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...

The Fourier decomposition method for nonlinear and non-stationary time series analysis.

Science.gov (United States)

Singh, Pushpendra; Joshi, Shiv Dutt; Patney, Rakesh Kumar; Saha, Kaushik

2017-03-01

for many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of 'Fourier intrinsic band functions' (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of band-limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a time-frequency-energy (TFE) distribution that reveals the intrinsic structure of a data. Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms.

Non-Fourier based thermal-mechanical tissue damage prediction for thermal ablation.

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Li, Xin; Zhong, Yongmin; Smith, Julian; Gu, Chengfan

2017-01-02

Prediction of tissue damage under thermal loads plays important role for thermal ablation planning. A new methodology is presented in this paper by combing non-Fourier bio-heat transfer, constitutive elastic mechanics as well as non-rigid motion of dynamics to predict and analyze thermal distribution, thermal-induced mechanical deformation and thermal-mechanical damage of soft tissues under thermal loads. Simulations and comparison analysis demonstrate that the proposed methodology based on the non-Fourier bio-heat transfer can account for the thermal-induced mechanical behaviors of soft tissues and predict tissue thermal damage more accurately than classical Fourier bio-heat transfer based model.

Fourier analysis for hydrostatic pressure sensing in a polarization-maintaining photonic crystal fiber

International Nuclear Information System (INIS)

Childs, Paul; Wong, Allan C. L.; Fu, H. Y.; Liao, Yanbiao; Tam, Hwayaw; Lu Chao; Wai, P. K. A.

2010-01-01

.We measured the hydrostatic pressure dependence of the birefringence and birefringent dispersion of a Sagnac interferometric sensor incorporating a length of highly birefringent photonic crystal fiber using Fourier analysis. Sensitivity of both the phase and chirp spectra to hydrostatic pressure is demonstrated. Using this analysis, phase-based measurements showed a good linearity with an effective sensitivity of 9.45nm/MPa and an accuracy of ±7.8kPa using wavelength-encoded data and an effective sensitivity of -55.7cm -1 /MPa and an accuracy of ±4.4kPa using wavenumber-encoded data. Chirp-based measurements, though nonlinear in response, showed an improvement in accuracy at certain pressure ranges with an accuracy of ±5.5kPa for the full range of measured pressures using wavelength-encoded data and dropping to within ±2.5kPa in the range of 0.17 to 0.4MPa using wavenumber-encoded data. Improvements of the accuracy demonstrated the usefulness of implementing chirp-based analysis for sensing purposes.

The Use of Continuous Wavelet Transform Based on the Fast Fourier Transform in the Analysis of Multi-channel Electrogastrography Recordings.

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Komorowski, Dariusz; Pietraszek, Stanislaw

2016-01-01

This paper presents the analysis of multi-channel electrogastrographic (EGG) signals using the continuous wavelet transform based on the fast Fourier transform (CWTFT). The EGG analysis was based on the determination of the several signal parameters such as dominant frequency (DF), dominant power (DP) and index of normogastria (NI). The use of continuous wavelet transform (CWT) allows for better visible localization of the frequency components in the analyzed signals, than commonly used short-time Fourier transform (STFT). Such an analysis is possible by means of a variable width window, which corresponds to the scale time of observation (analysis). Wavelet analysis allows using long time windows when we need more precise low-frequency information, and shorter when we need high frequency information. Since the classic CWT transform requires considerable computing power and time, especially while applying it to the analysis of long signals, the authors used the CWT analysis based on the fast Fourier transform (FFT). The CWT was obtained using properties of the circular convolution to improve the speed of calculation. This method allows to obtain results for relatively long records of EGG in a fairly short time, much faster than using the classical methods based on running spectrum analysis (RSA). In this study authors indicate the possibility of a parametric analysis of EGG signals using continuous wavelet transform which is the completely new solution. The results obtained with the described method are shown in the example of an analysis of four-channel EGG recordings, performed for a non-caloric meal.

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...

Validation of Fourier analysis of videokeratographic data.

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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.

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.

The geometric phase analysis method based on the local high resolution discrete Fourier transform for deformation measurement

International Nuclear Information System (INIS)

Dai, Xianglu; Xie, Huimin; Wang, Huaixi; Li, Chuanwei; Wu, Lifu; Liu, Zhanwei

2014-01-01

The geometric phase analysis (GPA) method based on the local high resolution discrete Fourier transform (LHR-DFT) for deformation measurement, defined as LHR-DFT GPA, is proposed to improve the measurement accuracy. In the general GPA method, the fundamental frequency of the image plays a crucial role. However, the fast Fourier transform, which is generally employed in the general GPA method, could make it difficult to locate the fundamental frequency accurately when the fundamental frequency is not located at an integer pixel position in the Fourier spectrum. This study focuses on this issue and presents a LHR-DFT algorithm that can locate the fundamental frequency with sub-pixel precision in a specific frequency region for the GPA method. An error analysis is offered and simulation is conducted to verify the effectiveness of the proposed method; both results show that the LHR-DFT algorithm can accurately locate the fundamental frequency and improve the measurement accuracy of the GPA method. Furthermore, typical tensile and bending tests are carried out and the experimental results verify the effectiveness of the proposed method. (paper)

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

Analysis of the intergranular fracture surface by the Fourier spectrum method

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Hao Yao; Tian Jifeng; Wang Zhongguang (National Lab. for Fatigue and Fracture of Materials, Inst. of Metal Research, Academia Sinica, Shen Yang (China))

1991-11-30

A quantitative analysis of the fracture surface of a 1045 steel was undertaken in order to relate important microstructural features to brittle intergranular fractures in the steel. It was found that the character of the profile was not random but periodic. There is a direct correspondence between the Fourier spectrum of the profile and the microstructure features. Utilization of secondary-electron line scanning facilitated the analysis of the fracture surface in this case. The results of the analysis from both the profile and the scanning line showed that the first autocorrelation length is related to the average grain size and that the total power corresponds to the impact energy of the fracture. (orig.).

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.

Fourier-Mellin moment-based intertwining map for image encryption

Science.gov (United States)

Kaur, Manjit; Kumar, Vijay

2018-03-01

In this paper, a robust image encryption technique that utilizes Fourier-Mellin moments and intertwining logistic map is proposed. Fourier-Mellin moment-based intertwining logistic map has been designed to overcome the issue of low sensitivity of an input image. Multi-objective Non-Dominated Sorting Genetic Algorithm (NSGA-II) based on Reinforcement Learning (MNSGA-RL) has been used to optimize the required parameters of intertwining logistic map. Fourier-Mellin moments are used to make the secret keys more secure. Thereafter, permutation and diffusion operations are carried out on input image using secret keys. The performance of proposed image encryption technique has been evaluated on five well-known benchmark images and also compared with seven well-known existing encryption techniques. The experimental results reveal that the proposed technique outperforms others in terms of entropy, correlation analysis, a unified average changing intensity and the number of changing pixel rate. The simulation results reveal that the proposed technique provides high level of security and robustness against various types of attacks.

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...

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

Spherical aberration compensation method for long focal-length measurement based on Talbot interferometry

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Luo, Yupeng; Huang, Xiao; Bai, Jian; Du, Juan; Liu, Qun; Luo, Yujie; Luo, Jia

2017-08-01

Large-aperture and long focal-length lens is widely used in high energy laser system. The method based on Talbot interferometry is a reliable method to measure the focal length of such elements. By employing divergent beam and two gratings of different periods, this method could realize full-aperture measurement, higher accuracy and better repeatability. However, it does not take into account the spherical aberration of the measured lens resulting in the moiré fringes bending, which will introduce measurement error. Furthermore, in long-focal measurement with divergent beam, this error is an important factor affecting the measurement accuracy. In this paper, we propose a new spherical aberration compensation method, which could significantly reduce the measurement error. Characterized by central-symmetric scanning window, the proposed method is based on the relationship between spherical aberration and the lens aperture. Angle data of moiré fringes in each scanning window is retrieved by Fourier analysis and statistically fitted to estimate a globally optimum value for spherical-aberration-free focal length calculation. Simulation and experiment have been carried out. Compared to the previous work, the proposed method is able to reduce the relative measurement error by 50%. The effect of scanning window size and shift step length on the results is also discussed.

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.

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...

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...

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)

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.

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.

Fourier analysis of the aerodynamic behavior of cup anemometers

International Nuclear Information System (INIS)

Pindado, Santiago; Pérez, Imanol; Aguado, Maite

2013-01-01

The calibration results (the transfer function) of an anemometer equipped with several cup rotors were analyzed and correlated with the aerodynamic forces measured on the isolated cups in a wind tunnel. The correlation was based on a Fourier analysis of the normal-to-the-cup aerodynamic force. Three different cup shapes were studied: typical conical cups, elliptical cups and porous cups (conical-truncated shape). Results indicated a good correlation between the anemometer factor, K, and the ratio between the first two coefficients in the Fourier series decomposition of the normal-to-the-cup aerodynamic force. (paper)

Discrete Fourier Transform Analysis in a Complex Vector Space

Science.gov (United States)

Dean, Bruce H.

2009-01-01

Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.

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

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)

An improved model for whole genome phylogenetic analysis by Fourier transform.

Science.gov (United States)

Yin, Changchuan; Yau, Stephen S-T

2015-10-07

DNA sequence similarity comparison is one of the major steps in computational phylogenetic studies. The sequence comparison of closely related DNA sequences and genomes is usually performed by multiple sequence alignments (MSA). While the MSA method is accurate for some types of sequences, it may produce incorrect results when DNA sequences undergone rearrangements as in many bacterial and viral genomes. It is also limited by its computational complexity for comparing large volumes of data. Previously, we proposed an alignment-free method that exploits the full information contents of DNA sequences by Discrete Fourier Transform (DFT), but still with some limitations. Here, we present a significantly improved method for the similarity comparison of DNA sequences by DFT. In this method, we map DNA sequences into 2-dimensional (2D) numerical sequences and then apply DFT to transform the 2D numerical sequences into frequency domain. In the 2D mapping, the nucleotide composition of a DNA sequence is a determinant factor and the 2D mapping reduces the nucleotide composition bias in distance measure, and thus improving the similarity measure of DNA sequences. To compare the DFT power spectra of DNA sequences with different lengths, we propose an improved even scaling algorithm to extend shorter DFT power spectra to the longest length of the underlying sequences. After the DFT power spectra are evenly scaled, the spectra are in the same dimensionality of the Fourier frequency space, then the Euclidean distances of full Fourier power spectra of the DNA sequences are used as the dissimilarity metrics. The improved DFT method, with increased computational performance by 2D numerical representation, can be applicable to any DNA sequences of different length ranges. We assess the accuracy of the improved DFT similarity measure in hierarchical clustering of different DNA sequences including simulated and real datasets. The method yields accurate and reliable phylogenetic trees

Polynomial Phase Estimation Based on Adaptive Short-Time Fourier Transform.

Science.gov (United States)

Jing, Fulong; Zhang, Chunjie; Si, Weijian; Wang, Yu; Jiao, Shuhong

2018-02-13

Polynomial phase signals (PPSs) have numerous applications in many fields including radar, sonar, geophysics, and radio communication systems. Therefore, estimation of PPS coefficients is very important. In this paper, a novel approach for PPS parameters estimation based on adaptive short-time Fourier transform (ASTFT), called the PPS-ASTFT estimator, is proposed. Using the PPS-ASTFT estimator, both one-dimensional and multi-dimensional searches and error propagation problems, which widely exist in PPSs field, are avoided. In the proposed algorithm, the instantaneous frequency (IF) is estimated by S-transform (ST), which can preserve information on signal phase and provide a variable resolution similar to the wavelet transform (WT). The width of the ASTFT analysis window is equal to the local stationary length, which is measured by the instantaneous frequency gradient (IFG). The IFG is calculated by the principal component analysis (PCA), which is robust to the noise. Moreover, to improve estimation accuracy, a refinement strategy is presented to estimate signal parameters. Since the PPS-ASTFT avoids parameter search, the proposed algorithm can be computed in a reasonable amount of time. The estimation performance, computational cost, and implementation of the PPS-ASTFT are also analyzed. The conducted numerical simulations support our theoretical results and demonstrate an excellent statistical performance of the proposed algorithm.

Uncertainty Principles and Fourier Analysis

Indian Academy of Sciences (India)

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.

Bladed wheels damage detection through Non-Harmonic Fourier Analysis improved algorithm

Science.gov (United States)

Neri, P.

2017-05-01

Recent papers introduced the Non-Harmonic Fourier Analysis for bladed wheels damage detection. This technique showed its potential in estimating the frequency of sinusoidal signals even when the acquisition time is short with respect to the vibration period, provided that some hypothesis are fulfilled. Anyway, previously proposed algorithms showed severe limitations in cracks detection at their early stage. The present paper proposes an improved algorithm which allows to detect a blade vibration frequency shift due to a crack whose size is really small compared to the blade width. Such a technique could be implemented for condition-based maintenance, allowing to use non-contact methods for vibration measurements. A stator-fixed laser sensor could monitor all the blades as they pass in front of the spot, giving precious information about the wheel health. This configuration determines an acquisition time for each blade which become shorter as the machine rotational speed increases. In this situation, traditional Discrete Fourier Transform analysis results in poor frequency resolution, being not suitable for small frequency shift detection. Non-Harmonic Fourier Analysis instead showed high reliability in vibration frequency estimation even with data samples collected in a short time range. A description of the improved algorithm is provided in the paper, along with a comparison with the previous one. Finally, a validation of the method is presented, based on finite element simulations results.

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.

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.

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.

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.

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.

Non-destructive testing of full-length bonded rock bolts based on HHT signal analysis

Science.gov (United States)

Shi, Z. M.; Liu, L.; Peng, M.; Liu, C. C.; Tao, F. J.; Liu, C. S.

2018-04-01

Full-length bonded rock bolts are commonly used in mining, tunneling and slope engineering because of their simple design and resistance to corrosion. However, the length of a rock bolt and grouting quality do not often meet the required design standards in practice because of the concealment and complexity of bolt construction. Non-destructive testing is preferred when testing a rock bolt's quality because of the convenience, low cost and wide detection range. In this paper, a signal analysis method for the non-destructive sound wave testing of full-length bonded rock bolts is presented, which is based on the Hilbert-Huang transform (HHT). First, we introduce the HHT analysis method to calculate the bolt length and identify defect locations based on sound wave reflection test signals, which includes decomposing the test signal via empirical mode decomposition (EMD), selecting the intrinsic mode functions (IMF) using the Pearson Correlation Index (PCI) and calculating the instantaneous phase and frequency via the Hilbert transform (HT). Second, six model tests are conducted using different grouting defects and bolt protruding lengths to verify the effectiveness of the HHT analysis method. Lastly, the influence of the bolt protruding length on the test signal, identification of multiple reflections from defects, bolt end and protruding end, and mode mixing from EMD are discussed. The HHT analysis method can identify the bolt length and grouting defect locations from signals that contain noise at multiple reflected interfaces. The reflection from the long protruding end creates an irregular test signal with many frequency peaks on the spectrum. The reflections from defects barely change the original signal because they are low energy, which cannot be adequately resolved using existing methods. The HHT analysis method can identify reflections from the long protruding end of the bolt and multiple reflections from grouting defects based on mutations in the instantaneous

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

Dynamic Allan Variance Analysis Method with Time-Variant Window Length Based on Fuzzy Control

Directory of Open Access Journals (Sweden)

Shanshan Gu

2015-01-01

Full Text Available To solve the problem that dynamic Allan variance (DAVAR with fixed length of window cannot meet the identification accuracy requirement of fiber optic gyro (FOG signal over all time domains, a dynamic Allan variance analysis method with time-variant window length based on fuzzy control is proposed. According to the characteristic of FOG signal, a fuzzy controller with the inputs of the first and second derivatives of FOG signal is designed to estimate the window length of the DAVAR. Then the Allan variances of the signals during the time-variant window are simulated to obtain the DAVAR of the FOG signal to describe the dynamic characteristic of the time-varying FOG signal. Additionally, a performance evaluation index of the algorithm based on radar chart is proposed. Experiment results show that, compared with different fixed window lengths DAVAR methods, the change of FOG signal with time can be identified effectively and the evaluation index of performance can be enhanced by 30% at least by the DAVAR method with time-variant window length based on fuzzy control.

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.

Optical polarimeter based on Fourier analysis and electronic control

International Nuclear Information System (INIS)

Vilardy, J; Salas, V.; Torres, C.

2016-01-01

In this paper, we show the design and implementation of an optical polarimeter using electronic control and the Fourier analysis. The polarimeter prototype will be used as a main tool for the students of the Universidad Popular del Cesar that belong to the following university programs: Electronics engineering (optoelectronics area), Math and Physics degree and the Master in Physics Sciences, in order to learning the theory and experimental aspects of the state of optical polarization via the Stokes vector measurement. Using the electronic polarimeter proposed in this paper, the students will be able to observe (in an optical bench) and understand the different interactions of the states of optical polarization when the optical waves pass through to the polarizers and retarder waves plates. The electronic polarimeter has a software that captures the optical intensity measurement and evaluates the Stokes vector. (Author)

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...

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

Quantitative evaluation of changes in eyeball shape in emmetropization and myopic changes based on elliptic fourier descriptors.

Science.gov (United States)

Ishii, Kotaro; Iwata, Hiroyoshi; Oshika, Tetsuro

2011-11-04

To evaluate changes in eyeball shape in emmetropization and myopic changes using magnetic resonance imaging (MRI) and elliptic Fourier descriptors (EFDs). The subjects were 105 patients (age range, 1 month-19 years) who underwent head MRI. The refractive error was determined in 30 patients, and eyeball shape was expressed numerically by principal components analysis of standardized EFDs. In the first principal component (PC1; the oblate-to-prolate change), the proportion of variance/total variance in the development of the eyeball shape was 76%. In all subjects, PC1 showed a significant correlation with age (Pearson r = -0.314; P = 0.001), axial length (AL, r = -0.378; P eyeball shape from oblate to prolate was clarified by quantitative analysis based on EFDs. The results showed clear differences between age groups with regard to changes in the shape of the eyeball, the correlation between these changes, and refractive status changes.

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.

Determination of Wind Turbine Near-Wake Length Based on Stability Analysis

International Nuclear Information System (INIS)

Sørensen, Jens N; Mikkelsen, Robert; Sarmast, Sasan; Ivanell, Stefan; Henningson, Dan

2014-01-01

A numerical study on the wake behind a wind turbine is carried out focusing on determining the length of the near-wake based on the instability onset of the trailing tip vortices shed from the turbine blades. The numerical model is based on large-eddy simulations (LES) of the Navier-Stokes equations using the actuator line (ACL) method. The wake is perturbed by applying stochastic or harmonic excitations in the neighborhood of the tips of the blades. The flow field is then analyzed to obtain the stability properties of the tip vortices in the wake of the wind turbine. As a main outcome of the study it is found that the amplification of specific waves (traveling structures) along the tip vortex spirals is responsible for triggering the instability leading to wake breakdown. The presence of unstable modes in the wake is related to the mutual inductance (vortex pairing) instability where there is an out-of-phase displacement of successive helix turns. Furthermore, using the non-dimensional growth rate, it is found that the pairing instability has a universal growth rate equal to π/2. Using this relationship, and the assumption that breakdown to turbulence occurs once a vortex has experienced sufficient growth, we provide an analytical relationship between the turbulence intensity and the stable wake length. The analysis leads to a simple expression for determining the length of the near wake. This expression shows that the near wake length is inversely proportional to thrust, tip speed ratio and the logarithmic of the turbulence intensity

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

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...

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

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.

Fourier Series

Indian Academy of Sciences (India)

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.

Fourier diffraction theorem for diffusion-based thermal tomography

International Nuclear Information System (INIS)

Baddour, Natalie

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

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

Motion analysis of optically trapped particles and cells using 2D Fourier analysis

DEFF Research Database (Denmark)

Kristensen, Martin Verner; Ahrendt, Peter; Lindballe, Thue Bjerring

2012-01-01

Motion analysis of optically trapped objects is demonstrated using a simple 2D Fourier transform technique. The displacements of trapped objects are determined directly from the phase shift between the Fourier transform of subsequent images. Using end-and side-view imaging, the stiffness...... of the trap is determined in three dimensions. The Fourier transform method is simple to implement and applicable in cases where the trapped object changes shape or where the lighting conditions change. This is illustrated by tracking a fluorescent particle and a myoblast cell, with subsequent determination...

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

Analysis and application of Fourier transform spectroscopy in atmospheric remote sensing

Science.gov (United States)

Park, J. H.

1984-01-01

An analysis method for Fourier transform spectroscopy is summarized with applications to various types of distortion in atmospheric absorption spectra. This analysis method includes the fast Fourier transform method for simulating the interferometric spectrum and the nonlinear least-squares method for retrieving the information from a measured spectrum. It is shown that spectral distortions can be simulated quite well and that the correct information can be retrieved from a distorted spectrum by this analysis technique.

Accuracy evaluation of Fourier series analysis and singular spectrum analysis for predicting the volume of motorcycle sales in Indonesia

Science.gov (United States)

Sasmita, Yoga; Darmawan, Gumgum

2017-08-01

This research aims to evaluate the performance of forecasting by Fourier Series Analysis (FSA) and Singular Spectrum Analysis (SSA) which are more explorative and not requiring parametric assumption. Those methods are applied to predicting the volume of motorcycle sales in Indonesia from January 2005 to December 2016 (monthly). Both models are suitable for seasonal and trend component data. Technically, FSA defines time domain as the result of trend and seasonal component in different frequencies which is difficult to identify in the time domain analysis. With the hidden period is 2,918 ≈ 3 and significant model order is 3, FSA model is used to predict testing data. Meanwhile, SSA has two main processes, decomposition and reconstruction. SSA decomposes the time series data into different components. The reconstruction process starts with grouping the decomposition result based on similarity period of each component in trajectory matrix. With the optimum of window length (L = 53) and grouping effect (r = 4), SSA predicting testing data. Forecasting accuracy evaluation is done based on Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). The result shows that in the next 12 month, SSA has MAPE = 13.54 percent, MAE = 61,168.43 and RMSE = 75,244.92 and FSA has MAPE = 28.19 percent, MAE = 119,718.43 and RMSE = 142,511.17. Therefore, to predict volume of motorcycle sales in the next period should use SSA method which has better performance based on its accuracy.

Fourier analysis of finite element preconditioned collocation schemes

Science.gov (United States)

Deville, Michel O.; Mund, Ernest H.

1990-01-01

The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.

Elliptical Fourier analysis: fundamentals, applications, and value for forensic anthropology.

Science.gov (United States)

Caple, Jodi; Byrd, John; Stephan, Carl N

2017-11-01

The numerical description of skeletal morphology enables forensic anthropologists to conduct objective, reproducible, and structured tests, with the added capability of verifying morphoscopic-based analyses. One technique that permits comprehensive quantification of outline shape is elliptical Fourier analysis. This curve fitting technique allows a form's outline to be approximated via the sum of multiple sine and cosine waves, permitting the profile perimeter of an object to be described in a dense (continuous) manner at a user-defined level of precision. A large amount of shape information (the entire perimeter) can thereby be collected in contrast to other methods relying on sparsely located landmarks where information falling in between the landmarks fails to be acquired. First published in 1982, elliptical Fourier analysis employment in forensic anthropology from 2000 onwards reflects a slow uptake despite large computing power that makes its calculations easy to conduct. Without hurdles arising from calculation speed or quantity, the slow uptake may partly reside with the underlying mathematics that on first glance is extensive and potentially intimidating. In this paper, we aim to bridge this gap by pictorially illustrating how elliptical Fourier harmonics work in a simple step-by-step visual fashion to facilitate universal understanding and as geared towards increased use in forensic anthropology. We additionally provide a short review of the method's utility for osteology, a summary of past uses in forensic anthropology, and software options for calculations that largely save the user the trouble of coding customized routines.

A Fourier analysis for a fast simulation algorithm. [for switching converters

Science.gov (United States)

King, Roger J.

1988-01-01

This paper presents a derivation of compact expressions for the Fourier series analysis of the steady-state solution of a typical switching converter. The modeling procedure for the simulation and the steady-state solution is described, and some desirable traits for its matrix exponential subroutine are discussed. The Fourier analysis algorithm was tested on a phase-controlled parallel-loaded resonant converter, providing an experimental confirmation.

