloted as a way to provide rapid quantitative pulmonary maps of ventilation and perfusion without the use of exogenous contrast agents. This method exploits fast pulmonary MRI acquisition of free-breathing proton (1H) pulmonary images and non-rigid registration to compensate for changes in position and shape of the thorax associated with breathing. In this way, ventilation imaging using conventional MRI systems can be undertaken but there has been no systematic evaluation of fundamental image quality measurements based on linear systems theory. We investigated the performance of free-breathing pulmonary ventilation imaging using a Fourier-based linear system description of each operation required to generate FDMRI ventilation maps. Twelve subjects with chronic obstructive pulmonary disease (COPD) or bronchiectasis underwent pulmonary function tests and MRI. Non-rigid registration was used to co-register the temporal series of pulmonary images. Pulmonary voxel intensities were aligned along a time axis and discrete Fourier transforms were performed on the periodic signal intensity pattern to generate frequency spectra. We determined the signal-to-noise ratio (SNR) of the FDMRI ventilation maps using a conventional approach (SNRC) and using the Fourier-based description (SNRF). Mean SNR was 4.7 ± 1.3 for subjects with bronchiectasis and 3.4 ± 1.8, for COPD subjects (p>.05). SNRF was significantly different than SNRC (p<.01). SNRF was approximately 50% of SNRC suggesting that the linear system model well-estimates the current approach.

16. A Fourier-based compressed sensing technique for accelerated CT image reconstruction using first-order methods

International Nuclear Information System (INIS)

Choi, Kihwan; Li, Ruijiang; Nam, Haewon; Xing, Lei

2014-01-01

As a solution to iterative CT image reconstruction, first-order methods are prominent for the large-scale capability and the fast convergence rate O(1/k 2 ). In practice, the CT system matrix with a large condition number may lead to slow convergence speed despite the theoretically promising upper bound. The aim of this study is to develop a Fourier-based scaling technique to enhance the convergence speed of first-order methods applied to CT image reconstruction. Instead of working in the projection domain, we transform the projection data and construct a data fidelity model in Fourier space. Inspired by the filtered backprojection formalism, the data are appropriately weighted in Fourier space. We formulate an optimization problem based on weighted least-squares in the Fourier space and total-variation (TV) regularization in image space for parallel-beam, fan-beam and cone-beam CT geometry. To achieve the maximum computational speed, the optimization problem is solved using a fast iterative shrinkage-thresholding algorithm with backtracking line search and GPU implementation of projection/backprojection. The performance of the proposed algorithm is demonstrated through a series of digital simulation and experimental phantom studies. The results are compared with the existing TV regularized techniques based on statistics-based weighted least-squares as well as basic algebraic reconstruction technique. The proposed Fourier-based compressed sensing (CS) method significantly improves both the image quality and the convergence rate compared to the existing CS techniques. (paper)

17. Correction for Eddy Current-Induced Echo-Shifting Effect in Partial-Fourier Diffusion Tensor Imaging.

Science.gov (United States)

Truong, Trong-Kha; Song, Allen W; Chen, Nan-Kuei

2015-01-01

In most diffusion tensor imaging (DTI) studies, images are acquired with either a partial-Fourier or a parallel partial-Fourier echo-planar imaging (EPI) sequence, in order to shorten the echo time and increase the signal-to-noise ratio (SNR). However, eddy currents induced by the diffusion-sensitizing gradients can often lead to a shift of the echo in k-space, resulting in three distinct types of artifacts in partial-Fourier DTI. Here, we present an improved DTI acquisition and reconstruction scheme, capable of generating high-quality and high-SNR DTI data without eddy current-induced artifacts. This new scheme consists of three components, respectively, addressing the three distinct types of artifacts. First, a k-space energy-anchored DTI sequence is designed to recover eddy current-induced signal loss (i.e., Type 1 artifact). Second, a multischeme partial-Fourier reconstruction is used to eliminate artificial signal elevation (i.e., Type 2 artifact) associated with the conventional partial-Fourier reconstruction. Third, a signal intensity correction is applied to remove artificial signal modulations due to eddy current-induced erroneous T2(∗) -weighting (i.e., Type 3 artifact). These systematic improvements will greatly increase the consistency and accuracy of DTI measurements, expanding the utility of DTI in translational applications where quantitative robustness is much needed.

18. A Fourier-based compressed sensing technique for accelerated CT image reconstruction using first-order methods.

Science.gov (United States)

Choi, Kihwan; Li, Ruijiang; Nam, Haewon; Xing, Lei

2014-06-21

As a solution to iterative CT image reconstruction, first-order methods are prominent for the large-scale capability and the fast convergence rate [Formula: see text]. In practice, the CT system matrix with a large condition number may lead to slow convergence speed despite the theoretically promising upper bound. The aim of this study is to develop a Fourier-based scaling technique to enhance the convergence speed of first-order methods applied to CT image reconstruction. Instead of working in the projection domain, we transform the projection data and construct a data fidelity model in Fourier space. Inspired by the filtered backprojection formalism, the data are appropriately weighted in Fourier space. We formulate an optimization problem based on weighted least-squares in the Fourier space and total-variation (TV) regularization in image space for parallel-beam, fan-beam and cone-beam CT geometry. To achieve the maximum computational speed, the optimization problem is solved using a fast iterative shrinkage-thresholding algorithm with backtracking line search and GPU implementation of projection/backprojection. The performance of the proposed algorithm is demonstrated through a series of digital simulation and experimental phantom studies. The results are compared with the existing TV regularized techniques based on statistics-based weighted least-squares as well as basic algebraic reconstruction technique. The proposed Fourier-based compressed sensing (CS) method significantly improves both the image quality and the convergence rate compared to the existing CS techniques.

19. Flux line patterns in Bi2Sr2Ca1Cu2Ox

International Nuclear Information System (INIS)

Weiss, F.; Hardy, V.; Provost, J.; Ruyter, A.; Simon, C.

1994-01-01

Results of the defect influence on the flux line lattice in Bi 2 Sr 2 Ca 1 Cu 2 O x single crystals are presented. These crystals, non irradiated or irradiated at GANIL with heavy ions (Pb 56+ , 6 GeV) have been decorated with Ni particles in the superconducting state using the Bitter technique. The defects involved are columnar defects. Resulting decorated flux line patterns have been characterized using scanning electron microscopy and computer image analysis. Disorder of the decorated flux line networks has been found to be strongly dependent on the defect density, which results from the irradiation. In order to characterize this disorder, a method for determining elastic energy terms in the deformation of flux line patterns has been investigated. This method can be applied if Fourier transforms of the decorated flux line patterns exhibit distinct reflections. (orig.)

20. Explosive Yield Estimation using Fourier Amplitude Spectra of Velocity Histories

Science.gov (United States)

Steedman, D. W.; Bradley, C. R.

2016-12-01

The Source Physics Experiment (SPE) is a series of explosive shots of various size detonated at varying depths in a borehole in jointed granite. The testbed includes an extensive array of accelerometers for measuring the shock environment close-in to the explosive source. One goal of SPE is to develop greater understanding of the explosion phenomenology in all regimes: from near-source, non-linear response to the far-field linear elastic region, and connecting the analyses from the respective regimes. For example, near-field analysis typically involves review of kinematic response (i.e., acceleration, velocity and displacement) in the time domain and looks at various indicators (e.g., peaks, pulse duration) to facilitate comparison among events. Review of far-field data more often is based on study of response in the frequency domain to facilitate comparison of event magnitudes. To try to "bridge the gap" between approaches, we have developed a scaling law for Fourier amplitude spectra of near-field velocity histories that successfully collapses data from a wide range of yields (100 kg to 5000 kg) and range to sensors in jointed granite. Moreover, we show that we can apply this scaling law to data from a new event to accurately estimate the explosive yield of that event. This approach presents a new way of working with near-field data that will be more compatible with traditional methods of analysis of seismic data and should serve to facilitate end-to-end event analysis. The goal is that this new approach to data analysis will eventually result in improved methods for discrimination of event type (i.e., nuclear or chemical explosion, or earthquake) and magnitude.