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

Using Musical Intervals to Demonstrate Superposition of Waves and Fourier Analysis

Science.gov (United States)

LoPresto, Michael C.

2013-01-01

What follows is a description of a demonstration of superposition of waves and Fourier analysis using a set of four tuning forks mounted on resonance boxes and oscilloscope software to create, capture and analyze the waveforms and Fourier spectra of musical intervals.

Adaptive synchrosqueezing based on a quilted short-time Fourier transform

Science.gov (United States)

Berrian, Alexander; Saito, Naoki

2017-08-01

In recent years, the synchrosqueezing transform (SST) has gained popularity as a method for the analysis of signals that can be broken down into multiple components determined by instantaneous amplitudes and phases. One such version of SST, based on the short-time Fourier transform (STFT), enables the sharpening of instantaneous frequency (IF) information derived from the STFT, as well as the separation of amplitude-phase components corresponding to distinct IF curves. However, this SST is limited by the time-frequency resolution of the underlying window function, and may not resolve signals exhibiting diverse time-frequency behaviors with sufficient accuracy. In this work, we develop a framework for an SST based on a "quilted" short-time Fourier transform (SST-QSTFT), which allows adaptation to signal behavior in separate time-frequency regions through the use of multiple windows. This motivates us to introduce a discrete reassignment frequency formula based on a finite difference of the phase spectrum, ensuring computational accuracy for a wider variety of windows. We develop a theoretical framework for the SST-QSTFT in both the continuous and the discrete settings, and describe an algorithm for the automatic selection of optimal windows depending on the region of interest. Using synthetic data, we demonstrate the superior numerical performance of SST-QSTFT relative to other SST methods in a noisy context. Finally, we apply SST-QSTFT to audio recordings of animal calls to demonstrate the potential of our method for the analysis of real bioacoustic signals.

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.

Discrete Fourier Transform-Based Multivariate Image Analysis: Application to Modeling of Aromatase Inhibitory Activity.

Science.gov (United States)

Barigye, Stephen J; Freitas, Matheus P; Ausina, Priscila; Zancan, Patricia; Sola-Penna, Mauro; Castillo-Garit, Juan A

2018-02-12

We recently generalized the formerly alignment-dependent multivariate image analysis applied to quantitative structure-activity relationships (MIA-QSAR) method through the application of the discrete Fourier transform (DFT), allowing for its application to noncongruent and structurally diverse chemical compound data sets. Here we report the first practical application of this method in the screening of molecular entities of therapeutic interest, with human aromatase inhibitory activity as the case study. We developed an ensemble classification model based on the two-dimensional (2D) DFT MIA-QSAR descriptors, with which we screened the NCI Diversity Set V (1593 compounds) and obtained 34 chemical compounds with possible aromatase inhibitory activity. These compounds were docked into the aromatase active site, and the 10 most promising compounds were selected for in vitro experimental validation. Of these compounds, 7419 (nonsteroidal) and 89 201 (steroidal) demonstrated satisfactory antiproliferative and aromatase inhibitory activities. The obtained results suggest that the 2D-DFT MIA-QSAR method may be useful in ligand-based virtual screening of new molecular entities of therapeutic utility.

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.

Fourier analysis of the parametric resonance in neutrino oscillations

International Nuclear Information System (INIS)

Koike, Masafumi; Ota, Toshihiko; Saito, Masako; Sato, Joe

2009-01-01

Parametric enhancement of the appearance probability of the neutrino oscillation under the inhomogeneous matter is studied. Fourier expansion of the matter density profile leads to a simple resonance condition and manifests that each Fourier mode modifies the energy spectrum of oscillation probability at around the corresponding energy; below the MSW resonance energy, a large-scale variation modifies the spectrum in high energies while a small-scale one does in low energies. In contrast to the simple parametric resonance, the enhancement of the oscillation probability is itself an slow oscillation as demonstrated by a numerical analysis with a single Fourier mode of the matter density. We derive an analytic solution to the evolution equation on the resonance energy, including the expression of frequency of the slow oscillation.

Analysis of wave motion in one-dimensional structures through fast-Fourier-transform-based wavelet finite element method

Science.gov (United States)

Shen, Wei; Li, Dongsheng; Zhang, Shuaifang; Ou, Jinping

2017-07-01

This paper presents a hybrid method that combines the B-spline wavelet on the interval (BSWI) finite element method and spectral analysis based on fast Fourier transform (FFT) to study wave propagation in One-Dimensional (1D) structures. BSWI scaling functions are utilized to approximate the theoretical wave solution in the spatial domain and construct a high-accuracy dynamic stiffness matrix. Dynamic reduction on element level is applied to eliminate the interior degrees of freedom of BSWI elements and substantially reduce the size of the system matrix. The dynamic equations of the system are then transformed and solved in the frequency domain through FFT-based spectral analysis which is especially suitable for parallel computation. A comparative analysis of four different finite element methods is conducted to demonstrate the validity and efficiency of the proposed method when utilized in high-frequency wave problems. Other numerical examples are utilized to simulate the influence of crack and delamination on wave propagation in 1D rods and beams. Finally, the errors caused by FFT and their corresponding solutions are presented.

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.

Improved detection of anterior left ventricular aneurysm with multiharmonic fourier analysis

International Nuclear Information System (INIS)

Valette, H.B.; Bourguignon, M.H.; Merlet, P.; Gregoire, M.C.; Le Guludec, D.; Pascal, O.; Briandet, P.; Syrota, A.

1990-01-01

Single and multiharmonic Fourier analysis of LAO 30-45 degrees gated blood-pool studies were performed in a selected group of 30 patients with a left ventricular anterior aneurysm proven by contrast angiography. The sensitivity of the first harmonic phase image for the diagnosis of ventricular aneurysm was 80%. The clear phase shift (greater than 110 degrees) between the normal and the aneurysmal areas was missing in six patients. Peak acceleration images (negative maximum of the second derivative of the Fourier series) were calculated for each pixel with the analytical Fourier formula using two or three harmonics. A clear phase shift (greater than 126 degrees) than appeared in all the patients. This improvement was related to the increased weight of the second and third harmonics in the aneurysmal area when compared to control patients or to patients with dilative cardiomyopathy. Multiharmonic Fourier analysis clearly improved the sensitivity of the diagnosis of anterior left ventricular aneurysm on LAO 30 degrees-45 degrees gated blood-pool images

Elliptic Fourier analysis of crown shapes in Quercus petraea trees

Directory of Open Access Journals (Sweden)

Ovidiu Hâruţa

2011-02-01

Full Text Available Shape is a fundamental morphological descriptor, significant in taxonomic research as well as in ecomorphology, one method of estimation being from digitally processed images. In the present study, were analysed shapes of Q. petraea crowns, pertaining to five different stem diameter classes, from three similar stands. Based on measurements on terrestrial digital vertical photos, crown size analysis was performed and correlations between crown and stem variables were tested. Linear regression equations between crown volumes and dbh, and crown volumes and stem volumes were derived, explaining more than half of data variability. Employment of elliptic Fourier analysis (EFA, a powerful analysis tool, permitted the extraction of the mean shape from crowns, characterized by high morphological variability. The extracted, most important, coefficients were used to reconstruct the average shape of the crowns, using Inverse Fourier Transform. A mean shape of the crown, corresponding to stand conditions in which competition is added as influential shaping factor, aside genetic program of the species, is described for each stem diameter class. Crown regions with highest shape variability, from the perspective of stage developmentof the trees, were determined. Accordingly, the main crown shape characteristics are: crown elongation, mass center, asymmetry with regard to the main axis, lateral regions symmetrical and asymmetrical variations.

Elliptic Fourier analysis of crown shapes in Quercus petraea trees

Directory of Open Access Journals (Sweden)

Ovidiu Hâruţa

2011-06-01

Full Text Available Shape is a fundamental morphological descriptor, significant in taxonomic research as well as in ecomorphology, one method of estimation being from digitally processed images. In the present study, were analysed shapes of Q. petraea crowns, pertaining to five different stem diameter classes, from three similar stands. Based on measurements on terrestrial digital vertical photos, crown size analysis was performed and correlations between crown and stem variables were tested. Linear regression equations between crown volumes and dbh, and crown volumes and stem volumes were derived, explaining more than half of data variability. Employment of elliptic Fourier analysis (EFA, a powerful analysis tool, permitted the extraction of the mean shape from crowns, characterized by high morphological variability. The extracted, most important, coefficients were used to reconstruct the average shape of the crowns, using Inverse Fourier Transform. A mean shape of the crown, corresponding to stand conditions in which competition is added as influential shaping factor, aside genetic program of the species, is described for each stem diameter class. Crown regions with highest shape variability, from the perspective of stage development of the trees, were determined. Accordingly, the main crown shape characteristics are: crown elongation, centroid position, asymmetry with regard to the main axis, lateral regions symmetrical and asymmetrical variations. 

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.

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.

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)

Quantitative heart scintigraphy using Fourier analysis of unformated list mode data

International Nuclear Information System (INIS)

Knopp, R.; Schmidt, H.; Reichmann, K.; Biersack, H.J.; Winkler, C.

1981-01-01

Fourier transformation in radioventriculography is used for smoothing of the left ventricular volume curves as well as for the evaluating of regional wall motions by means of amplitude and phase imaging. Our new method is based on Fourier transformation from unformatted list mode data, pixel by pixel. Determination of the Fourier coefficients of 4 harmonic waves as a maximum is performed and frame sequences are generated by Fourier resynthesis. As main advantages of the method can be regarded a) considerable improvement of the image quality and b) substantial reduction of time needed for data acquisition. (orig.) [de

New predictor of aortic enlargement in uncomplicated type B aortic dissection based on elliptic Fourier analysis.

Science.gov (United States)

Sato, Hiroshi; Ito, Toshiro; Kuroda, Yosuke; Uchiyama, Hiroki; Watanabe, Toshitaka; Yasuda, Naomi; Nakazawa, Junji; Harada, Ryo; Kawaharada, Nobuyoshi

2017-12-01

This study aimed to re-examine the conventional predictive factors for dissected aortic enlargement, such as the aortic and false lumen diameter and to consider whether the morphological elements of the dissected aorta could be predictors by quantifying the 'shape' of the true lumen based on elliptic Fourier analysis. A total of 80 patients with uncomplicated type B aortic dissection were included. The patients were divided into 'Enlargement group' and 'No Change group.' Between the 2 groups, the mean systolic blood pressure during follow-up, aortic and false lumen maximum diameters, and analysed morphological data were compared using each statistical method. The maximum aortic and false lumen diameters were significantly larger in the Enlargement group than in the No Change group (39.3 vs 35.9 mm; P = 0.0058) (23.5 vs 18.2 mm; P = 0.000095). The principal component 1, which is the data calculated by elliptic Fourier analysis, was significantly lower in the Enlargement group than in the No Change group (0.020 vs - 0.072; P = 0.000049). The mean systolic blood pressure ≥130 mmHg, aortic diameter, false lumen diameter and principal component 1 were included in the Cox proportional hazard model as covariates to determine the significant predictive variable. Principal component 1 demonstrated the only significance with aortic enlargement on multivariate analysis (odds ratio = 0.32; P = 0.048). The analysed and calculated morphological data of the shape of the true lumen can be more effective predictive factors of aortic enlargement of type B dissection than the conventional factors. © The Author 2017. Published by Oxford University Press on behalf of the European Association for Cardio-Thoracic Surgery. All rights reserved.

Vision-based online vibration estimation of the in-vessel inspection flexible robot with short-time Fourier transformation

International Nuclear Information System (INIS)

Wang, Hesheng; Chen, Weidong; Xu, Lifei; He, Tao

2015-01-01

Highlights: • Vision-based online vibration estimation method for a flexible arm is proposed. • The vibration signal is obtained by image processing in unknown environments. • Vibration parameters are estimated by short-time Fourier transformation. - Abstract: The vibration should be suppressed if it happens during the motion of a flexible robot or under the influence of external disturbance caused by its structural features and material properties, because the vibration may affect the positioning accuracy and image quality. In Tokamak environment, we need to get the real-time vibration information on vibration suppression of robotic arm, however, some sensors are not allowed in the extreme Tokamak environment. This paper proposed a vision-based method for online vibration estimation of a flexible manipulator, which is achieved by utilizing the environment image information from the end-effector camera to estimate its vibration. Short-time Fourier Transformation with adaptive window length method is used to estimate vibration parameters of non-stationary vibration signals. Experiments with one-link flexible manipulator equipped with camera are carried out to validate the feasibility of this method in this paper.

Vision-based online vibration estimation of the in-vessel inspection flexible robot with short-time Fourier transformation

Energy Technology Data Exchange (ETDEWEB)

Wang, Hesheng [Key Laboratory of System Control and Information Processing, Ministry of Education of China (China); Department of Automation, Shanghai Jiao Tong University, Shanghai 200240 (China); Chen, Weidong, E-mail: wdchen@sjtu.edu.cn [Key Laboratory of System Control and Information Processing, Ministry of Education of China (China); Department of Automation, Shanghai Jiao Tong University, Shanghai 200240 (China); Xu, Lifei; He, Tao [Key Laboratory of System Control and Information Processing, Ministry of Education of China (China); Department of Automation, Shanghai Jiao Tong University, Shanghai 200240 (China)

2015-10-15

Highlights: • Vision-based online vibration estimation method for a flexible arm is proposed. • The vibration signal is obtained by image processing in unknown environments. • Vibration parameters are estimated by short-time Fourier transformation. - Abstract: The vibration should be suppressed if it happens during the motion of a flexible robot or under the influence of external disturbance caused by its structural features and material properties, because the vibration may affect the positioning accuracy and image quality. In Tokamak environment, we need to get the real-time vibration information on vibration suppression of robotic arm, however, some sensors are not allowed in the extreme Tokamak environment. This paper proposed a vision-based method for online vibration estimation of a flexible manipulator, which is achieved by utilizing the environment image information from the end-effector camera to estimate its vibration. Short-time Fourier Transformation with adaptive window length method is used to estimate vibration parameters of non-stationary vibration signals. Experiments with one-link flexible manipulator equipped with camera are carried out to validate the feasibility of this method in this paper.

Research on FBG-based longitudinal-acousto-optic modulator with Fourier mode coupling method.

Science.gov (United States)

Li, Zhuoxuan; Pei, Li; Liu, Chao; Ning, Tigang; Yu, Shaowei

2012-10-20

Fourier mode coupling model was first applied to achieve the spectra property of a fiber Bragg grating (FBG)-based longitudinal-acousto-optic modulator. Compared with traditional analysis algorithms, such as the transfer matrix method, the Fourier mode coupling model could improve the computing efficiency up to 100 times with a guarantee of accuracy. In this paper, based on the theoretical analysis of this model, the spectra characteristics of the modulator in different frequencies and acoustically induced strains were numerically simulated. In the experiment, a uniform FBG was modulated by acoustic wave (AW) at 12 different frequencies. In particular, the modulator responses at 563 and 885.5 KHz with three different lead zirconate titanate (PZT) loads applied were plotted for illustration, and the linear fitting of experimental data demonstrated a good match with the simulation result. The acoustic excitation of the longitudinal wave is obtained using a conic silica horn attached to the surface of a shear-mode PZT plate paralleled to the fiber axis. This way of generating longitudinal AW with a transversal PZT may shed light on the optimal structural design for the FBG-based longitudinal-acousto-optic modulator.

Fourier-based approach to interpolation in single-slice helical computed tomography

International Nuclear Information System (INIS)

La Riviere, Patrick J.; Pan Xiaochuan

2001-01-01

It has recently been shown that longitudinal aliasing can be a significant and detrimental presence in reconstructed single-slice helical computed tomography (CT) volumes. This aliasing arises because the directly measured data in helical CT are generally undersampled by a factor of at least 2 in the longitudinal direction and because the exploitation of the redundancy of fanbeam data acquired over 360 degree sign to generate additional longitudinal samples does not automatically eliminate the aliasing. In this paper we demonstrate that for pitches near 1 or lower, the redundant fanbeam data, when used properly, can provide sufficient information to satisfy a generalized sampling theorem and thus to eliminate aliasing. We develop and evaluate a Fourier-based algorithm, called 180FT, that accomplishes this. As background we present a second Fourier-based approach, called 360FT, that makes use only of the directly measured data. Both Fourier-based approaches exploit the fast Fourier transform and the Fourier shift theorem to generate from the helical projection data a set of fanbeam sinograms corresponding to equispaced transverse slices. Slice-by-slice reconstruction is then performed by use of two-dimensional fanbeam algorithms. The proposed approaches are compared to their counterparts based on the use of linear interpolation - the 360LI and 180LI approaches. The aliasing suppression property of the 180FT approach is a clear advantage of the approach and represents a step toward the desirable goal of achieving uniform longitudinal resolution properties in reconstructed helical CT volumes

Data characteristic analysis of air conditioning load based on fast Fourier transform

Science.gov (United States)

Li, Min; Zhang, Yanchi; Xie, Da

2018-04-01

With the development of economy and the improvement of people's living standards, air conditioning equipment is more and more popular. The influence of air conditioning load for power grid is becoming more and more serious. In this context it is necessary to study the characteristics of air conditioning load. This paper analyzes the data of air conditioning power consumption in an office building. The data is used for Fast Fourier Transform by data analysis software. Then a series of maps are drawn for the transformed data. The characteristics of each map were analyzed separately. The hidden rules of these data are mined from the angle of frequency domain. And these rules are hard to find in the time domain.

Preservation of information in Fourier theory based deconvolved nuclear spectra

International Nuclear Information System (INIS)

Madan, V.K.; Gopalakrishnan, K.R.; Sharma, R.C.; Rattan, S.S.

1995-01-01

Nuclear spectroscopy is extremely useful to the internal radiation dosimetry for the estimation of body burden due to gamma emitters. Analysis of nuclear spectra is concerned with the extraction of qualitative and quantitative information embedded in the spectra. A spectral deconvolution method based on Fourier theory is probably the simplest method of deconvolving nuclear spectra. It is proved mathematically that the deconvolution method preserves the qualitative information. It is shown by using simulated spectra and an observed gamma ray spectrum that the method preserves the quantitative information. This may provide a novel approach of information extraction from a deconvolved spectrum. The paper discusses the methodology, mathematical analysis, and the results obtained by deconvolving spectra. (author). 6 refs., 2 tabs

Fast fourier algorithms in spectral computation and analysis of vibrating machines

International Nuclear Information System (INIS)

Farooq, U.; Hafeez, T.; Khan, M.Z.; Amir, M.

2001-01-01

In this work we have discussed Fourier and its history series, relationships among various Fourier mappings, Fourier coefficients, transforms, inverse transforms, integrals, analyses, discrete and fast algorithms for data processing and analysis of vibrating systems. The evaluation of magnitude of the source signal at transmission time, related coefficient matrix, intensity, and magnitude at the receiving end (stations). Matrix computation of Fourier transform has been explained, and applications are presented. The fast Fourier transforms, new computational scheme. have been tested with an example. The work also includes digital programs for obtaining the frequency contents of time function. It has been explained that how the fast Fourier algorithms (FFT) has decreased computational work by several order of magnitudes and split the spectrum of a signal into two (even and odd modes) at every successive step. That fast quantitative processing for discrete Fourier transforms' computations as well as signal splitting and combination provides an efficient. and reliable tool for spectral analyses. Fourier series decompose the given variable into a sum of oscillatory functions each having a specific frequency. These frequencies, with their corresponding amplitude and phase angles, constitute the frequency contents of the original time functions. These fast processing achievements, signals decomposition and combination may be carried out by the principle of superposition and convolution for, even, signals of different frequencies. Considerable information about a machine or a structure can be derived from variable speed and frequency tests. (author)

Analysis of gamma-ray spectra by using fast Fourier transform

International Nuclear Information System (INIS)

Tominaga, Shoji; Nagata, Shojiro; Nayatani, Yoshinobu; Ueda, Isamu; Sasaki, Satoshi.

1977-01-01

In order to simplify the mass data processing in a response matrix method for γ-ray spectral analysis, a method using a Fast Fourier Transform devised. The validity of the method was confirmed by a computer simulation for spectra of a NaI detector. The method uses the fact that spectral data can be represented by Fourier series with reduced number of terms. The estimation of intensities of γ-ray components is performed by a matrix operation using the compressed data of an observation spectrum and standard spectra in Fourier coefficients. The identification of γ-ray energies is also easy. Several features in the method and a general problem to be solved in a response matrix method are described. (auth.)

Use of fast Fourier transform in gamma-ray spectral analysis

International Nuclear Information System (INIS)

Tominaga, Shoji; Nayatani, Yoshinobu; Nagata, Shojiro; Sasaki, Takashi; Ueda, Isamu.

1978-01-01

In order to simplify the mass data processing in a response matrix method for γ-ray spectral analysis, a method using a Fast Fourier Transform has been devised. The validity of the method has been confirmed by computer simulation for spectra of a NaI detector. First, it is shown that spectral data can be represented by Fourier series with a reduced number of terms. Then the estimation of intensities of γ-ray components is performed by a matrix operation using the compressed data of an observation spectrum and standard spectra in Fourier coefficients. The identification of γ-ray energies is also easy. Several features of the method and a general problem to be solved in relation to a response matrix method are described. (author)

Miniature, Low-Power, Waveguide Based Infrared Fourier Transform Spectrometer for Spacecraft Remote Sensing

Science.gov (United States)

Hewagama, TIlak; Aslam, Shahid; Talabac, Stephen; Allen, John E., Jr.; Annen, John N.; Jennings, Donald E.

2011-01-01

Fourier transform spectrometers have a venerable heritage as flight instruments. However, obtaining an accurate spectrum exacts a penalty in instrument mass and power requirements. Recent advances in a broad class of non-scanning Fourier transform spectrometer (FTS) devices, generally called spatial heterodyne spectrometers, offer distinct advantages as flight optimized systems. We are developing a miniaturized system that employs photonics lightwave circuit principles and functions as an FTS operating in the 7-14 micrometer spectral region. The inteferogram is constructed from an ensemble of Mach-Zehnder interferometers with path length differences calibrated to mimic scan mirror sample positions of a classic Michelson type FTS. One potential long-term application of this technology in low cost planetary missions is the concept of a self-contained sensor system. We are developing a systems architecture concept for wide area in situ and remote monitoring of characteristic properties that are of scientific interest. The system will be based on wavelength- and resolution-independent spectroscopic sensors for studying atmospheric and surface chemistry, physics, and mineralogy. The self-contained sensor network is based on our concept of an Addressable Photonics Cube (APC) which has real-time flexibility and broad science applications. It is envisaged that a spatially distributed autonomous sensor web concept that integrates multiple APCs will be reactive and dynamically driven. The network is designed to respond in an event- or model-driven manner or reconfigured as needed.

Classification Technique for Ultrasonic Weld Inspection Signals using a Neural Network based on 2-dimensional fourier Transform and Principle Component Analysis

International Nuclear Information System (INIS)

Kim, Jae Joon

2004-01-01

Neural network-based signal classification systems are increasingly used in the analysis of large volumes of data obtained in NDE applications. Ultrasonic inspection methods on the other hand are commonly used in the nondestructive evaluation of welds to detect flaws. An important characteristic of ultrasonic inspection is the ability to identify the type of discontinuity that gives rise to a peculiar signal. Standard techniques rely on differences in individual A-scans to classify the signals. This paper proposes an ultrasonic signal classification technique based on the information tying in the neighboring signals. The approach is based on a 2-dimensional Fourier transform and the principal component analysis to generate a reduced dimensional feature vector for classification. Results of applying the technique to data obtained from the inspection of actual steel welds are presented

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)

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.

Non-Harmonic Fourier Analysis for bladed wheels damage detection

Science.gov (United States)

Neri, P.; Peeters, B.