1. Fourier analysis of time series an introduction

CERN Document Server

Bloomfield, Peter

2000-01-01

A new, revised edition of a yet unrivaled work on frequency domain analysis Long recognized for his unique focus on frequency domain methods for the analysis of time series data as well as for his applied, easy-to-understand approach, Peter Bloomfield brings his well-known 1976 work thoroughly up to date. With a minimum of mathematics and an engaging, highly rewarding style, Bloomfield provides in-depth discussions of harmonic regression, harmonic analysis, complex demodulation, and spectrum analysis. All methods are clearly illustrated using examples of specific data sets, while ample

2. High-resolution wave-theory-based ultrasound reflection imaging using the split-step fourier and globally optimized fourier finite-difference methods

Science.gov (United States)

Huang, Lianjie

2013-10-29

Methods for enhancing ultrasonic reflection imaging are taught utilizing a split-step Fourier propagator in which the reconstruction is based on recursive inward continuation of ultrasonic wavefields in the frequency-space and frequency-wave number domains. The inward continuation within each extrapolation interval consists of two steps. In the first step, a phase-shift term is applied to the data in the frequency-wave number domain for propagation in a reference medium. The second step consists of applying another phase-shift term to data in the frequency-space domain to approximately compensate for ultrasonic scattering effects of heterogeneities within the tissue being imaged (e.g., breast tissue). Results from various data input to the method indicate significant improvements are provided in both image quality and resolution.

3. FFT-BM, Code Accuracy Evaluations with the 1D Fast Fourier Transform (FFT) Methodology

International Nuclear Information System (INIS)

D'Auria, F.

2004-01-01

1 - Description of program or function: FFT-BM is an integrated version of the programs package performing code accuracy evaluations with the 1D Fast Fourier Transform (FFT) methodology. It contains two programs: - CASEM: Takes care of the complete manipulation of data in order to evaluate the quantities through which the FFT method quantifies the code accuracy. - AAWFTO completes the evaluation of the average accuracy (AA) and related weighted frequency (WF) values in order to obtain the AAtot and WFtot values characterising the global calculation performance. 2 - Methods: The Fast Fourier Transform, or FFT, which is based on the Fourier analysis method is an optimised method for calculating the amplitude Vs frequency, of functions or experimental or computed data. In order to apply this methodology, after selecting the parameters to be analyzed, it is necessary to choose the following parameters: - number of curves (exp + calc) to be analyzed; - number of time windows to be analyzed; - sampling frequency; - cut frequency; - time begin and time end of each time window. 3 - Restrictions on the complexity of the problem: Up to 30 curves (exp + calc) and 5 time windows may be analyzed

4. Adaptive Filtering to Enhance Noise Immunity of Impedance and Admittance Spectroscopy: Comparison with Fourier Transformation

Science.gov (United States)

Stupin, Daniil D.; Koniakhin, Sergei V.; Verlov, Nikolay A.; Dubina, Michael V.

2017-05-01

The time-domain technique for impedance spectroscopy consists of computing the excitation voltage and current response Fourier images by fast or discrete Fourier transformation and calculating their relation. Here we propose an alternative method for excitation voltage and current response processing for deriving a system impedance spectrum based on a fast and flexible adaptive filtering method. We show the equivalence between the problem of adaptive filter learning and deriving the system impedance spectrum. To be specific, we express the impedance via the adaptive filter weight coefficients. The noise-canceling property of adaptive filtering is also justified. Using the RLC circuit as a model system, we experimentally show that adaptive filtering yields correct admittance spectra and elements ratings in the high-noise conditions when the Fourier-transform technique fails. Providing the additional sensitivity of impedance spectroscopy, adaptive filtering can be applied to otherwise impossible-to-interpret time-domain impedance data. The advantages of adaptive filtering are justified with practical living-cell impedance measurements.

5. A Fourier transform method for Vsin i estimations under nonlinear Limb-Darkening laws

Energy Technology Data Exchange (ETDEWEB)

Levenhagen, R. S., E-mail: ronaldo.levenhagen@gmail.com [Universidade Federal de São Paulo, Depto. Ciências Exatas e da Terra, Rua Prof. Arthur Riedel, 275, Jd. Eldorado, CEP 09972-270 Diadema, SP (Brazil)

2014-12-10

Star rotation offers us a large horizon for the study of many important physical issues pertaining to stellar evolution. Currently, four methods are widely used to infer rotation velocities, namely those related to line width calibrations, on the fitting of synthetic spectra, interferometry, and on Fourier transforms (FTs) of line profiles. Almost all of the estimations of stellar projected rotation velocities using the Fourier method in the literature have been addressed with the use of linear limb-darkening (LD) approximations during the evaluation of rotation profiles and their cosine FTs, which in certain cases, lead to discrepant velocity estimates. In this work, we introduce new mathematical expressions of rotation profiles and their Fourier cosine transforms assuming three nonlinear LD laws—quadratic, square-root, and logarithmic—and study their applications with and without gravity-darkening (GD) and geometrical flattening (GF) effects. Through an analysis of He I models in the visible range accounting for both limb and GD, we find out that, for classical models without rotationally driven effects, all the Vsin i values are too close to each other. On the other hand, taking into account GD and GF, the Vsin i obtained with the linear law result in Vsin i values that are systematically smaller than those obtained with the other laws. As a rule of thumb, we apply these expressions to the FT method to evaluate the projected rotation velocity of the emission B-type star Achernar (α Eri).

6. Singularities of affine fibrations in the regularity theory of Fourier integral operators

International Nuclear Information System (INIS)

Ruzhansky, M V

2000-01-01

We consider regularity properties of Fourier integral operators in various function spaces. The most interesting case is the L p spaces, for which survey of recent results is given. For example, sharp orders are known for operators satisfying the so-called smooth factorization condition. Here this condition is analyzed in both real and complex settings. In the letter case, conditions for the continuity of Fourier integral operators are related to singularities of affine fibrations in C n (or subsets of C n ) specified by the kernels of Jacobi matrices of holomorphic maps. Singularities of such fibrations are analyzed in this paper in the general case. In particular, it is shown that if the dimension n or the rank of the Jacobi matrix is small, then all singularities of an affine fibration are removable. The fibration associated with a Fourier integral operator is given by the kernels of the Hessian of the phase function of the operator. On the basis of an analysis of singularities for operators commuting with translations we show in a number of cases that the factorization condition is satisfied, which leads to L p estimates for operators. In other cases, examples are given in which the factorization condition fails. The results are applied to deriving L p estimates for solutions of the Cauchy problem for hyperbolic partial differential operators

7. A perspective on two chemometrics tools: PCA and MCR, and introduction of a new one: Pattern recognition entropy (PRE), as applied to XPS and ToF-SIMS depth profiles of organic and inorganic materials

Science.gov (United States)

Chatterjee, Shiladitya; Singh, Bhupinder; Diwan, Anubhav; Lee, Zheng Rong; Engelhard, Mark H.; Terry, Jeff; Tolley, H. Dennis; Gallagher, Neal B.; Linford, Matthew R.

2018-03-01

X-ray photoelectron spectroscopy (XPS) and time-of-flight secondary ion mass spectrometry (ToF-SIMS) are much used analytical techniques that provide information about the outermost atomic and molecular layers of materials. In this work, we discuss the application of multivariate spectral techniques, including principal component analysis (PCA) and multivariate curve resolution (MCR), to the analysis of XPS and ToF-SIMS depth profiles. Multivariate analyses often provide insight into data sets that is not easily obtained in a univariate fashion. Pattern recognition entropy (PRE), which has its roots in Shannon's information theory, is also introduced. This approach is not the same as the mutual information/entropy approaches sometimes used in data processing. A discussion of the theory of each technique is presented. PCA, MCR, and PRE are applied to four different data sets obtained from: a ToF-SIMS depth profile through ca. 100 nm of plasma polymerized C3F6 on Si, a ToF-SIMS depth profile through ca. 100 nm of plasma polymerized PNIPAM (poly (N-isopropylacrylamide)) on Si, an XPS depth profile through a film of SiO2 on Si, and an XPS depth profile through a film of Ta2O5 on Ta. PCA, MCR, and PRE reveal the presence of interfaces in the films, and often indicate that the first few scans in the depth profiles are different from those that follow. PRE and backward difference PRE provide this information in a straightforward fashion. Rises in the PRE signals at interfaces suggest greater complexity to the corresponding spectra. Results from PCA, especially for the higher principal components, were sometimes difficult to understand. MCR analyses were generally more interpretable.