2015-11-01

The interaction between bladed wheels and the fluid distributed by the stator vanes results in cyclic loading of the rotating components. Compressors and turbines wheels are subject to vibration and fatigue issues, especially when resonance conditions are excited. Even if resonance conditions can be often predicted and avoided, high cycle fatigue failures can occur, causing safety issues and economic loss. Rigorous maintenance programs are then needed, forcing the system to expensive shut-down. Blade crack detection methods are beneficial for condition-based maintenance. While contact measurement systems are not always usable in exercise conditions (e.g. high temperature), non-contact methods can be more suitable. One (or more) stator-fixed sensor can measure all the blades as they pass by, in order to detect the damaged ones. The main drawback in this situation is the short acquisition time available for each blade, which is shortened by the high rotational speed of the components. A traditional Discrete Fourier Transform (DFT) analysis would result in a poor frequency resolution. A Non-Harmonic Fourier Analysis (NHFA) can be executed with an arbitrary frequency resolution instead, allowing to obtain frequency information even with short-time data samples. This paper shows an analytical investigation of the NHFA method. A data processing algorithm is then proposed to obtain frequency shift information from short time samples. The performances of this algorithm are then studied by experimental and numerical tests.

Ratio-based lengths of intervals to improve fuzzy time series forecasting.

Science.gov (United States)

Huarng, Kunhuang; Yu, Tiffany Hui-Kuang

2006-04-01

The objective of this study is to explore ways of determining the useful lengths of intervals in fuzzy time series. It is suggested that ratios, instead of equal lengths of intervals, can more properly represent the intervals among observations. Ratio-based lengths of intervals are, therefore, proposed to improve fuzzy time series forecasting. Algebraic growth data, such as enrollments and the stock index, and exponential growth data, such as inventory demand, are chosen as the forecasting targets, before forecasting based on the various lengths of intervals is performed. Furthermore, sensitivity analyses are also carried out for various percentiles. The ratio-based lengths of intervals are found to outperform the effective lengths of intervals, as well as the arbitrary ones in regard to the different statistical measures. The empirical analysis suggests that the ratio-based lengths of intervals can also be used to improve fuzzy time series forecasting.

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.

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

The evolution of GDP in USA using cyclic regression analysis

OpenAIRE

Catalin Angelo IOAN; Gina IOAN

2013-01-01

Based on the four major types of economic cycles (Kondratieff, Juglar, Kitchin, Kuznet), the paper aims to determine their actual length (for the U.S. economy) using cyclic regressions based on Fourier analysis.

Fully-automated identification of fish species based on otolith contour: using short-time Fourier transform and discriminant analysis (STFT-DA).

Science.gov (United States)

Salimi, Nima; Loh, Kar Hoe; Kaur Dhillon, Sarinder; Chong, Ving Ching

2016-01-01

Background. Fish species may be identified based on their unique otolith shape or contour. Several pattern recognition methods have been proposed to classify fish species through morphological features of the otolith contours. However, there has been no fully-automated species identification model with the accuracy higher than 80%. The purpose of the current study is to develop a fully-automated model, based on the otolith contours, to identify the fish species with the high classification accuracy. Methods. Images of the right sagittal otoliths of 14 fish species from three families namely Sciaenidae, Ariidae, and Engraulidae were used to develop the proposed identification model. Short-time Fourier transform (STFT) was used, for the first time in the area of otolith shape analysis, to extract important features of the otolith contours. Discriminant Analysis (DA), as a classification technique, was used to train and test the model based on the extracted features. Results. Performance of the model was demonstrated using species from three families separately, as well as all species combined. Overall classification accuracy of the model was greater than 90% for all cases. In addition, effects of STFT variables on the performance of the identification model were explored in this study. Conclusions. Short-time Fourier transform could determine important features of the otolith outlines. The fully-automated model proposed in this study (STFT-DA) could predict species of an unknown specimen with acceptable identification accuracy. The model codes can be accessed at http://mybiodiversityontologies.um.edu.my/Otolith/ and https://peerj.com/preprints/1517/. The current model has flexibility to be used for more species and families in future studies.

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...

Novel Fourier-based iterative reconstruction for sparse fan projection using alternating direction total variation minimization

International Nuclear Information System (INIS)

Jin Zhao; Zhang Han-Ming; Yan Bin; Li Lei; Wang Lin-Yuan; Cai Ai-Long

2016-01-01

Sparse-view x-ray computed tomography (CT) imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform (NUFFT) is presented in this work along with advanced total variation (TV) regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively. (paper)

Gas Measurement Using Static Fourier Transform Infrared Spectrometers.

Science.gov (United States)

Köhler, Michael H; Schardt, Michael; Rauscher, Markus S; Koch, Alexander W

2017-11-13

Online monitoring of gases in industrial processes is an ambitious task due to adverse conditions such as mechanical vibrations and temperature fluctuations. Whereas conventional Fourier transform infrared (FTIR) spectrometers use rather complex optical and mechanical designs to ensure stable operation, static FTIR spectrometers do not require moving parts and thus offer inherent stability at comparatively low costs. Therefore, we present a novel, compact gas measurement system using a static single-mirror Fourier transform spectrometer (sSMFTS). The system works in the mid-infrared range from 650 cm - 1 to 1250 cm - 1 and can be operated with a customized White cell, yielding optical path lengths of up to 120 cm for highly sensitive quantification of gas concentrations. To validate the system, we measure different concentrations of 1,1,1,2-Tetrafluoroethane (R134a) and perform a PLS regression analysis of the acquired infrared spectra. Thereby, the measured absorption spectra show good agreement with reference data. Since the system additionally permits measurement rates of up to 200 Hz and high signal-to-noise ratios, an application in process analysis appears promising.

Determination of Wind Turbine Near-Wake Length Based on Stability Analysis

DEFF Research Database (Denmark)

Sørensen, Jens Nørkær; Mikkelsen, Robert Flemming; Sarmast, Sasan

2014-01-01

A numerical study on the wake behind a wind turbine is carried out focusing on determining the length of the near-wake based on the instability onset of the trailing tip vortices shed from the turbine blades. The numerical model is based on large-eddy simulations (LES) of the Navier-Stokes equati......A numerical study on the wake behind a wind turbine is carried out focusing on determining the length of the near-wake based on the instability onset of the trailing tip vortices shed from the turbine blades. The numerical model is based on large-eddy simulations (LES) of the Navier...... of the study it is found that the amplification of specific waves (traveling structures) along the tip vortex spirals is responsible for triggering the instability leading to wake breakdown. The presence of unstable modes in the wake is related to the mutual inductance (vortex pairing) instability where...

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.

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

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

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.

Deficiencies of the cryptography based on multiple-parameter fractional Fourier transform.

Science.gov (United States)

Ran, Qiwen; Zhang, Haiying; Zhang, Jin; Tan, Liying; Ma, Jing

2009-06-01

Methods of image encryption based on fractional Fourier transform have an incipient flaw in security. We show that the schemes have the deficiency that one group of encryption keys has many groups of keys to decrypt the encrypted image correctly for several reasons. In some schemes, many factors result in the deficiencies, such as the encryption scheme based on multiple-parameter fractional Fourier transform [Opt. Lett.33, 581 (2008)]. A modified method is proposed to avoid all the deficiencies. Security and reliability are greatly improved without increasing the complexity of the encryption process. (c) 2009 Optical Society of America.

Instantaneous lineshape analysis of Fourier domain mode-locked lasers.

Science.gov (United States)

Todor, Sebastian; Biedermann, Benjamin; Wieser, Wolfgang; Huber, Robert; Jirauschek, Christian

2011-04-25

We present a theoretical and experimental analysis of the instantaneous lineshape of Fourier domain mode-locked (FDML) lasers, yielding good agreement. The simulations are performed employing a recently introduced model for FDML operation. Linewidths around 10 GHz are found, which is significantly below the sweep filter bandwidth. The effect of detuning between the sweep filter drive frequency and cavity roundtrip time is studied revealing features that cannot be resolved in the experiment, and shifting of the instantaneous power spectrum against the sweep filter center frequency is analyzed. We show that, in contrast to most other semiconductor based lasers, the instantaneous linewidth is governed neither by external noise sources nor by amplified spontaneous emission, but it is directly determined by the complex FDML dynamics.

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.)

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.)

Periodic transonic flow simulation using fourier-based algorithm

International Nuclear Information System (INIS)

Mohaghegh, Mohammad Reza; Malekjafarian, Majid

2014-01-01

The present research simulates time-periodic unsteady transonic flow around pitching airfoils via the solution of unsteady Euler and Navier-Stokes equations, using time spectral method (TSM) and compares it with the traditional methods like BDF and explicit structured adaptive grid method. The TSM uses a Fourier representation in time and hence solves for the periodic state directly without resolving transients (which consume most of the resources in a time-accurate scheme). Mathematical tools used here are discrete Fourier transformations. The TSM has been validated with 2D external aerodynamics test cases. These test cases are NACA 64A010 (CT6) and NACA 0012 (CT1 and CT5) pitching airfoils. Because of turbulent nature of flow, Baldwin-Lomax turbulence model has been used in viscous flow analysis with large oscillation amplitude (CT5 type). The results presented by the TSM are compared with experimental data and the two other methods. By enforcing periodicity and using Fourier representation in time that has a spectral accuracy, tremendous reduction of computational cost has been obtained compared to the conventional time-accurate methods. Results verify the small number of time intervals per pitching cycle (just four time intervals) required to capture the flow physics with small oscillation amplitude (CT6) and large oscillation amplitude (CT5) as compared to the other two methods.

Missing texture reconstruction method based on error reduction algorithm using Fourier transform magnitude estimation scheme.

Science.gov (United States)

Ogawa, Takahiro; Haseyama, Miki

2013-03-01

A missing texture reconstruction method based on an error reduction (ER) algorithm, including a novel estimation scheme of Fourier transform magnitudes is presented in this brief. In our method, Fourier transform magnitude is estimated for a target patch including missing areas, and the missing intensities are estimated by retrieving its phase based on the ER algorithm. Specifically, by monitoring errors converged in the ER algorithm, known patches whose Fourier transform magnitudes are similar to that of the target patch are selected from the target image. In the second approach, the Fourier transform magnitude of the target patch is estimated from those of the selected known patches and their corresponding errors. Consequently, by using the ER algorithm, we can estimate both the Fourier transform magnitudes and phases to reconstruct the missing areas.

Quasi-static analysis of flexible pavements based on predicted frequencies using Fast Fourier Transform and Artificial Neural Network

Directory of Open Access Journals (Sweden)

Ali Reza Ghanizadeh

2018-01-01

Full Text Available New trend in design of flexible pavements is mechanistic-empirical approach. The first step for applying this method is analyzing the pavement structure for several times and computation of critical stresses and strains, which needs a fast analysis method with good accuracy. This paper aims to introduce a new rapid pavement analysis approach, which can consider the history of loading and rate effect. To this end, 1200 flexible pavement sections were analyzed, and equivalent frequencies (EF were calculated using Fast Fourier Transform (FFT method at various depths of asphalt layer. A nonlinear regression equation has been presented for determining EF at different depths of asphalt layer. For more accurate predicting of EF at low frequencies, a feed-forward Artificial Neural Network (ANN was employed, which allows accurate prediction of EF. The frequencies obtained by the proposed regression equation and ANN were compared with frequencies observed in Virginia Smart Road project, and it was found that there is a good agreement between observed and predicted frequencies. Comparison of quasi-static analysis of flexible pavements by frequencies obtained using FFT method and full dynamic analysis by 3D-Move program approves that the critical responses of pavement computed by proposed quasi-static analysis approach are comparable to critical responses computed using full dynamic analysis. Keywords: Equivalent frequency, Fast Fourier Transform (FFT, Pavement quasi-static analysis, Dynamic modulus, Artificial Neural Network (ANN

Fourier-based integration of quasi-periodic gait accelerations for drift-free displacement estimation using inertial sensors.

Science.gov (United States)

Sabatini, Angelo Maria; Ligorio, Gabriele; Mannini, Andrea

2015-11-23

In biomechanical studies Optical Motion Capture Systems (OMCS) are considered the gold standard for determining the orientation and the position (pose) of an object in a global reference frame. However, the use of OMCS can be difficult, which has prompted research on alternative sensing technologies, such as body-worn inertial sensors. We developed a drift-free method to estimate the three-dimensional (3D) displacement of a body part during cyclical motions using body-worn inertial sensors. We performed the Fourier analysis of the stride-by-stride estimates of the linear acceleration, which were obtained by transposing the specific forces measured by the tri-axial accelerometer into the global frame using a quaternion-based orientation estimation algorithm and detecting when each stride began using a gait-segmentation algorithm. The time integration was performed analytically using the Fourier series coefficients; the inverse Fourier series was then taken for reconstructing the displacement over each single stride. The displacement traces were concatenated and spline-interpolated to obtain the entire trace. The method was applied to estimate the motion of the lower trunk of healthy subjects that walked on a treadmill and it was validated using OMCS reference 3D displacement data; different approaches were tested for transposing the measured specific force into the global frame, segmenting the gait and performing time integration (numerically and analytically). The width of the limits of agreements were computed between each tested method and the OMCS reference method for each anatomical direction: Medio-Lateral (ML), VerTical (VT) and Antero-Posterior (AP); using the proposed method, it was observed that the vertical component of displacement (VT) was within ±4 mm (±1.96 standard deviation) of OMCS data and each component of horizontal displacement (ML and AP) was within ±9 mm of OMCS data. Fourier harmonic analysis was applied to model stride-by-stride linear

Renal geology (quantitative renal stone analysis) by 'Fourier transform infrared spectroscopy'.

Science.gov (United States)

Singh, Iqbal

2008-01-01

To prospectively determine the precise stone composition (quantitative analysis) by using infrared spectroscopy in patients with urinary stone disease presenting to our clinic. To determine an ideal method for stone analysis suitable for use in a clinical setting. After routine and a detailed metabolic workup of all patients of urolithiasis, stone samples of 50 patients of urolithiasis satisfying the entry criteria were subjected to the Fourier transform infrared spectroscopic analysis after adequate sample homogenization at a single testing center. Calcium oxalate monohydrate and dihydrate stone mixture was most commonly encountered in 35 (71%) followed by calcium phosphate, carbonate apatite, magnesium ammonium hexahydrate and xanthine stones. Fourier transform infrared spectroscopy allows an accurate, reliable quantitative method of stone analysis. It also helps in maintaining a computerized large reference library. Knowledge of precise stone composition may allow the institution of appropriate prophylactic therapy despite the absence of any detectable metabolic abnormalities. This may prevent and or delay stone recurrence.

Extending electronic length frequency analysis in R

DEFF Research Database (Denmark)

Taylor, M. H.; Mildenberger, Tobias K.

2017-01-01

VBGF (soVBGF) requires a more intensive search due to two additional parameters. This work describes the implementation of two optimisation approaches ("simulated annealing" and "genetic algorithm") for growth function fitting using the open-source software "R." Using a generated LFQ data set......Electronic length frequency analysis (ELEFAN) is a system of stock assessment methods using length-frequency (LFQ) data. One step is the estimation of growth from the progression of LFQ modes through time using the von Bertalanffy growth function (VBGF). The option to fit a seasonally oscillating...... of the asymptotic length parameter (L-infinity) are found to have significant effects on parameter estimation error. An outlook provides context as to the significance of the R-based implementation for further testing and development, as well as the general relevance of the method for data-limited stock assessment....

Fourier analysis of intracranial aneurysms: towards an objective and quantitative evaluation of the shape of aneurysms

International Nuclear Information System (INIS)

Rohde, Stefan; Lahmann, Katharina; Nafe, Reinhold; Yan, Bernard; Berkefeld, Joachim; Beck, Juergen; Raabe, Andreas

2005-01-01

Shape irregularities of intracranial aneurysms may indicate an increased risk of rupture. To quantify morphological differences, Fourier analysis of the shape of intracranial aneurysms was introduced. We compared the morphology of 45 unruptured (UIA) and 46 ruptured intracranial aneurysms (RIA) in 70 consecutive patients on the basis of 3D-rotational angiography. Fourier analysis, coefficient of roundness and qualitative shape assessment were determined for each aneurysm. Morphometric analysis revealed significantly smaller coefficient of roundness (P<0.02) and higher values for Fourier amplitudes numbers 2, 3 and 7 (P<0.01) in the RIA group, indicating more complex and irregular morphology in RIA. Qualitative assessment from 3D-reconstructions showed surface irregularities in 78% of RIA and 42% of UIA (P<0.05). Our data have shown significant differences in shape between RIA and UIA, and further developments of Fourier analysis may provide an objective factor for the assessment of the risk of rupture. (orig.)

Analysis of tokamak plasma confinement modes using the fast Fourier transformation

International Nuclear Information System (INIS)

Mirmoeini, S.R.; Salar Elahi, A.; Ghoranneviss, M.

2016-01-01

The Fourier analysis is a satisfactory technique for detecting plasma confinement modes in tokamaks. The confinement mode of tokamak plasma was analysed using the fast Fourier transformation (FFT). For this purpose, we used the data of Mirnov coils that is one of the identifying tools in the IR-T1 tokamak, with and without external field (electric biasing), and then compared it with each other. After the Fourier analysis of Mirnov coil data, the diagram of power spectrum density was depicted in different angles of Mirnov coils in the 'presence of external field' as well as in the 'absence of external field'. The power spectrum density (PSD) interprets the manner of power distribution of a signal with frequency. In this article, the number of plasma modes and the safety factor q were obtained by using the mode number of q = m/n (m is the mode number). The maximum MHD activity was obtained in 30-35 kHz frequency, using the density of the energy spectrum. In addition, the number of different modes across 0-35 ms time was compared with each other in the presence and absence of the external field. (author)

Fourier analysis of cell-wise Block-Jacobi splitting in two-dimensional geometry

International Nuclear Information System (INIS)

Rosa, M.; Warsa, J. S.; Kelley, T. M.

2009-01-01

A Fourier analysis is conducted in two-dimensional (2D) geometry for the discrete ordinates (S N ) approximation of the neutron transport problem solved with Richardson iteration (Source Iteration) using the cell-wise Block-Jacobi (BJ) algorithm. The results of the Fourier analysis show that convergence of cell-wise BJ can degrade, leading to a spectral radius equal to 1, in problems containing optically thin cells. For problems containing cells that are optically thick, instead, the spectral radius tends to 0. Hence, in the optically thick-cell regime, cell-wise BJ is rapidly convergent even for problems that are scattering dominated, with a scattering ratio c close to 1. (authors)

Application of fast Fourier transform in thermo-magnetic convection analysis

International Nuclear Information System (INIS)

Pyrda, L

2014-01-01

Application of Fast Fourier Transform in thermo-magnetic convection is reported. Cubical enclosure filled with paramagnetic fluid heated from below and placed in the strong magnetic field gradients was investigated. The main aim of study was connected with identification of flow types, especially transition to turbulence. For this purpose the Fast Fourier Transform (FFT) analysis was applied. It was followed by the heat transfer characteristic for various values of magnetic induction gradient. The analysis was done at two Rayleigh numbers 7.89·10 5 and 1.86·10 6 with thermo-magnetic Rayleigh numbers up to 1.8·10 8 and 4.5·10 8 respectively. The presented results clearly indicate flow types and also demonstrate augmented heat transfer in dependence on magnetic induction gradient. Detailed analysis of flow transition to turbulent state was compared with transition line for natural convection reported in literature. The transition to turbulence in the case of thermo-magnetic convection of paramagnetic fluid was in very good agreement with transition in the case of natural convection.

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.

Multi-layer thickness determination using differential-based enhanced Fourier transforms of X-ray reflectivity data

Energy Technology Data Exchange (ETDEWEB)

Poust, Benjamin [Department of Materials Science and Engineering, University of California, Los Angeles, CA (United States); Northrop Grumman Space Technology, Redondo Beach, CA (United States); Sandhu, Rajinder [Northrop Grumman Space Technology, Redondo Beach, CA (United States); Goorsky, Mark [Department of Materials Science and Engineering, University of California, Los Angeles, CA (United States)

2009-08-15

Layer thickness determination of single and multi-layer structures is achieved using a new method for generating Fourier transforms (FTs) of X-ray reflectivity data. This enhanced Fourier analysis is compared to other techniques in the determination of AlN layer thickness deposited on sapphire. In addition to demonstrably improved results, the results also agree with thicknesses determined using simulations and TEM measurements. The effectiveness of the technique is further demonstrated using the more complicated metamorphic epitaxial multi-layer AlSb/InAs structures deposited on GaAs. The approach reported here is based upon differentiating the specular intensity with respect to the vertical reciprocal space coordinate Q{sub Z}. In general, differentiation is far more effective at removing the sloping background present in reflectivity scans than logarithmic compression alone, average subtraction alone, or other methods. When combined with any of the other enhancement techniques, however, differentiation yields distinguishable discrete Fourier transform (DFT) power spectrum peaks for even the weakest and most truncated of sloping oscillations that are present in many reflectivity scans from multi-layer structures. (Abstract Copyright [2009], Wiley Periodicals, Inc.)

Some studies on Fourier analysis in students experiment

OpenAIRE

大崎, 正雄

2016-01-01

Here we give some troubles in teaching and their solutions occured during the Software Science Experiment course, which is opened for the 4th semester in the Department of Software Science. One of the subjects of this experiment course is Fourier analysis using MyPC. Some students are not familiar with calculating the integration of sinusoidal function, and also some need support for drawing graphs with MS Excel. Typical mistakes and their settlements are given.

OTDM-WDM Conversion Based on Time-Domain Optical Fourier Transformation with Spectral Compression

DEFF Research Database (Denmark)

Mulvad, Hans Christian Hansen; Palushani, Evarist; Galili, Michael

2011-01-01

We propose a scheme enabling direct serial-to-parallel conversion of OTDM data tributaries onto a WDM grid, based on optical Fourier transformation with spectral compression. Demonstrations on 320 Gbit/s and 640 Gbit/s OTDM data are shown.......We propose a scheme enabling direct serial-to-parallel conversion of OTDM data tributaries onto a WDM grid, based on optical Fourier transformation with spectral compression. Demonstrations on 320 Gbit/s and 640 Gbit/s OTDM data are shown....

Brillouin Scattering Spectrum Analysis Based on Auto-Regressive Spectral Estimation

Science.gov (United States)

Huang, Mengyun; Li, Wei; Liu, Zhangyun; Cheng, Linghao; Guan, Bai-Ou

2018-06-01

Auto-regressive (AR) spectral estimation technology is proposed to analyze the Brillouin scattering spectrum in Brillouin optical time-domain refelectometry. It shows that AR based method can reliably estimate the Brillouin frequency shift with an accuracy much better than fast Fourier transform (FFT) based methods provided the data length is not too short. It enables about 3 times improvement over FFT at a moderate spatial resolution.

Brillouin Scattering Spectrum Analysis Based on Auto-Regressive Spectral Estimation

Science.gov (United States)

Huang, Mengyun; Li, Wei; Liu, Zhangyun; Cheng, Linghao; Guan, Bai-Ou

2018-03-01

Auto-regressive (AR) spectral estimation technology is proposed to analyze the Brillouin scattering spectrum in Brillouin optical time-domain refelectometry. It shows that AR based method can reliably estimate the Brillouin frequency shift with an accuracy much better than fast Fourier transform (FFT) based methods provided the data length is not too short. It enables about 3 times improvement over FFT at a moderate spatial resolution.

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.

Evaluation of removal of the size effect using data scaling and elliptic Fourier descriptors in otolith shape analysis, exemplified by the discrimination of two yellow croaker stocks along the Chinese coast

Science.gov (United States)

Zhao, Bo; Liu, Jinhu; Song, Junjie; Cao, Liang; Dou, Shuozeng

2017-11-01

Removal of the length effect in otolith shape analysis for stock identification using length scaling is an important issue; however, few studies have attempted to investigate the effectiveness or weakness of this methodology in application. The aim of this study was to evaluate whether commonly used size scaling methods and normalized elliptic Fourier descriptors (NEFDs) could effectively remove the size effect of fish in stock discrimination. To achieve this goal, length groups from two known geographical stocks of yellow croaker, Larimichthys polyactis, along the Chinese coast (five groups from the Changjiang River estuary of the East China Sea and three groups from the Bohai Sea) were subjected to otolith shape analysis. The results indicated that the variation of otolith shape caused by intra-stock fish length might exceed that due to inter-stock geographical separation, even when otolith shape variables are standardized with length scaling methods. This variation could easily result in misleading stock discrimination through otolith shape analysis. Therefore, conclusions about fish stock structure should be carefully drawn from otolith shape analysis because the observed discrimination may primarily be due to length effects, rather than differences among stocks. The application of multiple methods, such as otoliths shape analysis combined with elemental fingering, tagging or genetic analysis, is recommended for sock identification.