8. Applied geodesy

International Nuclear Information System (INIS)

Turner, S.

1987-01-01

This volume is based on the proceedings of the CERN Accelerator School's course on Applied Geodesy for Particle Accelerators held in April 1986. The purpose was to record and disseminate the knowledge gained in recent years on the geodesy of accelerators and other large systems. The latest methods for positioning equipment to sub-millimetric accuracy in deep underground tunnels several tens of kilometers long are described, as well as such sophisticated techniques as the Navstar Global Positioning System and the Terrameter. Automation of better known instruments such as the gyroscope and Distinvar is also treated along with the highly evolved treatment of components in a modern accelerator. Use of the methods described can be of great benefit in many areas of research and industrial geodesy such as surveying, nautical and aeronautical engineering, astronomical radio-interferometry, metrology of large components, deformation studies, etc

9. Applied mathematics

International Nuclear Information System (INIS)

Nedelec, J.C.

1988-01-01

The 1988 progress report of the Applied Mathematics center (Polytechnic School, France), is presented. The research fields of the Center are the scientific calculus, the probabilities and statistics and the video image synthesis. The research topics developed are: the analysis of numerical methods, the mathematical analysis of the physics and mechanics fundamental models, the numerical solution of complex models related to the industrial problems, the stochastic calculus and the brownian movement, the stochastic partial differential equations, the identification of the adaptive filtering parameters, the discrete element systems, statistics, the stochastic control and the development, the image synthesis techniques for education and research programs. The published papers, the congress communications and the thesis are listed [fr

10. Iterative wave-front reconstruction in the Fourier domain.

Science.gov (United States)

Bond, Charlotte Z; Correia, Carlos M; Sauvage, Jean-François; Neichel, Benoit; Fusco, Thierry

2017-05-15

The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data set which conform to specific boundary requirements, whereas wave-front sensor data is typically defined over a circular domain (the telescope pupil). Here we present an iterative Gerchberg routine modified for the purposes of discrete wave-front reconstruction which adapts the measurement data (wave-front sensor slopes) for Fourier analysis, fulfilling the requirements of the fast Fourier transform (FFT) and providing accurate reconstruction. The routine is used in the adaptation step only and can be coupled to any other Wiener-like or least-squares method. We compare simulations using this method with previous Fourier methods and show an increase in performance in terms of Strehl ratio and a reduction in noise propagation for a 40×40 SPHERE-like adaptive optics system. For closed loop operation with minimal iterations the Gerchberg method provides an improvement in Strehl, from 95.4% to 96.9% in K-band. This corresponds to ~ 40 nm improvement in rms, and avoids the high spatial frequency errors present in other methods, providing an increase in contrast towards the edge of the correctable band.

11. Electro-Optical Imaging Fourier-Transform Spectrometer

Science.gov (United States)

Chao, Tien-Hsin; Zhou, Hanying

2006-01-01

An electro-optical (E-O) imaging Fourier-transform spectrometer (IFTS), now under development, is a prototype of improved imaging spectrometers to be used for hyperspectral imaging, especially in the infrared spectral region. Unlike both imaging and non-imaging traditional Fourier-transform spectrometers, the E-O IFTS does not contain any moving parts. Elimination of the moving parts and the associated actuator mechanisms and supporting structures would increase reliability while enabling reductions in size and mass, relative to traditional Fourier-transform spectrometers that offer equivalent capabilities. Elimination of moving parts would also eliminate the vibrations caused by the motions of those parts. Figure 1 schematically depicts a traditional Fourier-transform spectrometer, wherein a critical time delay is varied by translating one the mirrors of a Michelson interferometer. The time-dependent optical output is a periodic representation of the input spectrum. Data characterizing the input spectrum are generated through fast-Fourier-transform (FFT) post-processing of the output in conjunction with the varying time delay.

12. Ballooning modes or Fourier modes in a toroidal plasma?

International Nuclear Information System (INIS)

Connor, J.W.; Taylor, J.B.

1987-01-01

The relationship between two different descriptions of eigenmodes in a torus is investigated. In one the eigenmodes are similar to Fourier modes in a cylinder and are highly localized near a particular rational surface. In the other they are the so-called ballooning modes that extend over many rational surfaces. Using a model that represents both drift waves and resistive interchanges the transition from one of these structures to the other is investigated. In this simplified model the transition depends on a single parameter which embodies the competition between toroidal coupling of Fourier modes (which enhances ballooning) and variation in frequency of Fourier modes from one rational surface to another (which diminishes ballooning). As the coupling is increased each Fourier mode acquires a sideband on an adjacent rational surface and these sidebands then expand across the radius to form the extended mode described by the conventional ballooning mode approximation. This analysis shows that the ballooning approximation is appropriate for drift waves in a tokamak but not for resistive interchanges in a pinch. In the latter the conventional ballooning effect is negligible but they may nevertheless show a ballooning feature. This is localized near the same rational surface as the primary Fourier mode and so does not lead to a radially extended structure

13. Comparative analysis of imaging configurations and objectives for Fourier microscopy.

Science.gov (United States)

Kurvits, Jonathan A; Jiang, Mingming; Zia, Rashid

2015-11-01

Fourier microscopy is becoming an increasingly important tool for the analysis of optical nanostructures and quantum emitters. However, achieving quantitative Fourier space measurements requires a thorough understanding of the impact of aberrations introduced by optical microscopes that have been optimized for conventional real-space imaging. Here we present a detailed framework for analyzing the performance of microscope objectives for several common Fourier imaging configurations. To this end, we model objectives from Nikon, Olympus, and Zeiss using parameters that were inferred from patent literature and confirmed, where possible, by physical disassembly. We then examine the aberrations most relevant to Fourier microscopy, including the alignment tolerances of apodization factors for different objective classes, the effect of magnification on the modulation transfer function, and vignetting-induced reductions of the effective numerical aperture for wide-field measurements. Based on this analysis, we identify an optimal objective class and imaging configuration for Fourier microscopy. In addition, the Zemax files for the objectives and setups used in this analysis have been made publicly available as a resource for future studies.

14. Screening retinal transplants with Fourier-domain OCT

Science.gov (United States)

Rao, Bin

2009-02-01

Transplant technologies have been studied for the recovery of vision loss from retinitis pigmentosa (RP) and age-related macular degeneration (AMD). In several rodent retinal degeneration models and in patients, retinal progenitor cells transplanted as layers to the subretinal space have been shown to restore or preserve vision. The methods for evaluation of transplants are expensive considering the large amount of animals. Alternatively, time-domain Stratus OCT was previously shown to be able to image the morphological structure of transplants to some extent, but could not clearly identify laminated transplants. The efficacy of screening retinal transplants with Fourier-domain OCT was studied on 37 S334ter line 3 rats with retinal degeneration 6-67 days after transplant surgery. The transplants were morphologically categorized as no transplant, detachment, rosettes, small laminated area and larger laminated area with both Fourier-domain OCT and histology. The efficacy of Fourier-domain OCT in screening retinal transplants was evaluated by comparing the categorization results with OCT and histology. Additionally, 4 rats were randomly selected for multiple OCT examinations (1, 5, 9, 14 and 21days post surgery) in order to determine the earliest image time of OCT examination since the transplanted tissue may need some time to show its tendency of growing. Finally, we demonstrated the efficacy of Fourier-domain OCT in screening retinal transplants in early stages and determined the earliest imaging time for OCT. Fourier-domain OCT makes itself valuable in saving resource spent on animals with unsuccessful transplants.