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.

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

A proposal of Fourier-Bessel expansion with optimized ensembles of bases to analyse two dimensional image

Science.gov (United States)

Yamasaki, K.; Fujisawa, A.; Nagashima, Y.

2017-09-01

It is a critical issue to find the best set of fitting function bases in mode structural analysis of two dimensional images like plasma emission profiles. The paper proposes a method to optimize a set of the bases in the case of Fourier-Bessel function series, using their orthonormal property, for more efficient and precise analysis. The method is applied on a tomography image of plasma emission obtained with the Maximum-likelihood expectation maximization method in a linear cylindrical device. The result demonstrates the excellency of the method that realizes the smaller residual error and minimum Akaike information criterion using smaller number of fitting function bases.

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...

Study on the algorithm of computational ghost imaging based on discrete fourier transform measurement matrix

Science.gov (United States)

Zhang, Leihong; Liang, Dong; Li, Bei; Kang, Yi; Pan, Zilan; Zhang, Dawei; Gao, Xiumin; Ma, Xiuhua

2016-07-01

On the basis of analyzing the cosine light field with determined analytic expression and the pseudo-inverse method, the object is illuminated by a presetting light field with a determined discrete Fourier transform measurement matrix, and the object image is reconstructed by the pseudo-inverse method. The analytic expression of the algorithm of computational ghost imaging based on discrete Fourier transform measurement matrix is deduced theoretically, and compared with the algorithm of compressive computational ghost imaging based on random measurement matrix. The reconstruction process and the reconstruction error are analyzed. On this basis, the simulation is done to verify the theoretical analysis. When the sampling measurement number is similar to the number of object pixel, the rank of discrete Fourier transform matrix is the same as the one of the random measurement matrix, the PSNR of the reconstruction image of FGI algorithm and PGI algorithm are similar, the reconstruction error of the traditional CGI algorithm is lower than that of reconstruction image based on FGI algorithm and PGI algorithm. As the decreasing of the number of sampling measurement, the PSNR of reconstruction image based on FGI algorithm decreases slowly, and the PSNR of reconstruction image based on PGI algorithm and CGI algorithm decreases sharply. The reconstruction time of FGI algorithm is lower than that of other algorithms and is not affected by the number of sampling measurement. The FGI algorithm can effectively filter out the random white noise through a low-pass filter and realize the reconstruction denoising which has a higher denoising capability than that of the CGI algorithm. The FGI algorithm can improve the reconstruction accuracy and the reconstruction speed of computational ghost imaging.

Elliptic Fourier Analysis of body shape variation of Hippocampus spp. (seahorse in Danajon Bank, Philippines

Directory of Open Access Journals (Sweden)

S. R. M. Tabugo-Rico

2017-12-01

Full Text Available Seahorses inhabit various ecosystems hence, had become a flagship species of the marine environment. The Philippines as a hot spot of biodiversity in Asia holds a number of species of seahorses. This serve as an exploratory study to describe body shape variation of selected common seahorse species: Hippocampus comes, Hippocampus histrix, Hippocampus spinosissimus and Hippocampus kuda from Danajon bank using Elliptic Fourier Analysis. The method was done to test whether significant yet subtle differences in body shape variation can be species-specific, habitat-influenced and provide evidence of sexual dimorphism. It is hypothesized that phenotypic divergence may provide evidence for genetic differentiation or mere adaptations to habitat variation. Results show significant considerable differences in the body shapes of the five populations based on the canonical variate analysis (CVA and multivariate analysis of variance (MANOVA with significant p values. Populations were found to be distinct from each other suggesting that body shape variation is species-specific, habitat-influenced and provided evidence for sexual dimorphism. Results of discriminant analysis show further support for species specific traits and sexual dimorphism. This study shows the application of the method of geometric morphometrics specifically elliptic fourier analysis in describing subtle body shape variation of selected Hippocampus species.

The DSP-based RTOF-correlator for high resolution Fourier diffractometers

Energy Technology Data Exchange (ETDEWEB)

Butenko, V A; Drozdov, V A; Kirilov, A S [Frank Lab. of Neutron Physics of the Academy of Sciences of Slovakia, Bratislava (Slovakia)

1996-12-31

To improve efficiency of the time-of-flight analysis, the correlation and the Fourier methods are used with a preliminary neutron flux modulation. In this case the elastically scattered neutron spectrum is calculated as a function of the cross-correlation of the detector signal and the neutron flux modulation. 10 refs.; 5 figs.

Cryo-EM image alignment based on nonuniform fast Fourier transform

International Nuclear Information System (INIS)

Yang Zhengfan; Penczek, Pawel A.

2008-01-01

In single particle analysis, two-dimensional (2-D) alignment is a fundamental step intended to put into register various particle projections of biological macromolecules collected at the electron microscope. The efficiency and quality of three-dimensional (3-D) structure reconstruction largely depends on the computational speed and alignment accuracy of this crucial step. In order to improve the performance of alignment, we introduce a new method that takes advantage of the highly accurate interpolation scheme based on the gridding method, a version of the nonuniform fast Fourier transform, and utilizes a multi-dimensional optimization algorithm for the refinement of the orientation parameters. Using simulated data, we demonstrate that by using less than half of the sample points and taking twice the runtime, our new 2-D alignment method achieves dramatically better alignment accuracy than that based on quadratic interpolation. We also apply our method to image to volume registration, the key step in the single particle EM structure refinement protocol. We find that in this case the accuracy of the method not only surpasses the accuracy of the commonly used real-space implementation, but results are achieved in much shorter time, making gridding-based alignment a perfect candidate for efficient structure determination in single particle analysis

Cryo-EM image alignment based on nonuniform fast Fourier transform.

Science.gov (United States)

Yang, Zhengfan; Penczek, Pawel A

2008-08-01

In single particle analysis, two-dimensional (2-D) alignment is a fundamental step intended to put into register various particle projections of biological macromolecules collected at the electron microscope. The efficiency and quality of three-dimensional (3-D) structure reconstruction largely depends on the computational speed and alignment accuracy of this crucial step. In order to improve the performance of alignment, we introduce a new method that takes advantage of the highly accurate interpolation scheme based on the gridding method, a version of the nonuniform fast Fourier transform, and utilizes a multi-dimensional optimization algorithm for the refinement of the orientation parameters. Using simulated data, we demonstrate that by using less than half of the sample points and taking twice the runtime, our new 2-D alignment method achieves dramatically better alignment accuracy than that based on quadratic interpolation. We also apply our method to image to volume registration, the key step in the single particle EM structure refinement protocol. We find that in this case the accuracy of the method not only surpasses the accuracy of the commonly used real-space implementation, but results are achieved in much shorter time, making gridding-based alignment a perfect candidate for efficient structure determination in single particle analysis.

Accurate determination of the diffusion coefficient of proteins by Fourier analysis with whole column imaging detection.

Science.gov (United States)

Zarabadi, Atefeh S; Pawliszyn, Janusz

2015-02-17

Analysis in the frequency domain is considered a powerful tool to elicit precise information from spectroscopic signals. In this study, the Fourier transformation technique is employed to determine the diffusion coefficient (D) of a number of proteins in the frequency domain. Analytical approaches are investigated for determination of D from both experimental and data treatment viewpoints. The diffusion process is modeled to calculate diffusion coefficients based on the Fourier transformation solution to Fick's law equation, and its results are compared to time domain results. The simulations characterize optimum spatial and temporal conditions and demonstrate the noise tolerance of the method. The proposed model is validated by its application for the electropherograms from the diffusion path of a set of proteins. Real-time dynamic scanning is conducted to monitor dispersion by employing whole column imaging detection technology in combination with capillary isoelectric focusing (CIEF) and the imaging plug flow (iPF) experiment. These experimental techniques provide different peak shapes, which are utilized to demonstrate the Fourier transformation ability in extracting diffusion coefficients out of irregular shape signals. Experimental results confirmed that the Fourier transformation procedure substantially enhanced the accuracy of the determined values compared to those obtained in the time domain.

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)

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.

Application of the windowed-Fourier-transform-based fringe analysis technique for investigating temperature and concentration fields in fluids.

Science.gov (United States)

Mohanan, Sharika; Srivastava, Atul

2014-04-10

The present work is concerned with the development and application of a novel fringe analysis technique based on the principles of the windowed-Fourier-transform (WFT) for the determination of temperature and concentration fields from interferometric images for a range of heat and mass transfer applications. Based on the extent of the noise level associated with the experimental data, the technique has been coupled with two different phase unwrapping methods: the Itoh algorithm and the quality guided phase unwrapping technique for phase extraction. In order to generate the experimental data, a range of experiments have been carried out which include cooling of a vertical flat plate in free convection conditions, combustion of mono-propellant flames, and growth of organic as well as inorganic crystals from their aqueous solutions. The flat plate and combustion experiments are modeled as heat transfer applications wherein the interest is to determine the whole-field temperature distribution. Aqueous-solution-based crystal growth experiments are performed to simulate the mass transfer phenomena and the interest is to determine the two-dimensional solute concentration field around the growing crystal. A Mach-Zehnder interferometer has been employed to record the path-integrated quantity of interest (temperature and/or concentration) in the form of interferometric images in the experiments. The potential of the WFT method has also been demonstrated on numerically simulated phase data for varying noise levels, and the accuracy in phase extraction have been quantified in terms of the root mean square errors. Three levels of noise, i.e., 0%, 10%, and 20% have been considered. Results of the present study show that the WFT technique allows an accurate extraction of phase values that can subsequently be converted into two-dimensional temperature and/or concentration distribution fields. Moreover, since WFT is a local processing technique, speckle patterns and the inherent

The vulnerability of electric equipment to carbon fibers of mixed lengths: An analysis

Science.gov (United States)

Elber, W.

1980-01-01

The susceptibility of a stereo amplifier to damage from a spectrum of lengths of graphite fibers was calculated. A simple analysis was developed by which such calculations can be based on test results with fibers of uniform lengths. A statistical analysis was applied for the conversation of data for various logical failure criteria.

The Fourier transform for certain hyperkähler fourfolds

CERN Document Server

Shen, Mingmin

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 \\mathrm{CH}^*(A). By using a codimension-2 algebraic cycle representing the Beauvilleâe"Bogomolov class, the authors give evidence for the existence of a similar decomposition for the Chow ring of Hyperkähler varieties deformation equivalent to the Hilbert scheme of length-2 subschemes on a K3 surface. They indeed establish the existence of such a decomposition for the Hilbert scheme of length-2 subschemes on a K3 surface and for the variety of lines on a very general cubic fourfold.

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.

Analysis of an atom laser based on the spatial control of the scattering length

International Nuclear Information System (INIS)

Carpentier, Alicia V.; Michinel, Humberto; Rodas-Verde, Maria I.; Perez-Garcia, Victor M.

2006-01-01

In this paper we analyze atom lasers based on the spatial modulation of the scattering length of a Bose-Einstein condensate. We demonstrate, through numerical simulations and approximate analytical methods, the controllable emission of matter-wave bursts and study the dependence of the process on the spatial shape of the scattering length along the axis of emission. We also study the role of an additional modulation of the scattering length in time

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)

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.

Combustion stratification study of partially premixed combustion using Fourier transform analysis of OH* chemiluminescence images

KAUST Repository

Izadi Najafabadi, Mohammad

2017-11-06

A relatively high level of stratification (qualitatively: lack of homogeneity) is one of the main advantages of partially premixed combustion over the homogeneous charge compression ignition concept. Stratification can smooth the heat release rate and improve the controllability of combustion. In order to compare stratification levels of different partially premixed combustion strategies or other combustion concepts, an objective and meaningful definition of “stratification level” is required. Such a definition is currently lacking; qualitative/quantitative definitions in the literature cannot properly distinguish various levels of stratification. The main purpose of this study is to objectively define combustion stratification (not to be confused with fuel stratification) based on high-speed OH* chemiluminescence imaging, which is assumed to provide spatial information regarding heat release. Stratification essentially being equivalent to spatial structure, we base our definition on two-dimensional Fourier transforms of photographs of OH* chemiluminescence. A light-duty optical diesel engine has been used to perform the OH* bandpass imaging on. Four experimental points are evaluated, with injection timings in the homogeneous regime as well as in the stratified partially premixed combustion regime. Two-dimensional Fourier transforms translate these chemiluminescence images into a range of spatial frequencies. The frequency information is used to define combustion stratification, using a novel normalization procedure. The results indicate that this new definition, based on Fourier analysis of OH* bandpass images, overcomes the drawbacks of previous definitions used in the literature and is a promising method to compare the level of combustion stratification between different experiments.

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...

Fourier X-ray line shape analysis of lattice defects from a single reflection

International Nuclear Information System (INIS)

Misra, N.K.; Bhanumurthy, K.

1981-01-01

A method of single reflection Fourier analysis has been described considering the fact that the rms strain (averaged over a distance) is not independent of averaging distance. Following the procedure of N.K. Misra and T.B. Ghosh (1976) and considering the initial slopes of dAsub(L)/dL against L curves, (Asub(L) is the Lsub(th) order Fourier coefficient) the effective size of the coherently diffracting domains and the rms strain in them are determined. The results of this analysis for pure Ti and Ag-3.55% Ga, Ag-15% In and Cu-12.46% Ge alloys compare fairly well with those obtained from different multiple reflections techniques. (author)

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.

Mountain Wave Analysis Using Fourier Methods

National Research Council Canada - National Science Library

Roadcap, John R

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...

Free vibration characteristics analysis of rectangular plate with rectangular opening based on Fourier series method

Directory of Open Access Journals (Sweden)

WANG Minhao

2017-08-01

Full Text Available Plate structures with openings are common in many engineering structures. The study of the vibration characteristics of such structures is directly related to the vibration reduction, noise reduction and stability analysis of an overall structure. This paper conducts research into the free vibration characteristics of a thin elastic plate with a rectangular opening parallel to the plate in an arbitrary position. We use the improved Fourier series to represent the displacement tolerance function of the rectangular plate with an opening. We can divide the plate into an eight zone plate to simplify the calculation. We then use linear springs, which are uniformly distributed along the boundary, to simulate the classical boundary conditions and the boundary conditions of the boundaries between the regions. According to the energy functional and variational method, we can obtain the overall energy functional. We can also obtain the generalized eigenvalue matrix equation by studying the extremum of the unknown improved Fourier series expansion coefficients. We can then obtain the natural frequencies and corresponding vibration modes of the rectangular plate with an opening by solving the equation. We then compare the calculated results with the finite element method to verify the accuracy and effectiveness of the method proposed in this paper. Finally, we research the influence of the boundary condition, opening size and opening position on the vibration characteristics of a plate with an opening. This provides a theoretical reference for practical engineering application.

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

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…

All-optical signal processing of OTDM and OFDM signals based on time-domain optical fourier transformation

DEFF Research Database (Denmark)

Galili, Michael; Guan, Pengyu; Lillieholm, Mads

2017-01-01

In the talk, we will review recent work on optical signal processing based on time lenses. Various applications of optical Fourier transformation for optical communications will be discussed.......In the talk, we will review recent work on optical signal processing based on time lenses. Various applications of optical Fourier transformation for optical communications will be discussed....

Nonadiabatic laser-induced alignment of molecules: Reconstructing ⟨ θ⟩ directly from ⟨ θ2D⟩ by Fourier analysis.

Science.gov (United States)

Søndergaard, Anders Aspegren; Shepperson, Benjamin; Stapelfeldt, Henrik

2017-07-07

We present an efficient, noise-robust method based on Fourier analysis for reconstructing the three-dimensional measure of the alignment degree, ⟨cos 2 θ⟩, directly from its two-dimensional counterpart, ⟨cos 2 θ 2D ⟩. The method applies to nonadiabatic alignment of linear molecules induced by a linearly polarized, nonresonant laser pulse. Our theoretical analysis shows that the Fourier transform of the time-dependent ⟨cos 2 θ 2D ⟩ trace over one molecular rotational period contains additional frequency components compared to the Fourier transform of ⟨cos 2 θ⟩. These additional frequency components can be identified and removed from the Fourier spectrum of ⟨cos 2 θ 2D ⟩. By rescaling of the remaining frequency components, the Fourier spectrum of ⟨cos 2 θ⟩ is obtained and, finally, ⟨cos 2 θ⟩ is reconstructed through inverse Fourier transformation. The method allows the reconstruction of the ⟨cos 2 θ⟩ trace from a measured ⟨cos 2 θ 2D ⟩ trace, which is the typical observable of many experiments, and thereby provides direct comparison to calculated ⟨cos 2 θ⟩ traces, which is the commonly used alignment metric in theoretical descriptions. We illustrate our method by applying it to the measurement of nonadiabatic alignment of I 2 molecules. In addition, we present an efficient algorithm for calculating the matrix elements of cos 2 θ 2D and any other observable in the symmetric top basis. These matrix elements are required in the rescaling step, and they allow for highly efficient numerical calculation of ⟨cos 2 θ 2D ⟩ and ⟨cos 2 θ⟩ in general.

Vibrational analysis of Fourier transform spectrum of the B u )–X g ...

Indian Academy of Sciences (India)

improved by putting the wave number of band origins in Deslandre table. The vibrational analysis was supported by determining the Franck–Condon factor and r-centroid values. Keywords. Fourier transform spectroscopy; electronic spectrum of selenium dimer; vibrational analysis; Franck–Condon factor; r-centroid values.

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

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

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

Fundamental and clinical evaluation of Fourier analysis for the detection of regional wall contraction abnormalities in the patients with myocardial infarction

International Nuclear Information System (INIS)

Murata, H.; Toyama, H.; Tabuchi, H.; Muraki, T.; Ohtake, E.; Chiba, K.; Yamada, H.

1982-01-01

The purpose of the present study are to evaluate fundamentally the method of Fourier analysis and to detect regional wall motion abnormality of the infarcted lesions by Fourier analysis. Fourier analyses were performed using the data obtained by first pass method in right anterior oblique projection (RAO) and by equilibrium method in left anterior oblique projection (LAO), and amplitude and phase were calculated. Amplitude and phase values needed to be corrected by R-R interval. On the detection of myocardial infarction, Fourier analyses in RAO and in LAO had same value for anterior infarctions. The analysis in RAO was more sensitive to detect infero-posterior lesions. On the other hand, the analysis in LAO was more sensitive for septal and lateral lesions

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.)

Fourier Transform Ultrasound Spectroscopy for the determination of wave propagation parameters.

Science.gov (United States)

Pal, Barnana

2017-01-01

The reported results for ultrasonic wave attenuation constant (α) in pure water show noticeable inconsistency in magnitude. A "Propagating-Wave" model analysis of the most popular pulse-echo technique indicates that this is a consequence of the inherent wave propagation characteristics in a bounded medium. In the present work Fourier Transform Ultrasound Spectroscopy (FTUS) is adopted to determine ultrasonic wave propagation parameters, the wave number (k) and attenuation constant (α) at 1MHz frequency in tri-distilled water at room temperature (25°C). Pulse-echo signals obtained under same experimental conditions regarding the exciting input signal and reflecting boundary wall of the water container for various lengths of water columns are captured. The Fast Fourier Transform (FFT) components of the echo signals are taken to compute k, α and r, the reflection constant at the boundary, using Oak Ridge and Oxford method. The results are compared with existing literature values. Copyright © 2016 Elsevier B.V. All rights reserved.

Fourier fringe analysis and its application to metrology of extreme physical phenomena: a review [Invited].

Science.gov (United States)

Takeda, Mitsuo

2013-01-01

The paper reviews a technique for fringe analysis referred to as Fourier fringe analysis (FFA) or the Fourier transform method, with a particular focus on its application to metrology of extreme physical phenomena. Examples include the measurement of extremely small magnetic fields with subfluxon sensitivity by electron wave interferometry, subnanometer wavefront evaluation of projection optics for extreme UV lithography, the detection of sub-Ångstrom distortion of a crystal lattice, and the measurement of ultrashort optical pulses in the femotsecond to attosecond range, which show how the advantages of FFA are exploited in these cutting edge applications.

Method for Car in Dangerous Action Detection by Means of Wavelet Multi Resolution Analysis Based on Appropriate Support Length of Base Function

OpenAIRE

Kohei Arai; Tomoko Nishikawa

2013-01-01

Multi-Resolution Analysis: MRA based on the mother wavelet function with which support length differs from the image of the automobile rear under run is performed, and the run characteristic of a car is searched for. Speed, deflection, etc. are analyzed and the method of detecting vehicles with high accident danger is proposed. The experimental results show that vehicles in a dangerous action can be detected by the proposed method.

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.

Mechanistic insights into nanotoxicity determined by synchrotron radiation-based Fourier-transform infrared imaging and multivariate analysis.

Science.gov (United States)

Riding, Matthew J; Trevisan, Júlio; Hirschmugl, Carol J; Jones, Kevin C; Semple, Kirk T; Martin, Francis L

2012-12-01

Our ability to identify the mechanisms by which carbon-based nanomaterials (CBNs) exert toxicity in cells is constrained by the lack of standardized methodologies to assay endpoint effects. Herein we describe a method of mechanistically identifying the effects of various CBN types in both prokaryotic and eukaryotic cells using multi-beam synchrotron radiation-based Fourier-transform infrared imaging (SR-FTIRI) at diffraction-limited resolution. This technique overcomes many of the inherent difficulties of assaying nanotoxicity and demonstrates exceptional sensitivity in identifying the effects of CBNs in cells at environmentally-relevant concentrations. We identify key mechanisms of nanotoxicity as the alteration of Amide and lipid biomolecules, but propose more specific bioactivity of CBNs occurs as a result of specific interactions between CBN structural conformation and cellular characteristics. Copyright © 2012 Elsevier Ltd. All rights reserved.

The derivative-free Fourier shell identity for photoacoustics.

Science.gov (United States)

Baddour, Natalie

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.

Image encryption based on fractal-structured phase mask in fractional Fourier transform domain

Science.gov (United States)

Zhao, Meng-Dan; Gao, Xu-Zhen; Pan, Yue; Zhang, Guan-Lin; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian

2018-04-01

We present an optical encryption approach based on the combination of fractal Fresnel lens (FFL) and fractional Fourier transform (FrFT). Our encryption approach is in fact a four-fold encryption scheme, including the random phase encoding produced by the Gerchberg–Saxton algorithm, a FFL, and two FrFTs. A FFL is composed of a Sierpinski carpet fractal plate and a Fresnel zone plate. In our encryption approach, the security is enhanced due to the more expandable key spaces and the use of FFL overcomes the alignment problem of the optical axis in optical system. Only using the perfectly matched parameters of the FFL and the FrFT, the plaintext can be recovered well. We present an image encryption algorithm that from the ciphertext we can get two original images by the FrFT with two different phase distribution keys, obtained by performing 100 iterations between the two plaintext and ciphertext, respectively. We test the sensitivity of our approach to various parameters such as the wavelength of light, the focal length of FFL, and the fractional orders of FrFT. Our approach can resist various attacks.

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

Principle and analysis of a rotational motion Fourier transform infrared spectrometer

Science.gov (United States)

Cai, Qisheng; Min, Huang; Han, Wei; Liu, Yixuan; Qian, Lulu; Lu, Xiangning

2017-09-01

Fourier transform infrared spectroscopy is an important technique in studying molecular energy levels, analyzing material compositions, and environmental pollutants detection. A novel rotational motion Fourier transform infrared spectrometer with high stability and ultra-rapid scanning characteristics is proposed in this paper. The basic principle, the optical path difference (OPD) calculations, and some tolerance analysis are elaborated. The OPD of this spectrometer is obtained by the continuously rotational motion of a pair of parallel mirrors instead of the translational motion in traditional Michelson interferometer. Because of the rotational motion, it avoids the tilt problems occurred in the translational motion Michelson interferometer. There is a cosine function relationship between the OPD and the rotating angle of the parallel mirrors. An optical model is setup in non-sequential mode of the ZEMAX software, and the interferogram of a monochromatic light is simulated using ray tracing method. The simulated interferogram is consistent with the theoretically calculated interferogram. As the rotating mirrors are the only moving elements in this spectrometer, the parallelism of the rotating mirrors and the vibration during the scan are analyzed. The vibration of the parallel mirrors is the main error during the rotation. This high stability and ultra-rapid scanning Fourier transform infrared spectrometer is a suitable candidate for airborne and space-borne remote sensing spectrometer.