15. Periodically distributed objects with quasicrystalline diffraction pattern

Energy Technology Data Exchange (ETDEWEB)

Wolny, Janusz, E-mail: wolny@fis.agh.edu.pl; Strzalka, Radoslaw [Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow (Poland); Kuczera, Pawel [Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow (Poland); Laboratory of Crystallography, ETH Zurich, Wolfgang-Pauli-Strasse 10, CH-8093 Zurich (Switzerland)

2015-03-30

It is possible to construct fully periodically distributed objects with a diffraction pattern identical to the one obtained for quasicrystals. These objects are probability distributions of distances obtained in the statistical approach to aperiodic structures distributed periodically. The diffraction patterns have been derived by using a two-mode Fourier transform—a very powerful method not used in classical crystallography. It is shown that if scaling is present in the structure, this two-mode Fourier transform can be reduced to a regular Fourier transform with appropriately rescaled scattering vectors and added phases. Detailed case studies for model sets 1D Fibonacci chain and 2D Penrose tiling are discussed. Finally, it is shown that crystalline, quasicrystalline, and approximant structures can be treated in the same way.

International Nuclear Information System (INIS)

Mallozzi, P.J.; Epstein, H.M.; Jung, R.G.; Applebaum, D.C.; Fairand, B.P.; Gallagher, W.J.; Uecker, R.L.; Muckerheide, M.C.

1979-01-01

17. Anatomic and energy variation of scatter compensation for digital chest radiography with Fourier deconvolution

International Nuclear Information System (INIS)

Floyd, C.E.; Beatty, P.T.; Ravin, C.E.

1988-01-01

The Fourier deconvolution algorithm for scatter compensation in digital chest radiography has been evaluated in four anatomically different regions at three energies. A shift invariant scatter distribution shape, optimized for the lung region at 140 kVp, was applied at 90 kVp and 120 kVp in the lung, retrocardiac, subdiaphragmatic, and thoracic spine regions. Scatter estimates from the deconvolution were compared with measured values. While some regional variation is apparent, the use of a shift invariant scatter distribution shape (optimized for a given energy) produces reasonable scatter compensation in the chest. A different set of deconvolution parameters were required at the different energies

18. Applications of asynoptic space - Time Fourier transform methods to scanning satellite measurements

Science.gov (United States)

Lait, Leslie R.; Stanford, John L.

1988-01-01

A method proposed by Salby (1982) for computing the zonal space-time Fourier transform of asynoptically acquired satellite data is discussed. The method and its relationship to other techniques are briefly described, and possible problems in applying it to real data are outlined. Examples of results obtained using this technique are given which demonstrate its sensitivity to small-amplitude signals. A number of waves are found which have previously been observed as well as two not heretofore reported. A possible extension of the method which could increase temporal and longitudinal resolution is described.

19. On the Approximation of Generalized Lipschitz Function by Euler Means of Conjugate Series of Fourier Series

Science.gov (United States)

Kushwaha, Jitendra Kumar

2013-01-01

Approximation theory is a very important field which has various applications in pure and applied mathematics. The present study deals with a new theorem on the approximation of functions of Lipschitz class by using Euler's mean of conjugate series of Fourier series. In this paper, the degree of approximation by using Euler's means of conjugate of functions belonging to Lip (ξ(t), p) class has been obtained. Lipα and Lip (α, p) classes are the particular cases of Lip (ξ(t), p) class. The main result of this paper generalizes some well-known results in this direction. PMID:24379744

20. Pfaff equation and Fourier analysis to phase extraction from an interferogram with carrier frequency

International Nuclear Information System (INIS)

Lara-Cortez, Francisco; Meneses-Fabian, Cruz; Rodriguez-Zurita, Gustavo

2011-01-01

In the phase extraction techniques, one of the steps most used is to calculate the phase unwrapping from the wrapped phase, which is generally obtained via the inverse tangent function. With the idea to avoid this process, in the present manuscript a method based in the solution of the Pfaff equations is proposed. It is shown that the Pfaff equation is formed with the phase gradient and an auxiliary vector. The phase gradient is obtained from an interference patron with carrier frequency by applying the Fourier transform method and the partial derivatives. In the present manuscript, mathematical analysis, numerical simulation, and the phase extraction of some experimental interferograms are shown.