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)

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.

Time Lens based Optical Fourier Transformation for All-Optical Signal Processing of Spectrally-Efficient Data

DEFF Research Database (Denmark)

Guan, Pengyu; Røge, Kasper Meldgaard; Lillieholm, Mads

2017-01-01

We review recent progress in the use of time lens based optical Fourier transformation for advanced all-optical signal processing. A novel time lens based complete optical Fourier transformation (OFT) technique is introduced. This complete OFT is based on two quadratic phase-modulation stages using...... four-wave mixing (FWM), separated by a dispersive medium, which enables time-to-frequency and frequency-to-time conversions simultaneously, thus performing an exchange between the temporal and spectral profiles of the input signal. Using the proposed complete OFT, several advanced all-optical signal......, such as orthogonal frequency division multiplexing (OFDM), Nyquist wavelength-division multiplexing (Nyquist-WDM) and Nyquist optical time division multiplexing (Nyquist-OTDM) signals....

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)

Short-time variations of the solar neutrino luminosity (Fourier analysis of the argon-37 production rate data)

International Nuclear Information System (INIS)

Haubold, H.J.; Gerth, E.

1985-01-01

We continue the Fourier analysis of the argon-37 production rate for runs 18--80 observed in Davis' well known solar neutrino experiment. The method of Fourier analysis with the unequally-spaced data of Davis and associates is described and the discovered periods we compare with our recently published results for the analysis of runs 18--69 (Haubold and Gerth, 1983). The harmonic analysis of the data of runs 18--80 shows time variations of the solar neutrino flux with periods π = 8.33; 5.26; 2.13; 1.56; 0.83; 0.64; 0.54; and 0.50 years, respectively, which confirms our earlier computations

[Continuum based fast Fourier transform processing of infrared spectrum].

Science.gov (United States)

Liu, Qing-Jie; Lin, Qi-Zhong; Wang, Qin-Jun; Li, Hui; Li, Shuai

2009-12-01

To recognize ground objects with infrared spectrum, high frequency noise removing is one of the most important phases in spectrum feature analysis and extraction. A new method for infrared spectrum preprocessing was given combining spectrum continuum processing and Fast Fourier Transform (CFFT). Continuum was firstly removed from the noise polluted infrared spectrum to standardize hyper-spectra. Then the spectrum was transformed into frequency domain (FD) with fast Fourier transform (FFT), separating noise information from target information After noise eliminating from useful information with a low-pass filter, the filtered FD spectrum was transformed into time domain (TD) with fast Fourier inverse transform. Finally the continuum was recovered to the spectrum, and the filtered infrared spectrum was achieved. Experiment was performed for chlorite spectrum in USGS polluted with two kinds of simulated white noise to validate the filtering ability of CFFT by contrast with cubic function of five point (CFFP) in time domain and traditional FFT in frequency domain. A circle of CFFP has limited filtering effect, so it should work much with more circles and consume more time to achieve better filtering result. As for conventional FFT, Gibbs phenomenon has great effect on preprocessing result at edge bands because of special character of rock or mineral spectra, while works well at middle bands. Mean squared error of CFFT is 0. 000 012 336 with cut-off frequency of 150, while that of FFT and CFFP is 0. 000 061 074 with cut-off frequency of 150 and 0.000 022 963 with 150 working circles respectively. Besides the filtering result of CFFT can be improved by adjusting the filter cut-off frequency, and has little effect on working time. The CFFT method overcomes the Gibbs problem of FFT in spectrum filtering, and can be more convenient, dependable, and effective than traditional TD filter methods.

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

Telomere length analysis.

Science.gov (United States)

Canela, Andrés; Klatt, Peter; Blasco, María A

2007-01-01

Most somatic cells of long-lived species undergo telomere shortening throughout life. Critically short telomeres trigger loss of cell viability in tissues, which has been related to alteration of tissue function and loss of regenerative capabilities in aging and aging-related diseases. Hence, telomere length is an important biomarker for aging and can be used in the prognosis of aging diseases. These facts highlight the importance of developing methods for telomere length determination that can be employed to evaluate telomere length during the human aging process. Telomere length quantification methods have improved greatly in accuracy and sensitivity since the development of the conventional telomeric Southern blot. Here, we describe the different methodologies recently developed for telomere length quantification, as well as their potential applications for human aging studies.

Electron tomography, three-dimensional Fourier analysis and colour prediction of a three-dimensional amorphous biophotonic nanostructure

Science.gov (United States)

Shawkey, Matthew D.; Saranathan, Vinodkumar; Pálsdóttir, Hildur; Crum, John; Ellisman, Mark H.; Auer, Manfred; Prum, Richard O.

2009-01-01

Organismal colour can be created by selective absorption of light by pigments or light scattering by photonic nanostructures. Photonic nanostructures may vary in refractive index over one, two or three dimensions and may be periodic over large spatial scales or amorphous with short-range order. Theoretical optical analysis of three-dimensional amorphous nanostructures has been challenging because these structures are difficult to describe accurately from conventional two-dimensional electron microscopy alone. Intermediate voltage electron microscopy (IVEM) with tomographic reconstruction adds three-dimensional data by using a high-power electron beam to penetrate and image sections of material sufficiently thick to contain a significant portion of the structure. Here, we use IVEM tomography to characterize a non-iridescent, three-dimensional biophotonic nanostructure: the spongy medullary layer from eastern bluebird Sialia sialis feather barbs. Tomography and three-dimensional Fourier analysis reveal that it is an amorphous, interconnected bicontinuous matrix that is appropriately ordered at local spatial scales in all three dimensions to coherently scatter light. The predicted reflectance spectra from the three-dimensional Fourier analysis are more precise than those predicted by previous two-dimensional Fourier analysis of transmission electron microscopy sections. These results highlight the usefulness, and obstacles, of tomography in the description and analysis of three-dimensional photonic structures. PMID:19158016

Time-Frequency Analysis of Non-Stationary Biological Signals with Sparse Linear Regression Based Fourier Linear Combiner

Directory of Open Access Journals (Sweden)

Yubo Wang

2017-06-01

Full Text Available It is often difficult to analyze biological signals because of their nonlinear and non-stationary characteristics. This necessitates the usage of time-frequency decomposition methods for analyzing the subtle changes in these signals that are often connected to an underlying phenomena. This paper presents a new approach to analyze the time-varying characteristics of such signals by employing a simple truncated Fourier series model, namely the band-limited multiple Fourier linear combiner (BMFLC. In contrast to the earlier designs, we first identified the sparsity imposed on the signal model in order to reformulate the model to a sparse linear regression model. The coefficients of the proposed model are then estimated by a convex optimization algorithm. The performance of the proposed method was analyzed with benchmark test signals. An energy ratio metric is employed to quantify the spectral performance and results show that the proposed method Sparse-BMFLC has high mean energy (0.9976 ratio and outperforms existing methods such as short-time Fourier transfrom (STFT, continuous Wavelet transform (CWT and BMFLC Kalman Smoother. Furthermore, the proposed method provides an overall 6.22% in reconstruction error.

Time-Frequency Analysis of Non-Stationary Biological Signals with Sparse Linear Regression Based Fourier Linear Combiner.

Science.gov (United States)

Wang, Yubo; Veluvolu, Kalyana C

2017-06-14

It is often difficult to analyze biological signals because of their nonlinear and non-stationary characteristics. This necessitates the usage of time-frequency decomposition methods for analyzing the subtle changes in these signals that are often connected to an underlying phenomena. This paper presents a new approach to analyze the time-varying characteristics of such signals by employing a simple truncated Fourier series model, namely the band-limited multiple Fourier linear combiner (BMFLC). In contrast to the earlier designs, we first identified the sparsity imposed on the signal model in order to reformulate the model to a sparse linear regression model. The coefficients of the proposed model are then estimated by a convex optimization algorithm. The performance of the proposed method was analyzed with benchmark test signals. An energy ratio metric is employed to quantify the spectral performance and results show that the proposed method Sparse-BMFLC has high mean energy (0.9976) ratio and outperforms existing methods such as short-time Fourier transfrom (STFT), continuous Wavelet transform (CWT) and BMFLC Kalman Smoother. Furthermore, the proposed method provides an overall 6.22% in reconstruction error.

The effect of shape, length and diameter of implants on primary stability based on resonance frequency analysis

Directory of Open Access Journals (Sweden)

Hamidreza Barikani

2014-01-01

Full Text Available Background: The aim of this in vitro study was to evaluate the effect of shape, diameter and length of implants on their primary stability based on resonance frequency analysis. Materials and Methods: Replace select tapered and Branemark MK III implants were selected. Each of these two selected groups was divided into nine subgroups based on the implant length (IL (short, medium and long and the implant diameter (ID (narrow platform [NP], regular platform [RP] and wide platform [WP]. Five implants were assigned to each of the nine subgroups. Implants were placed in artificial bone blocks with bone quality similar to D3 bone. Immediately after the implant placement, its primary stability was measured using Osstell Mentor equipment. T-test and Tukey′s honest significant difference Post hoc were performed for data analysis. Statistical significance was defined at P < 0.05. Results: Replace select system showed significantly higher primary stability compared to the Branemark system, when using the short implants for all three diameters (P ≤ 0.004. However, in medium length implants there were no significant differences between the two implant systems (P ≥ 0.31. In long implants, only when the NP and RP implants were used, the Replace Select system showed significantly higher primary stability compared to the Branemark system (P = 0.000. In the replace select system, long implants had a significantly higher primary stability compared to medium and short length implants (P ≤ 0.003. In the NP and RP Branemark implants, short implants showed significantly lower primary stability compared to medium and long implants (P ≤ 0.002. However, in WP Branemark implants, primary stability increased significantly with increasing the IL from short to medium and from medium to long (P = 0.000. There were also significant differences between NP and the two other wider implants in both systems (P = 0.000. Conclusion: The use of tapered implants is

Study on time-varying velocity measurement with self-mixing laser diode based on Discrete Chirp-Fourier Transform

International Nuclear Information System (INIS)

Zhang Zhaoyun; Gao Yang; Zhao Xinghai; Zhao Xiang

2011-01-01

Laser's optical output power and frequency are modulated when the optical beam is back-scattered into the active cavity of the laser. By signal processing, the Doppler frequency can be acquired, and the target's velocity can be calculated. Based on these properties, an interferometry velocity sensor can be designed. When target move in time-varying velocity mode, it is difficult to extract the target's velocity. Time-varying velocity measurement by self-mixing laser diode is explored. A mathematics model was proposed for the time-varying velocity (invariable acceleration) measurement by self-mixing laser diode. Based on this model, a Discrete Chirp-Fourier Transform (DCFT) method was applied, DCFT is analogous to DFT. We show that when the signal length N is prime, the magnitudes of all the side lobes are 1, whereas the magnitudes of the main lobe is √N, And the coordinates of the main lobe shows the target's velocity and acceleration information. The simulation results prove the validity of the algorithm even in the situation of low SNR when N is prime.

The fit of an X-ray diffraction profile by Fourier analysis

International Nuclear Information System (INIS)

Bourniquel, B.; Feron, J.

1985-01-01

The fast Fourier transform algorithm commonly used for line profile analysis requires a list of values of the diffracted intensity with constant sintheta step; raw data are usually obtained at constant 2theta step; to interpolate between the measured values an analytic expression of the profile function is very useful. Statistical estimation is used to fit an analytic function to data; the only assumption made is the continuity of this function and no critical initialization is needed. Three different expressions are used: a Fourier sum for the peak and two polynomials of a suitable variable for the tails; the algorithm provides continuity for the function and its first derivative. Simulated examples using a Lorentzian and a Gaussian function are given and several criteria of goodness of fit are examined. The program runs on a PDP 11/03 digital computer with only 45 kbytes available memory. (orig.)

Experimental demonstration of an OFDM receiver based on a silicon-nanophot onic discrete Fourier transform filter

DEFF Research Database (Denmark)

Da Ros, Francesco; Nolle, Markus; Meuer, C.

2014-01-01

We experimentally demonstrate the demultiplexing of 8×13.4 Gbaud OFDM-QPSK subcarriers using a silicon nanophotonic-based discrete Fourier transform (DFT) filter. All eight subcarriers showed less than 1.5 dB OSNR penalty compared to the theoretical limit.......We experimentally demonstrate the demultiplexing of 8×13.4 Gbaud OFDM-QPSK subcarriers using a silicon nanophotonic-based discrete Fourier transform (DFT) filter. All eight subcarriers showed less than 1.5 dB OSNR penalty compared to the theoretical limit....

Generalized functions and Fourier analysis dedicated to Stevan Pilipović on the occasion of his 65th birthday

CERN Document Server

Toft, Joachim; Vindas, Jasson; Wahlberg, Patrik

2017-01-01

This book gives an excellent and up-to-date overview on the convergence and joint progress in the fields of Generalized Functions and Fourier Analysis, notably in the core disciplines of pseudodifferential operators, microlocal analysis and time-frequency analysis. The volume is a collection of chapters addressing these fields, their interaction, their unifying concepts and their applications and is based on scientific activities related to the International Association for Generalized Functions (IAGF) and the ISAAC interest groups on Pseudo-Differential Operators (IGPDO) and on Generalized Functions (IGGF), notably on the longstanding collaboration of these groups within ISAAC.

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)

Fourier Transform Infrared Spectroscopy as a Tool in Analysis of Proteus mirabilis Endotoxins.

Science.gov (United States)

Żarnowiec, Paulina; Czerwonka, Grzegorz; Kaca, Wiesław

2017-01-01

Fourier transform infrared spectroscopy (FT-IR) was used to scan whole bacterial cells as well as lipopolysaccharides (LPSs, endotoxins) isolated from them. Proteus mirabilis cells, with chemically defined LPSs, served as a model for the ATR FT-IR method. The paper focuses on three steps of infrared spectroscopy: (1) sample preparation, (2) IR scanning, and (3) multivariate analysis of IR data (principal component analysis, PCA).

Time lens based optical fourier transformation for advanced processing of spectrally-efficient OFDM and N-WDM signals

DEFF Research Database (Denmark)

Guan, Pengyu; Røge, Kasper Meldgaard; Morioka, Toshio

2016-01-01

We review recent progress in the use of time lens based optical Fourier transformation for advanced optical signal processing, with focus on all-optical generation, detection and format conversion of spectrally-efficient OFDM and N-WDM signals.......We review recent progress in the use of time lens based optical Fourier transformation for advanced optical signal processing, with focus on all-optical generation, detection and format conversion of spectrally-efficient OFDM and N-WDM signals....

Utilização de filtro de transformada de fourier para a minimização de ruídos em sinais analíticos Utilization of fourier transform filter for noise minimization in analytical signals

Directory of Open Access Journals (Sweden)

Eduardo O. Cerqueira

2000-10-01

Full Text Available Instrumental data always present some noise. The analytical data information and instrumental noise generally has different frequencies. Thus is possible to remove the noise using a digital filter based on Fourier transform and inverse Fourier transform. This procedure enhance the signal/noise ratio and consecutively increase the detection limits on instrumental analysis. The basic principle of Fourier transform filter with modifications implemented to improve its performance is presented. A numerical example, as well as a real voltammetric example are showed to demonstrate the Fourier transform filter implementation. The programs to perform the Fourier transform filter, in Matlab and Visual Basic languages, are included as appendices

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.

Fourier Magnitude-Based Privacy-Preserving Clustering on Time-Series Data

Science.gov (United States)

Kim, Hea-Suk; Moon, Yang-Sae

Privacy-preserving clustering (PPC in short) is important in publishing sensitive time-series data. Previous PPC solutions, however, have a problem of not preserving distance orders or incurring privacy breach. To solve this problem, we propose a new PPC approach that exploits Fourier magnitudes of time-series. Our magnitude-based method does not cause privacy breach even though its techniques or related parameters are publicly revealed. Using magnitudes only, however, incurs the distance order problem, and we thus present magnitude selection strategies to preserve as many Euclidean distance orders as possible. Through extensive experiments, we showcase the superiority of our magnitude-based approach.

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)

Errors in Length-weight Parameters at FishBase.org

OpenAIRE

Michael Courtney; Simeon Cole-Fletcher; Lucas Marin-Salcedo; Ajaya Rana

2011-01-01

Background: FishBase.org is an on-line database of fish related data that has been cited over 1500 times in the fisheries literature. Length-weight relationships in fish traditionally employ the model, W(L) = aL^b^, where L is length and W is weight. Parameters a and b are catalogued by FishBase for a large number of sources and species. FishBase.org detects outliers in a plot of log(a) vs. b to identify dubious length-weight parameters.

Investigations of new cardiac functional imaging using Fourier analysis of gated blood-pool study

International Nuclear Information System (INIS)

Maeda, H.; Takeda, K.; Nakagawa, T.; Yamaguchi, N.; Taguchi, M.; Konishi, T.; Hamada, M.

1982-01-01

A new cardiac functional imaging, using temporal Fourier analysis of 28-frame gated cardiac blood-pool studies, was developed. A time-activity curve of each pixel was approximated by its Fourier series. Approximation by the sum for terms to the 3rd frequency of its Fourier series was considered to be most reasonable because of having the least aberration due to statistical fluctuation and close agreement between the global left ventricular curve and the regional fitted curves in normal subjects. To evaluate the ventricular systolic and diastolic performances, 9 parameters were analyzed from thus fitted curves on a pixel-by-pixel basis and displayed on a colour CRT in 64x64 matrix form. In patients with hypertrophic obstructive cardiomyopathy and other cardiac lesions, detailed information on the regional ventricular systolic and diastolic performances was clearly visualized by this method, which was difficult to obtain from the usual functional images of phase and amplitude at the fundamental frequency alone

An Interactive System For Fourier Analysis Of Artichoke Flower Shape.

Science.gov (United States)

Impedovo, Sebastiano; Fanelli, Anna M.; Ligouras, Panagiotis

1984-06-01

In this paper we present an interactive system which allows the Fourier analysis of the artichoke flower-head profile. The system consistsof a DEC pdp 11/34 computer with both a a track-following device and a Tektronix 4010/1 graphic and alpha numeric display on-line. Some experiments have been carried out taking into account some different parental types of artichoke flower-head samples. It is shown here that a narrow band of only eight harmonics is sufficient to classify different artichoke flower shapes.

Vibrational analysis of Fourier transform spectrum of the B 3− u (0

Indian Academy of Sciences (India)

... microwave, was recorded on BOMEM DA8 Fourier transform spectrometer at an apodized resolution of 0.035 cm-1. Vibrational constants were improved by putting the wave number of band origins in Deslandre table. The vibrational analysis was supported by determining the Franck–Condon factor and -centroid values.

Evaluation of natural mandibular shape asymmetry: an approach by using elliptical Fourier analysis.

Science.gov (United States)

Niño-Sandoval, Tania C; Morantes Ariza, Carlos F; Infante-Contreras, Clementina; Vasconcelos, Belmiro Ce

2018-04-05

The purpose of this study was to demonstrate that asymmetry is a natural occurring phenomenon in the mandibular shape by using elliptical Fourier analysis. 164 digital orthopantomographs from Colombian patients of both sexes aged 18 to 25 years were collected. Curves from left and right hemimandible were digitized. An elliptical Fourier analysis was performed with 20 harmonics. In the general sexual dimorphism a principal component analysis (PCA) and a hotelling T 2 from the multivariate warp space were employed. Exploratory analysis of general asymmetry and sexual dimorphism by side was made with a Procrustes Fit. A non-parametric multivariate analysis of variance (MANOVA) was applied to assess differentiation of skeletal classes of each hemimandible, and a Procrustes analysis of variance (ANOVA) was applied to search any relation between skeletal class and side in both sexes. Significant values were found in general asymmetry, general sexual dimorphism, in dimorphism by side (p < 0.0001), asymmetry by sex, and differences between Class I, II, and III (p < 0.005). However, a relation of skeletal classes and side was not found. The mandibular asymmetry by shape is present in all patients and should not be articulated exclusively to pathological processes, therefore, along with sexual dimorphism and differences between skeletal classes must be taken into account for improving mandibular prediction systems.

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

The deconvolution of Doppler-broadened positron annihilation measurements using fast Fourier transforms and power spectral analysis

International Nuclear Information System (INIS)

Schaffer, J.P.; Shaughnessy, E.J.; Jones, P.L.

1984-01-01

A deconvolution procedure which corrects Doppler-broadened positron annihilation spectra for instrument resolution is described. The method employs fast Fourier transforms, is model independent, and does not require iteration. The mathematical difficulties associated with the incorrectly posed first order Fredholm integral equation are overcome by using power spectral analysis to select a limited number of low frequency Fourier coefficients. The FFT/power spectrum method is then demonstrated for an irradiated high purity single crystal sapphire sample. (orig.)

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)

Some consequences of the Fourier analysis on the Lorentz group for relativistic quantum mechanics

International Nuclear Information System (INIS)

Mavrodiev, S.Ch.

1974-01-01

On the basis of the analogy between the nonrelativistic and relativistic Fourier analysis the uncertainty relation for rapidity and relativistic relative coordinate is formaly derived. A geometricla interpretation of the behaviour of the elastic scattering differential cross section is given too

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.

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

The hyperbolic chemical bond: Fourier analysis of ground and first excited state potential energy curves of HX (X = H-Ne).

Science.gov (United States)

Harrison, John A

2008-09-04

RHF/aug-cc-pVnZ, UHF/aug-cc-pVnZ, and QCISD/aug-cc-pVnZ, n = 2-5, potential energy curves of H2 X (1) summation g (+) are analyzed by Fourier transform methods after transformation to a new coordinate system via an inverse hyperbolic cosine coordinate mapping. The Fourier frequency domain spectra are interpreted in terms of underlying mathematical behavior giving rise to distinctive features. There is a clear difference between the underlying mathematical nature of the potential energy curves calculated at the HF and full-CI levels. The method is particularly suited to the analysis of potential energy curves obtained at the highest levels of theory because the Fourier spectra are observed to be of a compact nature, with the envelope of the Fourier frequency coefficients decaying in magnitude in an exponential manner. The finite number of Fourier coefficients required to describe the CI curves allows for an optimum sampling strategy to be developed, corresponding to that required for exponential and geometric convergence. The underlying random numerical noise due to the finite convergence criterion is also a clearly identifiable feature in the Fourier spectrum. The methodology is applied to the analysis of MRCI potential energy curves for the ground and first excited states of HX (X = H-Ne). All potential energy curves exhibit structure in the Fourier spectrum consistent with the existence of resonances. The compact nature of the Fourier spectra following the inverse hyperbolic cosine coordinate mapping is highly suggestive that there is some advantage in viewing the chemical bond as having an underlying hyperbolic nature.

Performance of a MEMS-based AO-OCT system using Fourier Reconstruction

Energy Technology Data Exchange (ETDEWEB)

Evans, J; Zawadzki, R; Jones, S; Olivier, S; Werner, J S

2009-01-21

Adaptive optics (AO) and optical coherence tomography (OCT) are powerful imaging modalities that, when combined, can provide high-resolution (3.5 {micro}m isotropic), 3-D images of the retina. The AO-OCT system at UC Davis has demonstrated the utility of this technology for microscopic, volumetric, in vivo retinal imaging. The current system uses an AOptix bimorph deformable mirror (DM) for low-order, high-stroke correction and a 140-actuator Boston Micromachines DM for high-order correction. Developments to improve performance or functionality of the instrument are on-going. Based on previous work in system characterization we have focused on improved AO control. We present preliminary results and remaining challenges for a newly implemented Fourier transform reconstructor (FTR). The previously reported error budget analysis is also reviewed and updated, with consideration of how to improve both the amount of residual error and the robustness of the system. Careful characterization of the AO system will lead to improved performance and inform the design of future systems.

Sorghum cobalt analysis on not determined wave length with atomic ...

African Journals Online (AJOL)

This study was to know the better wave length on measuring cobalt content in forage sorghum hybrid (Sorghum bicolor) with an atomic absorption spectrophotometer. The analysis was on background correction mode with three wave lengths; 240.8, 240.7 (determined wave length or recommended wave length) and 240.6 ...

The fractional Fourier transform as a simulation tool for lens-based X-ray microscopy

DEFF Research Database (Denmark)

Pedersen, Anders Filsøe; Simons, Hugh; Detlefs, Carsten

2018-01-01

The fractional Fourier transform (FrFT) is introduced as a tool for numerical simulations of X-ray wavefront propagation. By removing the strict sampling requirements encountered in typical Fourier optics, simulations using the FrFT can be carried out with much decreased detail, allowing...... the attenuation from the entire CRL using one or two effective apertures without loss of accuracy, greatly accelerating simulations involving CRLs. To demonstrate the applicability and accuracy of the FrFT, the imaging resolution of a CRL-based imaging system is estimated, and the FrFT approach is shown...

Diffusion tensor MRI shows progressive changes in the hippocampus and dentate gyrus after status epilepticus in rat - histological validation with Fourier-based analysis.

Science.gov (United States)

Salo, Raimo A; Miettinen, Tuukka; Laitinen, Teemu; Gröhn, Olli; Sierra, Alejandra

2017-05-15

Imaging markers for monitoring disease progression, recovery, and treatment efficacy are a major unmet need for many neurological diseases, including epilepsy. Recent evidence suggests that diffusion tensor imaging (DTI) provides high microstructural contrast even outside major white matter tracts. We hypothesized that in vivo DTI could detect progressive microstructural changes in the dentate gyrus and the hippocampal CA3bc in the rat brain after status epilepticus (SE). To test this hypothesis, we induced SE with systemic kainic acid or pilocarpine in adult male Wistar rats and subsequently scanned them using in vivo DTI at five time-points: prior to SE, and 10, 20, 34, and 79 days post SE. In order to tie the DTI findings to changes in the tissue microstructure, myelin- and glial fibrillary acidic protein (GFAP)-stained sections from the same animals underwent Fourier analysis. We compared the Fourier analysis parameters, anisotropy index and angle of myelinated axons or astrocyte processes, to corresponding DTI parameters, fractional anisotropy (FA) and the orientation angle of the principal eigenvector. We found progressive detectable changes in DTI parameters in both the dentate gyrus (FA, axial diffusivity [D || ], linear anisotropy [CL] and spherical anisotropy [CS], pFourier analysis revealed that both myelinated axons and astrocyte processes played a role in the water diffusion anisotropy changes detected by DTI in individual portions of the dentate gyrus (suprapyramidal blade, mid-portion, and infrapyramidal blade). In the whole dentate gyrus, myelinated axons markedly contributed to the water diffusion changes. In CA3bc as well as in CA3b and CA3c, both myelinated axons and astrocyte processes contributed to water diffusion anisotropy and orientation. Our study revealed that DTI is a promising method for noninvasive detection of microstructural alterations in the hippocampus proper. These alterations may be potential imaging markers for epileptogenesis

Multi-band Image Registration Method Based on Fourier Transform

Institute of Scientific and Technical Information of China (English)

庹红娅; 刘允才

2004-01-01

This paper presented a registration method based on Fourier transform for multi-band images which is involved in translation and small rotation. Although different band images differ a lot in the intensity and features,they contain certain common information which we can exploit. A model was given that the multi-band images have linear correlations under the least-square sense. It is proved that the coefficients have no effect on the registration progress if two images have linear correlations. Finally, the steps of the registration method were proposed. The experiments show that the model is reasonable and the results are satisfying.

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.

Automated magnification calibration in transmission electron microscopy using Fourier analysis of replica images

International Nuclear Information System (INIS)

Laak, Jeroen A.W.M. van der; Dijkman, Henry B.P.M.; Pahlplatz, Martin M.M.

2006-01-01

The magnification factor in transmission electron microscopy is not very precise, hampering for instance quantitative analysis of specimens. Calibration of the magnification is usually performed interactively using replica specimens, containing line or grating patterns with known spacing. In the present study, a procedure is described for automated magnification calibration using digital images of a line replica. This procedure is based on analysis of the power spectrum of Fourier transformed replica images, and is compared to interactive measurement in the same images. Images were used with magnification ranging from 1,000x to 200,000x. The automated procedure deviated on average 0.10% from interactive measurements. Especially for catalase replicas, the coefficient of variation of automated measurement was considerably smaller (average 0.28%) compared to that of interactive measurement (average 3.5%). In conclusion, calibration of the magnification in digital images from transmission electron microscopy may be performed automatically, using the procedure presented here, with high precision and accuracy

An illustration of harmonic regression based on the results of the fast Fourier transformation

Directory of Open Access Journals (Sweden)

Bertfai Imre

2002-01-01

Full Text Available The well-known methodology of the Fourier analysis is put against the background in the 2nd half of the century parallel to the development of the time-domain approach in the analysis of mainly economical time series. However, from the author's point of view, the former possesses some hidden analytical advantages which deserve to be re-introduced to the toolbox of analysts. This paper, through several case studies, reports research results for computer algorithm providing a harmonic model for time series. The starting point of the particular method is a harmonic analysis (Fourier-analysis or Lomb-periodogram. The results are optimized in a multifold manner resulting in a model which is easy to handle and able to forecast the underlying data. The results provided are particularly free from limitations characteristic for that methods. Furthermore, the calculated results are easy to interpret and use for further decisions. Nevertheless, the author intends to enhance the procedure in several ways. The method shown seems to be very effective and useful in modeling time series consisting of periodic terms. An additional advantage is the easy interpretation of the obtained parameters.

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...

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

Simple surface structure determination from Fourier transforms of angle-resolved photoemission extended fine structure

Energy Technology Data Exchange (ETDEWEB)

Zheng, Y. [Pennsylvania State Univ., University Park, PA (United States)]|[Lawrence Berkeley Lab., CA (United States); Shirley, D.A. [Pennsylvania State Univ., University Park, PA (United States)

1995-02-01

The authors show by Fourier analyses of experimental data, with no further treatment, that the positions of all the strong peaks in Fourier transforms of angle-resolved photoemission extended fine structure (ARPEFS) from adsorbed surfaces can be explicitly predicted from a trial structure with an accuracy of about {+-} 0.3 {angstrom} based on a single-scattering cluster model together with the concept of a strong backscattering cone, and without any additional analysis. This characteristic of ARPEFS Fourier transforms can be developed as a simple method for determining the structures of adsorbed surfaces to an accuracy of about {+-} 0.1 {angstrom}.

Influence of solder joint length to the mechanical aspect during the thermal stress analysis

Science.gov (United States)

Tan, J. S.; Khor, C. Y.; Rahim, Wan Mohd Faizal Wan Abd; Ishak, Muhammad Ikman; Rosli, M. U.; Jamalludin, Mohd Riduan; Zakaria, M. S.; Nawi, M. A. M.; Aziz, M. S. Abdul; Ani, F. Che

2017-09-01

Solder joint is an important interconnector in surface mount technology (SMT) assembly process. The real time stress, strain and displacement of the solder joint is difficult to observe and assess the experiment. To tackle these problems, simulation analysis was employed to study the von Mises stress, strain and displacement in the thermal stress analysis by using Finite element based software. In this study, a model of leadless electronic package was considered. The thermal stress analysis was performed to investigate the effect of the solder length to those mechanical aspects. The simulation results revealed that solder length gives significant effect to the maximum von Mises stress to the solder joint. Besides, changes in solder length also influence the displacement of the solder joint in the thermal environment. The increment of the solder length significantly reduces the von Mises stress and strain on the solder joint. Thus, the understanding of the physical parameter for solder joint is important for engineer prior to designing the solder joint of the electronic component.

Optical Path Length Calibration: A Standard Approach for Use in Absorption Cell-Based IR-Spectrometric Gas Analysis

Directory of Open Access Journals (Sweden)

Javis Anyangwe Nwaboh

2014-01-01

Full Text Available We employed a comparison method to determine the optical path length of gas cells which can be used in spectroscopic setup based on laser absorption spectroscopy or FTIR. The method is based on absorption spectroscopy itself. A reference gas cell, whose length is a priori known and desirably traceable to the international system of units (SI, and a gas mixture are used to calibrate the path length of a cell under test. By comparing spectra derived from pressure-dependent measurements on the two cells, the path length of the gas cell under test is determined. The method relies neither on the knowledge of the gas concentration nor on the line strength parameter of the probed transition which is very rarely traceable to the SI and of which the uncertainty is often relatively large. The method is flexible such that any infrared light source and infrared active molecule with isolated lines can be used. We elaborate on the method, substantiate the method by reporting results of this calibration procedure applied to multipass and single pass gas cells of lengths from 0.38 m to 21 m, and compare this to other methods. The relative combined uncertainty of the path length results determined using the comparison method was found to be in the ±0.4% range.

Proposal of AAA-battery-size one-shot ATR Fourier spectroscopic imager for on-site analysis: Simultaneous measurement of multi-components with high accuracy

Science.gov (United States)

Hosono, Satsuki; Qi, Wei; Sato, Shun; Suzuki, Yo; Fujiwara, Masaru; Hiramatsu, Hiroyuki; Suzuki, Satoru; Abeygunawardhana, P. K. W.; Wada, Kenji; Nishiyama, Akira; Ishimaru, Ichiro

2015-03-01

For simultaneous measurement of multi-components on-site like factories, the ultra-compact (diameter: 9[mm], length: 45[mm], weight: 200[g]) one-shot ATR (Attenuated Total Reflection) Fourier spectroscopic imager was proposed. Because the proposed one-shot Fourier spectroscopic imaging is based on spatial-phase-shift interferometer, interferograms could be obtained with simple optical configurations. We introduced the transmission-type relativeinclined phase-shifter, that was constructed with a cuboid prism and a wedge prism, onto the optical Fourier transform plane of infinity corrected optical systems. And also, small light-sources and cameras in the mid-infrared light region, whose size are several millimeter on a side, are essential components for the ultra-compact spectroscopic configuration. We selected the Graphite light source (light source area: 1.7×1.7[mm], maker: Hawkeye technologies) whose radiation factor was high. Fortunately, in these days we could apply the cost-effective 2-dimensional light receiving device for smartphone (e.g. product name: LEPTON, maker: FLIR, price: around 400USD). In the case of alcoholic drinks factory, conventionally workers measure glucose and ethanol concentrations by bringing liquid solution back to laboratories every day. The high portable spectroscopy will make it possible to measure multi-components simultaneously on manufacturing scene. But we found experimentally that absorption spectrum of glucose and water and ethanol were overlapped each other in near infrared light region. But for mid-infrared light region, we could distinguish specific absorption peaks of glucose (@10.5[μm]) and ethanol (@11.5[μm]) independently from water absorption. We obtained standard curve between absorption (@9.6[μm]) and ethanol concentration with high correlation coefficient 0.98 successfully by ATR imaging-type 2-dimensional Fourier spectroscopy (wavelength resolution: 0.057[μm]) with the graphite light source (maker: Hawkeye

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

Fourier techniques for an analysis of eclipsing binary light curves. Pt. 6b

International Nuclear Information System (INIS)

Demircan, O.

1980-01-01

This is a continuation of a previous paper which appeared in this journal (Demircan, 1980b) and aims at ascertaining some other relations between the integral transforms of the light curves of eclipsing binary systems. The appropriate use of these relations should facilitate the numerical computations for an analysis of eclipsing binary light curves by different Fourier techniques. (orig.)

Fourier analysis of spherically averaged momentum densities for some gaseous molecules

International Nuclear Information System (INIS)

Tossel, J.A.; Moore, J.H.

1981-01-01

The spherically averaged autocorrelation function, B(r), of the position-space wavefunction, psi(anti r), is calculated by numerical Fourier transformation from spherically averaged momentum densities, rho(p), obtained from either theoretical wavefunctions or (e,2e) electron-impact ionization experiments. Inspection of B(r) for the π molecular orbitals of C 4 H 6 established that autocorrelation function differences, ΔB(r), can be qualitatively related to bond lengths and numbers of bonding interactions. Differences between B(r) functions obtained from different approximate wavefunctions for a given orbital can be qualitatively understood in terms of wavefunction difference, Δpsi(1anti r), maps for these orbitals. Comparison of the B(r) function for the 1αsub(u) orbital of C 4 H 6 obtained from (e,2e) momentum densities with that obtained from an ab initio SCF MO wavefunction shows differences consistent with expected correlation effects. Thus, B(r) appears to be a useful quantity for relating spherically averaged momentum distributions to position-space wavefunction differences. (orig.)

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.

THE IMAGE REGISTRATION OF FOURIER-MELLIN BASED ON THE COMBINATION OF PROJECTION AND GRADIENT PREPROCESSING

Directory of Open Access Journals (Sweden)

D. Gao

2017-09-01

Full Text Available Image registration is one of the most important applications in the field of image processing. The method of Fourier Merlin transform, which has the advantages of high precision and good robustness to change in light and shade, partial blocking, noise influence and so on, is widely used. However, not only this method can’t obtain the unique mutual power pulse function for non-parallel image pairs, even part of image pairs also can’t get the mutual power function pulse. In this paper, an image registration method based on Fourier-Mellin transformation in the view of projection-gradient preprocessing is proposed. According to the projection conformational equation, the method calculates the matrix of image projection transformation to correct the tilt image; then, gradient preprocessing and Fourier-Mellin transformation are performed on the corrected image to obtain the registration parameters. Eventually, the experiment results show that the method makes the image registration of Fourier-Mellin transformation not only applicable to the registration of the parallel image pairs, but also to the registration of non-parallel image pairs. What’s more, the better registration effect can be obtained

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.

Investigation of Cyprus thermal tenancy using nine year MODIS LST data and Fourier analysis

Science.gov (United States)

Skarlatos, D.; Miliaresis, G.; Georgiou, A.

2013-08-01

Land Surface Temperature (LST) is an extremely important parameter that controls the exchange of long wave radiation between surface and atmosphere. It is a good indicator of the energy balance at the Earth's surface and it is one of the key parameters in the physics of land-surface processes on regional as well as global scale. This paper utilizes monthly night and day averaged LST MODIS imagery over Cyprus for a 9 year period. Fourier analysis and Least squares estimation fitting are implemented to analyze mean daily data over Cyprus in an attempt to investigate possible temperature tenancy over these years and possible differences among areas with different land cover and land use, such as Troodos Mountain and Nicosia, the main city in the center of the island. The analysis of data over a long time period, allows questions such as whether there is a tenancy to temperature increase, to be answered in a statistically better way, provided that `noise' is removed correctly. Dealing with a lot of data, always provides a more accurate estimation, but on the other hand, more noise in implemented on the data, especially when dealing with temperature which is subject to daily and annual cycles. A brief description over semi-automated data acquisition and standardization using object-oriented programming and GIS-based techniques, will be presented. The paper fully describes the time series analysis implemented, the Fourier method and how it was used to analyze and filter mean daily data with high frequency. Comparison of mean monthly daily LST against day and night LSTs is also performed over the 9 year period in order to investigate whether use of the extended data series provide significant advantage over short.

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

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.

Automated acid and base number determination of mineral-based lubricants by fourier transform infrared spectroscopy: commercial laboratory evaluation.

Science.gov (United States)

Winterfield, Craig; van de Voort, F R

2014-12-01

The Fluid Life Corporation assessed and implemented Fourier transform infrared spectroscopy (FTIR)-based methods using American Society for Testing and Materials (ASTM)-like stoichiometric reactions for determination of acid and base number for in-service mineral-based oils. The basic protocols, quality control procedures, calibration, validation, and performance of these new quantitative methods are assessed. ASTM correspondence is attained using a mixed-mode calibration, using primary reference standards to anchor the calibration, supplemented by representative sample lubricants analyzed by ASTM procedures. A partial least squares calibration is devised by combining primary acid/base reference standards and representative samples, focusing on the main spectral stoichiometric response with chemometrics assisting in accounting for matrix variability. FTIR(AN/BN) methodology is precise, accurate, and free of most interference that affects ASTM D664 and D4739 results. Extensive side-by-side operational runs produced normally distributed differences with mean differences close to zero and standard deviations of 0.18 and 0.26 mg KOH/g, respectively. Statistically, the FTIR methods are a direct match to the ASTM methods, with superior performance in terms of analytical throughput, preparation time, and solvent use. FTIR(AN/BN) analysis is a viable, significant advance for in-service lubricant analysis, providing an economic means of trending samples instead of tedious and expensive conventional ASTM(AN/BN) procedures. © 2014 Society for Laboratory Automation and Screening.

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

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…

Analysis of the Interference Modulation Depth in the Fourier Transform Spectrometer

Directory of Open Access Journals (Sweden)

Rilong Liu

2015-01-01

Full Text Available Based on the principle of the Michelson interferometer, the paper briefly describes the theoretical significance and calculates and deduces three expressions of the interference modulation depth. The influence of the surface shape error of plane mirror on modulation depth is analyzed, and the tolerance of error is also pointed out. Moreover, the dependence of modulation depth on the reflectance change of beam splitter interface is also analyzed, and the curve is given. It is concluded that this paper is of general significance for the Fourier transform spectrometer based on the principle of the Michelson two-beam interference.

VLSI Design of a Variable-Length FFT/IFFT Processor for OFDM-Based Communication Systems

Directory of Open Access Journals (Sweden)

Jen-Chih Kuo

2003-12-01

Full Text Available The technique of {orthogonal frequency division multiplexing (OFDM} is famous for its robustness against frequency-selective fading channel. This technique has been widely used in many wired and wireless communication systems. In general, the {fast Fourier transform (FFT} and {inverse FFT (IFFT} operations are used as the modulation/demodulation kernel in the OFDM systems, and the sizes of FFT/IFFT operations are varied in different applications of OFDM systems. In this paper, we design and implement a variable-length prototype FFT/IFFT processor to cover different specifications of OFDM applications. The cached-memory FFT architecture is our suggested VLSI system architecture to design the prototype FFT/IFFT processor for the consideration of low-power consumption. We also implement the twiddle factor butterfly {processing element (PE} based on the {{coordinate} rotation digital computer (CORDIC} algorithm, which avoids the use of conventional multiplication-and-accumulation unit, but evaluates the trigonometric functions using only add-and-shift operations. Finally, we implement a variable-length prototype FFT/IFFT processor with TSMC 0.35 μm 1P4M CMOS technology. The simulations results show that the chip can perform (64-2048-point FFT/IFFT operations up to 80 MHz operating frequency which can meet the speed requirement of most OFDM standards such as WLAN, ADSL, VDSL (256∼2K, DAB, and 2K-mode DVB.

Application of the fractional Fourier transform to the design of LCOS based optical interconnects and fiber switches.

Science.gov (United States)

Robertson, Brian; Zhang, Zichen; Yang, Haining; Redmond, Maura M; Collings, Neil; Liu, Jinsong; Lin, Ruisheng; Jeziorska-Chapman, Anna M; Moore, John R; Crossland, William A; Chu, D P

2012-04-20

It is shown that reflective liquid crystal on silicon (LCOS) spatial light modulator (SLM) based interconnects or fiber switches that use defocus to reduce crosstalk can be evaluated and optimized using a fractional Fourier transform if certain optical symmetry conditions are met. Theoretically the maximum allowable linear hologram phase error compared to a Fourier switch is increased by a factor of six before the target crosstalk for telecom applications of -40 dB is exceeded. A Gerchberg-Saxton algorithm incorporating a fractional Fourier transform modified for use with a reflective LCOS SLM is used to optimize multi-casting holograms in a prototype telecom switch. Experiments are in close agreement to predicted performance.

ESTIMATION OF STATURE BASED ON FOOT LENGTH

Directory of Open Access Journals (Sweden)

Vidyullatha Shetty

2015-01-01

Full Text Available BACKGROUND : Stature is the height of the person in the upright posture. It is an important measure of physical identity. Estimation of body height from its segments or dismember parts has important considerations for identifications of living or dead human body or remains recovered from disasters or other similar conditions. OBJECTIVE : Stature is an important indicator for identification. There are numerous means to establish stature and their significance lies in the simplicity of measurement, applicability and accuracy in prediction. Our aim of the study was to review the relationship between foot length and body height. METHODS : The present study reviews various prospective studies which were done to estimate the stature. All the measurements were taken by using standard measuring devices and standard anthropometric techniques. RESULTS : This review shows there is a correlation between stature and foot dimensions it is found to be positive and statistically highly significant. Prediction of stature was found to be most accurate by multiple regression analysis. CONCLUSIONS : Stature and gender estimation can be done by using foot measurements and stud y will help in medico - legal cases in establishing identity of an individual and this would be useful for Anatomists and Anthropologists to calculate stature based on foot length

Research On Variable-Length Transfer Delay and Delayed Signal Cancellation Based PLLs

DEFF Research Database (Denmark)

Golestan, Saeed; Guerrero, Josep M.; Quintero, Juan Carlos Vasquez

2018-01-01

large frequency drifts are anticipated and a high accuracy is required. To the best of authors' knowledge, the small-signal modeling of a variable-length delay-based PLL has not yet been conducted. The main aim of this paper is to cover this gap. The tuning procedure and analysis of these PLLs...

Using Fourier-Motzkin-Elimination to Derive Capacity Models of Container Vessels

DEFF Research Database (Denmark)

Ajspur, Mai Lise; Jensen, Rune Møller

2017-01-01

Due to its high computational complexity, Fourier-Motzkin-Elimination (FME) is mainly known as a theoretical approach to determine feasibility of a linear program (LP). Current applications of FME in static program analysis and logic programming is based on the fact that it is a transformation...

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...

Fourier analysis algorithm for the posterior corneal keratometric data: clinical usefulness in keratoconus.

Science.gov (United States)

Sideroudi, Haris; Labiris, Georgios; Georgantzoglou, Kimon; Ntonti, Panagiota; Siganos, Charalambos; Kozobolis, Vassilios

2017-07-01

To develop an algorithm for the Fourier analysis of posterior corneal videokeratographic data and to evaluate the derived parameters in the diagnosis of Subclinical Keratoconus (SKC) and Keratoconus (KC). This was a cross-sectional, observational study that took place in the Eye Institute of Thrace, Democritus University, Greece. Eighty eyes formed the KC group, 55 eyes formed the SKC group while 50 normal eyes populated the control group. A self-developed algorithm in visual basic for Microsoft Excel performed a Fourier series harmonic analysis for the posterior corneal sagittal curvature data. The algorithm decomposed the obtained curvatures into a spherical component, regular astigmatism, asymmetry and higher order irregularities for averaged central 4 mm and for each individual ring separately (1, 2, 3 and 4 mm). The obtained values were evaluated for their diagnostic capacity using receiver operating curves (ROC). Logistic regression was attempted for the identification of a combined diagnostic model. Significant differences were detected in regular astigmatism, asymmetry and higher order irregularities among groups. For the SKC group, the parameters with high diagnostic ability (AUC > 90%) were the higher order irregularities, the asymmetry and the regular astigmatism, mainly in the corneal periphery. Higher predictive accuracy was identified using diagnostic models that combined the asymmetry, regular astigmatism and higher order irregularities in averaged 3and 4 mm area (AUC: 98.4%, Sensitivity: 91.7% and Specificity:100%). Fourier decomposition of posterior Keratometric data provides parameters with high accuracy in differentiating SKC from normal corneas and should be included in the prompt diagnosis of KC. © 2017 The Authors Ophthalmic & Physiological Optics © 2017 The College of Optometrists.

Threshold Research on Highway Length under Typical Landscape Patterns Based on Drivers’ Physiological Performance

Directory of Open Access Journals (Sweden)

Xia Zhao

2015-01-01

Full Text Available The appropriately landscaped highway scenes may not only help improve road safety and comfort but also help protect ecological environment. Yet there is very little research data on highway length threshold with consideration of distinctive landscape patterns. Against this backdrop, the paper aims to quantitatively analyze highway landscape’s effect on driving behavior based on drivers’ physiological performance and quantify highway length thresholds under three typical landscape patterns, namely, “open,” “semiopen,” and “vertical” ones. The statistical analysis was based on data collected in a driving simulator and electrocardiograph. Specifically, vehicle-related data, ECG data, and supplemental subjective stress perception were collected. The study extracted two characteristic indices, lane deviation and LF/HF, and extrapolated the drivers’ U-shaped physiological response to landscape patterns. Models on highway length were built based on LF/HF’s variation trend with highway length. The results revealed that the theoretical highway length threshold tended to increase when the landscape pattern was switched to open, semiopen, and vertical ones. And the reliability and accuracy of the results were validated by questionnaires and field operational tests. Findings from this research will assist practitioners in taking active environmental countermeasures pertaining to different roadside landscape patterns.

Quantitative analysis of lattice disorder and crystallite size in organic semiconductor thin films

KAUST Repository

Rivnay, Jonathan

2011-07-07

The crystallite size and cumulative lattice disorder of three prototypical, high-performing organic semiconducting materials are investigated using a Fourier-transform peak shape analysis routine based on the method of Warren and Averbach (WA). A thorough incorporation of error propagation throughout the multistep analysis and a weighted fitting of Fourier-transformed data to the WA model allows for more accurate results than typically obtained and for determination of confidence bounds. We compare results obtained when assuming two types of column-length distributions, and discuss the benefits of each model in terms of simplicity and accuracy. For strongly disordered materials, the determination of a crystallite size is greatly hindered because disorder dominates the coherence length, not finite size. A simple analysis based on trends of peak widths and Lorentzian components of pseudo-Voigt line shapes as a function of diffraction order is also discussed as an approach to more easily and qualitatively assess the amount and type of disorder present in a sample. While applied directly to organic systems, this methodology is general for the accurate deconvolution of crystalline size and lattice disorder for any material investigated with diffraction techniques. © 2011 American Physical Society.

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

Stability analysis of CMFD acceleration for the wavelet expansion method of neutron transport equation

International Nuclear Information System (INIS)

Zheng Youqi; Wu Hongchun; Cao Liangzhi

2013-01-01

This paper describes the stability analysis for the coarse mesh finite difference (CMFD) acceleration used in the wavelet expansion method. The nonlinear CMFD acceleration scheme is transformed by linearization and the Fourier ansatz is introduced into the linearized formulae. The spectral radius is defined as the stability criterion, which is the least upper bound (LUB) of the largest eigenvalue of Fourier analysis matrix. The stability analysis considers the effect of mesh size (spectral length), coarse mesh division and scattering ratio. The results show that for the wavelet expansion method, the CMFD acceleration is conditionally stable. The small size of fine mesh brings stability and fast convergent. With the increase of the mesh size, the stability becomes worse. The scattering ratio does not impact the stability obviously. It makes the CMFD acceleration highly efficient in the strong scattering case. The results of Fourier analysis are verified by the numerical tests based on a homogeneous slab problem.

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.

Fourier-based magnetic induction tomography for mapping resistivity

International Nuclear Information System (INIS)

Puwal, Steffan; Roth, Bradley J.

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.

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)

Screening and confirmation criteria for hormone residue analysis using liquid chromatography accurate mass time-of-flight, Fourier transform ion cyclotron resonance and orbitrap mass spectrometry techniques

NARCIS (Netherlands)

Nielen, M.W.F.; Engelen, M.C. van; Zuiderent, R.; Ramaker, R.

2007-01-01

An emerging trend is recognised in hormone and veterinary drug residue analysis from liquid chromatography tandem mass spectrometry (LC/MS/MS) based screening and confirmation towards accurate mass alternatives such as LC coupled with time-of-flight (TOF), Fourier transform ion cyclotron resonance

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....

The propagation of stochastic pixel noise into magnitude and phase values in the Fourier analysis of digital images

International Nuclear Information System (INIS)

Holden, J.E.; Halama, J.R.; Hasegawa, B.H.

1986-01-01

The use of Fourier analysis in nuclear medicine gated blood ventriculography provides a useful example of the application of Fourier methods to digital medical imaging. In particular, the nuclear medicine experience demonstrates that there is diagnostic significance not only in the pixel averages of temporal Fourier magnitude and phase computed in various image regions, but also in the distributions of the individual pixel values about those averages. However, a region containing pixels that are perfectly synchronous on average would still yield a finite distribution of calculated Fourier coefficients due to the propagation of stochastic pixel noise into the calculated values. The authors have studied this noise component of both the magnitude and phase distributions using phantom studies and computer simulation. In both approaches, several thousand one-pixel 'ventriculograms' were generated, all identical to each other except for stochastic noise. Fourier magnitudes and phases at several frequencies were calculated and histograms generated. A theoretical prediction of the distributions was developed and shown to fit the experimental results well. The authors' formalism can be used to estimate study count requirements or, for fixed study counts, to assess the stochastic noise contribution in the interpretation of measured phase and magnitude distributions. (author)

Estimation of Interchannel Time Difference in Frequency Subbands Based on Nonuniform Discrete Fourier Transform

Directory of Open Access Journals (Sweden)

Qiu Bo

2008-01-01

Full Text Available Binaural cue coding (BCC is an efficient technique for spatial audio rendering by using the side information such as interchannel level difference (ICLD, interchannel time difference (ICTD, and interchannel correlation (ICC. Of the side information, the ICTD plays an important role to the auditory spatial image. However, inaccurate estimation of the ICTD may lead to the audio quality degradation. In this paper, we develop a novel ICTD estimation algorithm based on the nonuniform discrete Fourier transform (NDFT and integrate it with the BCC approach to improve the decoded auditory image. Furthermore, a new subjective assessment method is proposed for the evaluation of auditory image widths of decoded signals. The test results demonstrate that the NDFT-based scheme can achieve much wider and more externalized auditory image than the existing BCC scheme based on the discrete Fourier transform (DFT. It is found that the present technique, regardless of the image width, does not deteriorate the sound quality at the decoder compared to the traditional scheme without ICTD estimation.

Fourier transform infrared microspectroscopy for the analysis of the biochemical composition of C. elegans worms.

Science.gov (United States)

Sheng, Ming; Gorzsás, András; Tuck, Simon

2016-01-01

Changes in intermediary metabolism have profound effects on many aspects of C. elegans biology including growth, development and behavior. However, many traditional biochemical techniques for analyzing chemical composition require relatively large amounts of starting material precluding the analysis of mutants that cannot be grown in large amounts as homozygotes. Here we describe a technique for detecting changes in the chemical compositions of C. elegans worms by Fourier transform infrared microspectroscopy. We demonstrate that the technique can be used to detect changes in the relative levels of carbohydrates, proteins and lipids in one and the same worm. We suggest that Fourier transform infrared microspectroscopy represents a useful addition to the arsenal of techniques for metabolic studies of C. elegans worms.

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

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.

Adaptive Fourier decomposition based R-peak detection for noisy ECG Signals.

Science.gov (United States)

Ze Wang; Chi Man Wong; Feng Wan

2017-07-01

An adaptive Fourier decomposition (AFD) based R-peak detection method is proposed for noisy ECG signals. Although lots of QRS detection methods have been proposed in literature, most detection methods require high signal quality. The proposed method extracts the R waves from the energy domain using the AFD and determines the R-peak locations based on the key decomposition parameters, achieving the denoising and the R-peak detection at the same time. Validated by clinical ECG signals in the MIT-BIH Arrhythmia Database, the proposed method shows better performance than the Pan-Tompkin (PT) algorithm in both situations of a native PT and the PT with a denoising process.

Prediction of valid acidity in intact apples with Fourier transform near infrared spectroscopy.

Science.gov (United States)

Liu, Yan-De; Ying, Yi-Bin; Fu, Xia-Ping

2005-03-01

To develop nondestructive acidity prediction for intact Fuji apples, the potential of Fourier transform near infrared (FT-NIR) method with fiber optics in interactance mode was investigated. Interactance in the 800 nm to 2619 nm region was measured for intact apples, harvested from early to late maturity stages. Spectral data were analyzed by two multivariate calibration techniques including partial least squares (PLS) and principal component regression (PCR) methods. A total of 120 Fuji apples were tested and 80 of them were used to form a calibration data set. The influences of different data preprocessing and spectra treatments were also quantified. Calibration models based on smoothing spectra were slightly worse than that based on derivative spectra, and the best result was obtained when the segment length was 5 nm and the gap size was 10 points. Depending on data preprocessing and PLS method, the best prediction model yielded correlation coefficient of determination (r2) of 0.759, low root mean square error of prediction (RMSEP) of 0.0677, low root mean square error of calibration (RMSEC) of 0.0562. The results indicated the feasibility of FT-NIR spectral analysis for predicting apple valid acidity in a nondestructive way.

The Sensetivity of Flood Frequency Analysis on Record Length in Continuous United States

Science.gov (United States)

Hu, L.; Nikolopoulos, E. I.; Anagnostou, E. N.

2017-12-01

In flood frequency analysis (FFA), sufficiently long data series are important to get more reliable results. Compared to return periods of interest, at-site FFA usually needs large data sets. Generally, the precision of at site estimators and time-sampling errors are associated with the length of a gauged record. In this work, we quantify the difference with various record lengths. we use generalized extreme value (GEV) and Log Pearson type III (LP3), two traditional methods on annual maximum stream flows to undertake FFA, and propose quantitative ways, relative difference in median and interquartile range (IQR) to compare the flood frequency performances on different record length from selected 350 USGS gauges, which have more than 70 years record length in Continuous United States. Also, we group those gauges into different regions separately based on hydrological unit map and discuss the geometry impacts. The results indicate that long record length can avoid imposing an upper limit on the degree of sophistication. Working with relatively longer record length may lead accurate results than working with shorter record length. Furthermore, the influence of hydrologic unites for the watershed boundary dataset on those gauges also be presented. The California region is the most sensitive to record length, while gauges in the east perform steady.

[Research of dual-photoelastic-modulator-based beat frequency modulation and Fourier-Bessel transform imaging spectrometer].

Science.gov (United States)

Wang, Zhi-Bin; Zhang, Rui; Wang, Yao-Li; Huang, Yan-Fei; Chen, You-Hua; Wang, Li-Fu; Yang, Qiang

2014-02-01

As the existing photoelastic-modulator(PEM) modulating frequency in the tens of kHz to hundreds of kHz between, leading to frequency of modulated interference signal is higher, so ordinary array detector cannot effectively caprure interference signal..A new beat frequency modulation method based on dual-photoelastic-modulator (Dual-PEM) and Fourier-Bessel transform is proposed as an key component of dual-photoelastic-modulator-based imaging spectrometer (Dual-PEM-IS) combined with charge coupled device (CCD). The dual-PEM are operated as an electro-optic circular retardance modulator, Operating the PEMs at slightly different resonant frequencies w1 and w2 respectively, generates a differential signal at a much lower heterodyne frequency that modulates the incident light. This method not only retains the advantages of the existing PEM, but also the frequency of modulated photocurrent decreased by 2-3 orders of magnitude (10-500 Hz) and can be detected by common array detector, and the incident light spectra can be obtained by Fourier-Bessel transform of low frequency component in the modulated signal. The method makes the PEM has the dual capability of imaging and spectral measurement. The basic principle is introduced, the basic equations is derived, and the feasibility is verified through the corresponding numerical simulation and experiment. This method has' potential applications in imaging spectrometer technology, and analysis of the effect of deviation of the optical path difference. This work provides the necessary theoretical basis for remote sensing of new Dual-PEM-IS and for engineering implementation of spectra inversion.

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.

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.

Comparative study of freshwater crayfish, Cherax spp. (crustaceae: decapoda: parastacidae) from Papua, Indonesia based on length-weight analysis

Science.gov (United States)

Hamidah, H.; Abinawanto, Bowolaksono, A.

2017-07-01

The freshwater crayfish is one of the most important fish species as the protein resources. Lake and rivers are the habitat of crayfish in Papua. Morphological characters of crayfish, such as color, total body lengths (L) and body weight (W) were influenced by the habitat. The purpose of the study, therefore, was to compare the total body length and body weight as well as the unique color of crayfish from Uter lake (Atinjo district), Seremuk river (Haha village), Baliem river (Pike village; Hubukiak district, Jayawijaya), and Baliem river (Wesaput village; Wesaput district). Length-weight (body length; LB versus wet weight; WWT) relationships were determined for male and female crayfish (Cherax spp.) The length-weight relationships of total individuals was W = 0,022215.L3,159. This regression differed significantly (R2 = 97.5 %) between locations. Both males and females exhibited positive allometric growth as statistical difference was observed in the mean of the wet weight and body length between males and females. Besides, Canonical function was subjected to determine population distribution based on length-weight data.

Mapping agroecological zones and time lag in vegetation growth by means of Fourier analysis of time series of NDVI images

Science.gov (United States)

Menenti, M.; Azzali, S.; Verhoef, W.; Van Swol, R.

1993-01-01

Examples are presented of applications of a fast Fourier transform algorithm to analyze time series of images of Normalized Difference Vegetation Index values. The results obtained for a case study on Zambia indicated that differences in vegetation development among map units of an existing agroclimatic map were not significant, while reliable differences were observed among the map units obtained using the Fourier analysis.

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

Noise analysis of the measurement of group delay in Fourier white-light interferometric cross correlation

International Nuclear Information System (INIS)

Laude, Vincent

2002-01-01

The problem of noise analysis in measuring the group delay introduced by a dispersive optical element by use of white-light interferometric cross correlation is investigated. Two noise types, detection noise and position noise, are specifically analyzed. Detection noise is shown to be highly sensitive to the spectral content of the white-light source at the frequency considered and to the temporal acquisition window. Position noise, which arises from the finite accuracy of the measurement of the scanning mirror's position, can severely damage the estimation of the group delay. Such is shown to be the case for fast Fourier transform-based estimation algorithms. A new algorithm that is insensitive to scanning delay errors is proposed, and subfemtosecond accuracy is obtained without any postprocessing

Length bias correction in gene ontology enrichment analysis using logistic regression.

Science.gov (United States)

Mi, Gu; Di, Yanming; Emerson, Sarah; Cumbie, Jason S; Chang, Jeff H

2012-01-01

When assessing differential gene expression from RNA sequencing data, commonly used statistical tests tend to have greater power to detect differential expression of genes encoding longer transcripts. This phenomenon, called "length bias", will influence subsequent analyses such as Gene Ontology enrichment analysis. In the presence of length bias, Gene Ontology categories that include longer genes are more likely to be identified as enriched. These categories, however, are not necessarily biologically more relevant. We show that one can effectively adjust for length bias in Gene Ontology analysis by including transcript length as a covariate in a logistic regression model. The logistic regression model makes the statistical issue underlying length bias more transparent: transcript length becomes a confounding factor when it correlates with both the Gene Ontology membership and the significance of the differential expression test. The inclusion of the transcript length as a covariate allows one to investigate the direct correlation between the Gene Ontology membership and the significance of testing differential expression, conditional on the transcript length. We present both real and simulated data examples to show that the logistic regression approach is simple, effective, and flexible.

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.

Joint variable frame rate and length analysis for speech recognition under adverse conditions

DEFF Research Database (Denmark)

Tan, Zheng-Hua; Kraljevski, Ivan

2014-01-01

This paper presents a method that combines variable frame length and rate analysis for speech recognition in noisy environments, together with an investigation of the effect of different frame lengths on speech recognition performance. The method adopts frame selection using an a posteriori signal......-to-noise (SNR) ratio weighted energy distance and increases the length of the selected frames, according to the number of non-selected preceding frames. It assigns a higher frame rate and a normal frame length to a rapidly changing and high SNR region of a speech signal, and a lower frame rate and an increased...... frame length to a steady or low SNR region. The speech recognition results show that the proposed variable frame rate and length method outperforms fixed frame rate and length analysis, as well as standalone variable frame rate analysis in terms of noise-robustness....

A hybrid WDM/OCDMA ring with a dynamic add/drop function based on Fourier code for local area networks.

Science.gov (United States)

Choi, Yong-Kyu; Hosoya, Kenta; Lee, Chung Ghiu; Hanawa, Masanori; Park, Chang-Soo

2011-03-28

We propose and experimentally demonstrate a hybrid WDM/OCDMA ring with a dynamic add/drop function based on Fourier code for local area networks. Dynamic function is implemented by mechanically tuning the Fourier encoder/decoder for optical code division multiple access (OCDMA) encoding/decoding. Wavelength division multiplexing (WDM) is utilized for node assignment and 4-chip Fourier code recovers the matched signal from the codes. For an optical source well adapted to WDM channels and its short optical pulse generation, reflective semiconductor optical amplifiers (RSOAs) are used with a fiber Bragg grating (FBG) and gain-switched. To demonstrate we experimentally investigated a two-node hybrid WDM/OCDMA ring with a 4-chip Fourier encoder/decoder fabricated by cascading four FBGs with the bit error rate (BER) of <10(-9) for the node span of 10.64 km at 1.25 Gb/s.

Recent progress in synchrotron-based frequency-domain Fourier-transform THz-EPR.

Science.gov (United States)

Nehrkorn, Joscha; Holldack, Karsten; Bittl, Robert; Schnegg, Alexander

2017-07-01

We describe frequency-domain Fourier-transform THz-EPR as a method to assign spin-coupling parameters of high-spin (S>1/2) systems with very large zero-field splittings. The instrumental foundations of synchrotron-based FD-FT THz-EPR are presented, alongside with a discussion of frequency-domain EPR simulation routines. The capabilities of this approach is demonstrated for selected mono- and multinuclear HS systems. Finally, we discuss remaining challenges and give an outlook on the future prospects of the technique. Copyright © 2017 Elsevier Inc. All rights reserved.

Comparative measurement of collagen bundle orientation by Fourier analysis and semiquantitative evaluation: reliability and agreement in Masson's trichrome, Picrosirius red and confocal microscopy techniques.

Science.gov (United States)

Marcos-Garcés, V; Harvat, M; Molina Aguilar, P; Ferrández Izquierdo, A; Ruiz-Saurí, A

2017-08-01

Measurement of collagen bundle orientation in histopathological samples is a widely used and useful technique in many research and clinical scenarios. Fourier analysis is the preferred method for performing this measurement, but the most appropriate staining and microscopy technique remains unclear. Some authors advocate the use of Haematoxylin-Eosin (H&E) and confocal microscopy, but there are no studies comparing this technique with other classical collagen stainings. In our study, 46 human skin samples were collected, processed for histological analysis and stained with Masson's trichrome, Picrosirius red and H&E. Five microphotographs of the reticular dermis were taken with a 200× magnification with light microscopy, polarized microscopy and confocal microscopy, respectively. Two independent observers measured collagen bundle orientation with semiautomated Fourier analysis with the Image-Pro Plus 7.0 software and three independent observers performed a semiquantitative evaluation of the same parameter. The average orientation for each case was calculated with the values of the five pictures. We analyzed the interrater reliability, the consistency between Fourier analysis and average semiquantitative evaluation and the consistency between measurements in Masson's trichrome, Picrosirius red and H&E-confocal. Statistical analysis for reliability and agreement was performed with the SPSS 22.0 software and consisted of intraclass correlation coefficient (ICC), Bland-Altman plots and limits of agreement and coefficient of variation. Interrater reliability was almost perfect (ICC > 0.8) with all three histological and microscopy techniques and always superior in Fourier analysis than in average semiquantitative evaluation. Measurements were consistent between Fourier analysis by one observer and average semiquantitative evaluation by three observers, with an almost perfect agreement with Masson's trichrome and Picrosirius red techniques (ICC > 0.8) and a strong

Fast Fourier transformation in vibration analysis of physically active systems

International Nuclear Information System (INIS)

Hafeez, T.; Amir, M.; Farooq, U.; Day, P.

2003-01-01

Vibration of all physical systems may be expressed as the summation of an infinite number of sine and cosine terms known as Fourier series. The basic vibration analysis tool used is the frequency 'spectrum' (a graph of vibration where the amplitude of vibration is plotted against frequency). When a particular rotating component begins to fail, its vibration tends to increase. Spectra graphs are powerful diagnostic tool for detecting components' degradation. Spectra obtained with accelerometers located at the various locations on the components and their analysis in practice from rotating machines enable early detecting of incipient failure. Consequence of unexpected failure can be catastrophic and costly. This study provides basis to relate defective component by its constituent frequencies and then to the known discrete frequency of its 'signature' or 'thumbprint' to predict and verify the sustained dynamic behavior of machine designs harmful effects of forced vibration. The spectra for gearbox of a vane with teeth damaged fault are presented here which signified the importance of FFT analysis as diagnostic tool. This may be helpful to predictive maintenance of the machinery. (author)

Development of PC-based FFT system for reactor dynamic analysis

International Nuclear Information System (INIS)

Ansari, S.; Baig, A.R.

1993-03-01

A personal computer based fast fourier transform (FFT) analyzer has been developed for frequency spectrum analysis of signals from nuclear reactor. The system can perform window smoothing, computation of auto- and cross-power spectral density, coherence and auto and cross-correlation functions. The feature of 16 analogue signals acquisition with high precision and high sampling frequency makes the analyzer suitable for malfunction diagnosis of nuclear reactors using reactor noise analysis. The development work for the fourier analyzer was undertaken as a part of IAEA research contract no. 5925/RB. The applications of the FFT analyzer are described in reactor transfer function measurements and nuclear instrumentation channels frequency response testing. (author)

A class of Fourier integrals based on the electric potential of an elongated dipole.

Science.gov (United States)

Skianis, Georgios Aim

2014-01-01

In the present paper the closed expressions of a class of non tabulated Fourier integrals are derived. These integrals are associated with a group of functions at space domain, which represent the electric potential of a distribution of elongated dipoles which are perpendicular to a flat surface. It is shown that the Fourier integrals are produced by the Fourier transform of the Green's function of the potential of the dipole distribution, times a definite integral in which the distribution of the polarization is involved. Therefore the form of this distribution controls the expression of the Fourier integral. Introducing various dipole distributions, the respective Fourier integrals are derived. These integrals may be useful in the quantitative interpretation of electric potential anomalies produced by elongated dipole distributions, at spatial frequency domain.

Angular acceptance analysis of an infrared focal plane array with a built-in stationary Fourier transform spectrometer.

Science.gov (United States)

Gillard, Frédéric; Ferrec, Yann; Guérineau, Nicolas; Rommeluère, Sylvain; Taboury, Jean; Chavel, Pierre

2012-06-01

Stationary Fourier transform spectrometry is an interesting concept for building reliable field or embedded spectroradiometers, especially for the mid- and far- IR. Here, a very compact configuration of a cryogenic stationary Fourier transform IR (FTIR) spectrometer is investigated, where the interferometer is directly integrated in the focal plane array (FPA). We present a theoretical analysis to explain and describe the fringe formation inside the FTIR-FPA structure when illuminated by an extended source positioned at a finite distance from the detection plane. The results are then exploited to propose a simple front lens design compatible with a handheld package.

Time sequence analysis of flickering auroras. I - Application of Fourier analysis. [in atmosphere

Science.gov (United States)

Berkey, F. T.; Silevitch, M. B.; Parsons, N. R.

1980-01-01

Using a technique that enables one to digitize the brightness of auroral displays from individual fields of a video signal, we have analyzed the frequency content of flickering aurora. Through the application of Fourier analysis to our data, we have found that flickering aurora contains a wide range of enhanced frequencies, although the dominant frequency enhancement generally occurs in the range 6-12 Hz. Each incidence of flickering that we observed was associated with increased radio wave absorption. Furthermore, we have found that flickering occurs in bright auroral surges, the occurrence of which is not limited to the 'breakup' phase of auroral substorms. Our results are interpreted in terms of a recently proposed theory of fluctuating double layers that accounts for a number of the observational features.

Pre-processing of Fourier transform infrared spectra by means of multivariate analysis implemented in the R environment.

Science.gov (United States)

Banas, Krzysztof; Banas, Agnieszka; Gajda, Mariusz; Pawlicki, Bohdan; Kwiatek, Wojciech M; Breese, Mark B H

2015-04-21

Pre-processing of Fourier transform infrared (FTIR) spectra is typically the first and crucial step in data analysis. Very often hyperspectral datasets include the regions characterized by the spectra of very low intensity, for example two-dimensional (2D) maps where the areas with only support materials (like mylar foil) are present. In that case segmentation of the complete dataset is required before subsequent evaluation. The method proposed in this contribution is based on a multivariate approach (hierarchical cluster analysis), and shows its superiority when compared to the standard method of cutting-off by using only the mean spectral intensity. Both techniques were implemented and their performance was tested in the R statistical environment - open-source platform - that is a favourable solution if the repeatability and transparency are the key aspects.

Non-Fourier Vernotte-Cattaneo numerical model for heat conduction in a BWR fuel rod

Energy Technology Data Exchange (ETDEWEB)

Espinosa-Martinez, E.G.; Vazquez-Rodriguez, A.; Varela-Ham, J.R.; Espinosa-Paredes, G., E-mail: gepe@xanum.uam.mx [Universidad Autonoma Metropolitana, Area de Ingenieria en Recursos Energeticos, Iztapalapa (Mexico)

2014-07-01

A fuel rod mathematical model based on transient heat conduction as constitutive Non-Fourier law for Light Water Reactors (LWRs) transient analysis is presented. The structure of the fuel pellet is affected due to high temperatures and irradiation, which eventually produce fracture or cracks. In principle the fractures are saturated of gas. Then, the Fourier law of the heat conduction is not strictly applicable to describe these phenomena, where the physical properties such as thermal conductivity, heat capacity and density correspond to a heterogeneous material due to gas, and therefore the thermal diffusion process due to molecular transport in the fuel pellet is affected. From the point of view of nuclear reactor safety analysis, the heat transfer from the fuel to the coolant is crucial and superheating of the wall can cause the cladding failure. In the classical theory of diffusion, the Fourier law of heat conduction is used to describe the relation between the heat flux vector and the temperature gradient assuming that the heat propagation speeds are infinite. The Non-Fourier approach presented in this work eliminates the assumption of an infinite thermal wave speed, therefore time-dependent heat sources were considered in the fuel rod heat transfer model. The numerical experiments in a BWR, show that the Non-Fourier approach is crucial in the pressurization transients such as turbine trip and reactor isolation. (author)

Non-Fourier Vernotte-Cattaneo numerical model for heat conduction in a BWR fuel rod

International Nuclear Information System (INIS)

Espinosa-Martinez, E.G.; Vazquez-Rodriguez, A.; Varela-Ham, J.R.; Espinosa-Paredes, G.

2014-01-01

A fuel rod mathematical model based on transient heat conduction as constitutive Non-Fourier law for Light Water Reactors (LWRs) transient analysis is presented. The structure of the fuel pellet is affected due to high temperatures and irradiation, which eventually produce fracture or cracks. In principle the fractures are saturated of gas. Then, the Fourier law of the heat conduction is not strictly applicable to describe these phenomena, where the physical properties such as thermal conductivity, heat capacity and density correspond to a heterogeneous material due to gas, and therefore the thermal diffusion process due to molecular transport in the fuel pellet is affected. From the point of view of nuclear reactor safety analysis, the heat transfer from the fuel to the coolant is crucial and superheating of the wall can cause the cladding failure. In the classical theory of diffusion, the Fourier law of heat conduction is used to describe the relation between the heat flux vector and the temperature gradient assuming that the heat propagation speeds are infinite. The Non-Fourier approach presented in this work eliminates the assumption of an infinite thermal wave speed, therefore time-dependent heat sources were considered in the fuel rod heat transfer model. The numerical experiments in a BWR, show that the Non-Fourier approach is crucial in the pressurization transients such as turbine trip and reactor isolation. (author)

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

Fourier mode analysis of slab-geometry transport iterations in spatially periodic media

International Nuclear Information System (INIS)

Larsen, E W; Zika, M R

1999-01-01

We describe a Fourier analysis of the diffusion-synthetic acceleration (DSA) and transport-synthetic acceleration (TSA) iteration schemes for a spatially periodic, but otherwise arbitrarily heterogeneous, medium. Both DSA and TSA converge more slowly in a heterogeneous medium than in a homogeneous medium composed of the volume-averaged scattering ratio. In the limit of a homogeneous medium, our heterogeneous analysis contains eigenvalues of multiplicity two at ''resonant'' wave numbers. In the presence of material heterogeneities, error modes corresponding to these resonant wave numbers are ''excited'' more than other error modes. For DSA and TSA, the iteration spectral radius may occur at these resonant wave numbers, in which case the material heterogeneities most strongly affect iterative performance

Speciation of Bactrocera dorsalis complex based on aedeagus length

International Nuclear Information System (INIS)

Osamu Iwahashi

2000-01-01

A species complex of Bactrocera dorsalis (Hendel) in Southeast Asia is composed of 52 species (Drew and Hancock, 1994) and while some of these species are economically very important, distinguishing them based on morphological characters has been difficult (White and Elson-Harris 1992). Specifically, there is considerable difficulty in differentiating between males of two pairs of sympatric species, B. philippinensis Drew and Hancock/B. occipitalis (Bezzi) in the Philippines and B. carambolae Drew and Hancock/B. papayae Drew and Hancock in Indonesia. This may be, in part, because the evolutionary processes within this species complex are still very dynamic, and that natural hybridisation between sympatric species pairs might be occurring on a regular basis (He and Haymer 1997). Iwaizumi et al. (1997) developed a simple method to differentiate the two sets of sympatric species based on aedeagus lengths. However, these flies had been reared artificially under laboratory conditions and only a small number of specimens (n=5) was used. Consequently, they were not able to obtain a frequency distribution of the aedeagus length for each species. Iwahashi (1998) measured a larger number of wild flies collected on Guimaras Is, Philippines, and found that flies with the aedeagus length of 2.89 mm are B. philippinensis. Iwahashi (1999) also showed that the measurement of the aedeagal length of fruit flies is a reliable characteristic for distinguishing between the 2 sympatric species pairs in the B. dorsalis complex. This being so, it may also be interesting to interpret phylogenetic relationships among B. dorsalis complex species based on the aedeagus length. Thus, aedeagus lengths of different populations of five B. dorsalis complex species are measured and their relationships discussed

Importance of Viral Sequence Length and Number of Variable and Informative Sites in Analysis of HIV Clustering.

Science.gov (United States)

Novitsky, Vlad; Moyo, Sikhulile; Lei, Quanhong; DeGruttola, Victor; Essex, M

2015-05-01

To improve the methodology of HIV cluster analysis, we addressed how analysis of HIV clustering is associated with parameters that can affect the outcome of viral clustering. The extent of HIV clustering and tree certainty was compared between 401 HIV-1C near full-length genome sequences and subgenomic regions retrieved from the LANL HIV Database. Sliding window analysis was based on 99 windows of 1,000 bp and 45 windows of 2,000 bp. Potential associations between the extent of HIV clustering and sequence length and the number of variable and informative sites were evaluated. The near full-length genome HIV sequences showed the highest extent of HIV clustering and the highest tree certainty. At the bootstrap threshold of 0.80 in maximum likelihood (ML) analysis, 58.9% of near full-length HIV-1C sequences but only 15.5% of partial pol sequences (ViroSeq) were found in clusters. Among HIV-1 structural genes, pol showed the highest extent of clustering (38.9% at a bootstrap threshold of 0.80), although it was significantly lower than in the near full-length genome sequences. The extent of HIV clustering was significantly higher for sliding windows of 2,000 bp than 1,000 bp. We found a strong association between the sequence length and proportion of HIV sequences in clusters, and a moderate association between the number of variable and informative sites and the proportion of HIV sequences in clusters. In HIV cluster analysis, the extent of detectable HIV clustering is directly associated with the length of viral sequences used, as well as the number of variable and informative sites. Near full-length genome sequences could provide the most informative HIV cluster analysis. Selected subgenomic regions with a high extent of HIV clustering and high tree certainty could also be considered as a second choice.

Fourier Spectroscopy: A Bayesian Way

Directory of Open Access Journals (Sweden)

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.

Electrospray Ionization Fourier Transform Ion Cyclotron Resonance Analysis of Large Polymerases Chain Reaction Products

International Nuclear Information System (INIS)

Wunschel, David S.; Pasa Tolic, Ljiljana; Feng, Bingbing; Smith, Richard D.

2000-01-01

We have attempted to expand the size range of PCR products that can be analyzed by electroscopy ionization (ESI) Fourier transformion cyclotron resonance (FTICR) mass spectrometry. The mass measurement accuracy obtained illustrates that a signel base substitution could be identified at the size of PCR product with a 7 tesla ESI-FTICR

Thermal parameter identification for non-Fourier heat transfer from molecular dynamics

Science.gov (United States)

Singh, Amit; Tadmor, Ellad B.

2015-10-01

Fourier's law leads to a diffusive model of heat transfer in which a thermal signal propagates infinitely fast and the only material parameter is the thermal conductivity. In micro- and nano-scale systems, non-Fourier effects involving coupled diffusion and wavelike propagation of heat can become important. An extension of Fourier's law to account for such effects leads to a Jeffreys-type model for heat transfer with two relaxation times. We propose a new Thermal Parameter Identification (TPI) method for obtaining the Jeffreys-type thermal parameters from molecular dynamics simulations. The TPI method makes use of a nonlinear regression-based approach for obtaining the coefficients in analytical expressions for cosine and sine-weighted averages of temperature and heat flux over the length of the system. The method is applied to argon nanobeams over a range of temperature and system sizes. The results for thermal conductivity are found to be in good agreement with standard Green-Kubo and direct method calculations. The TPI method is more efficient for systems with high diffusivity and has the advantage, that unlike the direct method, it is free from the influence of thermostats. In addition, the method provides the thermal relaxation times for argon. Using the determined parameters, the Jeffreys-type model is able to reproduce the molecular dynamics results for a short-duration heat pulse where wavelike propagation of heat is observed thereby confirming the existence of second sound in argon. An implementation of the TPI method in MATLAB is available as part of the online supplementary material.

Fourier transform infrared spectroscopy microscopic imaging classification based on spatial-spectral features

Science.gov (United States)

Liu, Lian; Yang, Xiukun; Zhong, Mingliang; Liu, Yao; Jing, Xiaojun; Yang, Qin

2018-04-01

The discrete fractional Brownian incremental random (DFBIR) field is used to describe the irregular, random, and highly complex shapes of natural objects such as coastlines and biological tissues, for which traditional Euclidean geometry cannot be used. In this paper, an anisotropic variable window (AVW) directional operator based on the DFBIR field model is proposed for extracting spatial characteristics of Fourier transform infrared spectroscopy (FTIR) microscopic imaging. Probabilistic principal component analysis first extracts spectral features, and then the spatial features of the proposed AVW directional operator are combined with the former to construct a spatial-spectral structure, which increases feature-related information and helps a support vector machine classifier to obtain more efficient distribution-related information. Compared to Haralick’s grey-level co-occurrence matrix, Gabor filters, and local binary patterns (e.g. uniform LBPs, rotation-invariant LBPs, uniform rotation-invariant LBPs), experiments on three FTIR spectroscopy microscopic imaging datasets show that the proposed AVW directional operator is more advantageous in terms of classification accuracy, particularly for low-dimensional spaces of spatial characteristics.

Taylor-plasticity-based analysis of length scale effects in void growth

KAUST Repository

Liu, Junxian

2014-09-25

We have studied the void growth problem by employing the Taylor-based strain gradient plasticity theories, from which we have chosen the following three, namely, the mechanism-based strain gradient (MSG) plasticity (Gao et al 1999 J. Mech. Phys. Solids 47 1239, Huang et al 2000 J. Mech. Phys. Solids 48 99-128), the Taylor-based nonlocal theory (TNT; 2001 Gao and Huang 2001 Int. J. Solids Struct. 38 2615) and the conventional theory of MSG (CMSG; Huang et al 2004 Int. J. Plast. 20 753). We have addressed the following three issues which occur when plastic deformation at the void surface is unconstrained. (1) Effects of elastic deformation. Elasticity is essential for cavitation instability. It is therefore important to guarantee that the gradient term entering the Taylor model is the effective plastic strain gradient instead of the total strain gradient. We propose a simple elastic-plastic decomposition method. When the void size approaches the minimum allowable initial void size related to the maximum allowable geometrically necessary dislocation density, overestimation of the flow stress due to the negligence of the elastic strain gradient is on the order of lεY/R0 near the void surface, where l, εY and R0 are, respectively, the intrinsic material length scale, the yield strain and the initial void radius. (2) MSG intrinsic inconsistency, which was initially mentioned in Gao et al (1999 J. Mech. Phys. Solids 47 1239) but has not been the topic of follow-up studies. We realize that MSG higher-order stress arises due to the linear-strain-field approximation within the mesoscale cell with a nonzero size, lε. Simple analysis shows that within an MSG mesoscale cell near the void surface, the difference between microscale and mesoscale strains is on the order of (lε/R0)2, indicating that when lε/R0 ∼ 1.0, the higher-order stress effect can make the MSG result considerably different from the TNT or CMSG results. (3) Critical condition for cavitation instability

Study on sampling of continuous linear system based on generalized Fourier transform

Science.gov (United States)

Li, Huiguang

2003-09-01

In the research of signal and system, the signal's spectrum and the system's frequency characteristic can be discussed through Fourier Transform (FT) and Laplace Transform (LT). However, some singular signals such as impulse function and signum signal don't satisfy Riemann integration and Lebesgue integration. They are called generalized functions in Maths. This paper will introduce a new definition -- Generalized Fourier Transform (GFT) and will discuss generalized function, Fourier Transform and Laplace Transform under a unified frame. When the continuous linear system is sampled, this paper will propose a new method to judge whether the spectrum will overlap after generalized Fourier transform (GFT). Causal and non-causal systems are studied, and sampling method to maintain system's dynamic performance is presented. The results can be used on ordinary sampling and non-Nyquist sampling. The results also have practical meaning on research of "discretization of continuous linear system" and "non-Nyquist sampling of signal and system." Particularly, condition for ensuring controllability and observability of MIMO continuous systems in references 13 and 14 is just an applicable example of this paper.

Validity of plant fiber length measurement : a review of fiber length measurement based on kenaf as a model

Science.gov (United States)

James S. Han; Theodore. Mianowski; Yi-yu. Lin

1999-01-01

The efficacy of fiber length measurement techniques such as digitizing, the Kajaani procedure, and NIH Image are compared in order to determine the optimal tool. Kenaf bast fibers, aspen, and red pine fibers were collected from different anatomical parts, and the fiber lengths were compared using various analytical tools. A statistical analysis on the validity of the...

Optical movie encryption based on a discrete multiple-parameter fractional Fourier transform

International Nuclear Information System (INIS)

Zhong, Zhi; Zhang, Yujie; Shan, Mingguang; Wang, Ying; Zhang, Yabin; Xie, Hong

2014-01-01

A movie encryption scheme is proposed using a discrete multiple-parameter fractional Fourier transform and theta modulation. After being modulated by sinusoidal amplitude grating, each frame of the movie is transformed by a filtering procedure and then multiplexed into a complex signal. The complex signal is multiplied by a pixel scrambling operation and random phase mask, and then encrypted by a discrete multiple-parameter fractional Fourier transform. The movie can be retrieved by using the correct keys, such as a random phase mask, a pixel scrambling operation, the parameters in a discrete multiple-parameter fractional Fourier transform and a time sequence. Numerical simulations have been performed to demonstrate the validity and the security of the proposed method. (paper)

Fourier series analysis of a cylindrical pressure vessel subjected to axial end load and external pressure

International Nuclear Information System (INIS)

Brar, Gurinder Singh; Hari, Yogeshwar; Williams, Dennis K.

2013-01-01

Pressure Vessel Code, Section VIII, Division 2 and ASME STS-1. -- Highlights: • Fourier series is used to predict the load carrying capacity of cylindrical vessel. • Reliability approach used for analysis as against the deterministic approach. • Cylindrical pressure vessel is subjected to axial end load and external pressure. • Axisymmetric and asymmetric analysis carried out for imperfect pressure vessels. • Results are compared to the recommendations laid out in ASME B and PV Code

Holographic memory system based on projection recording of computer-generated 1D Fourier holograms.

Science.gov (United States)

Betin, A Yu; Bobrinev, V I; Donchenko, S S; Odinokov, S B; Evtikhiev, N N; Starikov, R S; Starikov, S N; Zlokazov, E Yu

2014-10-01

Utilization of computer generation of holographic structures significantly simplifies the optical scheme that is used to record the microholograms in a holographic memory record system. Also digital holographic synthesis allows to account the nonlinear errors of the record system to improve the microholograms quality. The multiplexed record of holograms is a widespread technique to increase the data record density. In this article we represent the holographic memory system based on digital synthesis of amplitude one-dimensional (1D) Fourier transform holograms and the multiplexed record of these holograms onto the holographic carrier using optical projection scheme. 1D Fourier transform holograms are very sensitive to orientation of the anamorphic optical element (cylindrical lens) that is required for encoded data object reconstruction. The multiplex record of several holograms with different orientation in an optical projection scheme allowed reconstruction of the data object from each hologram by rotating the cylindrical lens on the corresponding angle. Also, we discuss two optical schemes for the recorded holograms readout: a full-page readout system and line-by-line readout system. We consider the benefits of both systems and present the results of experimental modeling of 1D Fourier holograms nonmultiplex and multiplex record and reconstruction.

FOURIER COEFFICIENTS OF CONTINUOUS FUNCTIONS WITH RESPECT TO LOCALIZED HAAR SYSTEM

Directory of Open Access Journals (Sweden)

E. S. Belkina

2017-06-01

Full Text Available We construct a nontrivial example of a continuous function f* on [0, 1]² which is orthogonal to tensor products of Haar functions supported on intervals of the same length. This example clarifies the possible behaviour of Fourier coefficients of continuous functions with respect to a localized Haar system. The function f* has fractal structure. We give lower bounds on its smoothness.

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.

Topological analysis of polymeric melts: chain-length effects and fast-converging estimators for entanglement length.

Science.gov (United States)

Hoy, Robert S; Foteinopoulou, Katerina; Kröger, Martin

2009-09-01

Primitive path analyses of entanglements are performed over a wide range of chain lengths for both bead spring and atomistic polyethylene polymer melts. Estimators for the entanglement length N_{e} which operate on results for a single chain length N are shown to produce systematic O(1/N) errors. The mathematical roots of these errors are identified as (a) treating chain ends as entanglements and (b) neglecting non-Gaussian corrections to chain and primitive path dimensions. The prefactors for the O(1/N) errors may be large; in general their magnitude depends both on the polymer model and the method used to obtain primitive paths. We propose, derive, and test new estimators which eliminate these systematic errors using information obtainable from the variation in entanglement characteristics with chain length. The new estimators produce accurate results for N_{e} from marginally entangled systems. Formulas based on direct enumeration of entanglements appear to converge faster and are simpler to apply.

An Image Matching Method Based on Fourier and LOG-Polar Transform

Directory of Open Access Journals (Sweden)

Zhijia Zhang

2014-04-01

Full Text Available This Traditional template matching methods are not appropriate for the situation of large angle rotation between two images in the online detection for industrial production. Aiming at this problem, Fourier transform algorithm was introduced to correct image rotation angle based on its rotatary invariance in time-frequency domain, orienting image under test in the same direction with reference image, and then match these images using matching algorithm based on log-polar transform. Compared with the current matching algorithms, experimental results show that the proposed algorithm can not only match two images with rotation of arbitrary angle, but also possess a high matching accuracy and applicability. In addition, the validity and reliability of algorithm was verified by simulated matching experiment targeting circular images.

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.

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

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.

Node Detection and Internode Length Estimation of Tomato Seedlings Based on Image Analysis and Machine Learning

Directory of Open Access Journals (Sweden)

Kyosuke Yamamoto

2016-07-01

Full Text Available Seedling vigor in tomatoes determines the quality and growth of fruits and total plant productivity. It is well known that the salient effects of environmental stresses appear on the internode length; the length between adjoining main stem node (henceforth called node. In this study, we develop a method for internode length estimation using image processing technology. The proposed method consists of three steps: node detection, node order estimation, and internode length estimation. This method has two main advantages: (i as it uses machine learning approaches for node detection, it does not require adjustment of threshold values even though seedlings are imaged under varying timings and lighting conditions with complex backgrounds; and (ii as it uses affinity propagation for node order estimation, it can be applied to seedlings with different numbers of nodes without prior provision of the node number as a parameter. Our node detection results show that the proposed method can detect 72% of the 358 nodes in time-series imaging of three seedlings (recall = 0.72, precision = 0.78. In particular, the application of a general object recognition approach, Bag of Visual Words (BoVWs, enabled the elimination of many false positives on leaves occurring in the image segmentation based on pixel color, significantly improving the precision. The internode length estimation results had a relative error of below 15.4%. These results demonstrate that our method has the ability to evaluate the vigor of tomato seedlings quickly and accurately.

Elliptical Fourier descriptors of outline and morphological analysis in caudal view of foramen magnum of the tropical raccoon (Procyon cancrivorus) (Linnaeus, 1758).

Science.gov (United States)

Samuel, O M; Casanova, P M; Olopade, J O

2018-03-01

To evaluate sexual-size dimorphism and attempt at categorization of inter-individual shapes of foramen magnum outlines using Fourier descriptors which allow for shape outline evaluations with a resultant specimen character definition. Individual characterization and quantification of foramen magnum shapes in direct caudal view based on elliptical Fourier technique was applied to 46 tropical raccoon skulls (26 females, 20 males). Incremental number of harmonics demonstrates morphological contributions of such descriptors with their relations to specific anatomical constructions established. The initial harmonics (1st to 3rd) described the general foramen shapes while the second (4th to 12th) demonstrated fine morphological details. Sexual-size dimorphism was observed in females (87.1%) and 91.7% in males, normalization of size produces 75% in females and 83% in males. With respect to foramen magnum dimorphism analysis, the result obtained through elliptic Fourier analysis was comparatively better in detail information of outline contours than earlier classical methods. The first four effective principal components defined 70.63% of its shape properties while the rest (22.51%) constituted fine details of morphology. Both size and shape seems important in sexual dimorphisms in this species, this investigation suggest clinical implications, taxonomic and anthropologic perspectives in foramen characterization magnum characterization and further postulates an increased possibility of volume reduction cerebellar protrusion, ontogenic magnum shape irregularities in the sample population with neurologic consequences especially among females. Copyright © 2017 Elsevier Masson SAS. All rights reserved.

Multiscaling for systems with a broad continuum of characteristic lengths and times: Structural transitions in nanocomposites.

Science.gov (United States)

Pankavich, S; Ortoleva, P

2010-06-01

The multiscale approach to N-body systems is generalized to address the broad continuum of long time and length scales associated with collective behaviors. A technique is developed based on the concept of an uncountable set of time variables and of order parameters (OPs) specifying major features of the system. We adopt this perspective as a natural extension of the commonly used discrete set of time scales and OPs which is practical when only a few, widely separated scales exist. The existence of a gap in the spectrum of time scales for such a system (under quasiequilibrium conditions) is used to introduce a continuous scaling and perform a multiscale analysis of the Liouville equation. A functional-differential Smoluchowski equation is derived for the stochastic dynamics of the continuum of Fourier component OPs. A continuum of spatially nonlocal Langevin equations for the OPs is also derived. The theory is demonstrated via the analysis of structural transitions in a composite material, as occurs for viral capsids and molecular circuits.

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

Fourier optics along a hybrid optical fiber for Bessel-like beam generation and its applications in multiple-particle trapping.

Science.gov (United States)

Kim, Jongki; Jeong, Yoonseob; Lee, Sejin; Ha, Woosung; Shin, Jeon-Soo; Oh, Kyunghwan

2012-02-15

Highly efficient Bessel-like beam generation was achieved based on a new all-fiber method that implements Fourier transformation of a micro annular aperture along a concatenated composite optical fiber. The beam showed unique characteristics of tilted washboard optical potential in the transverse plane and sustained a nondiffracting length over 400 μm along the axial direction. Optical trapping of multiple dielectric particles and living Jurkat cells were successfully demonstrated along the axial direction of the beam in the water.

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

Introduction to partial differential equations from Fourier series to boundary-value problems

CERN Document Server

Broman, Arne

2010-01-01

This well-written, advanced-level text introduces students to Fourier analysis and some of its applications. The self-contained treatment covers Fourier series, orthogonal systems, Fourier and Laplace transforms, Bessel functions, and partial differential equations of the first and second orders. Over 260 exercises with solutions reinforce students' grasp of the material. 1970 edition.

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.

Dataset of Fourier transform-infrared coupled with chemometric analysis used to distinguish accessions of Garcinia mangostana L. in Peninsular Malaysia

Directory of Open Access Journals (Sweden)

Sri A’jilah Samsir

2016-09-01

Full Text Available In this dataset, we distinguish 15 accessions of Garcinia mangostana from Peninsular Malaysia using Fourier transform-infrared spectroscopy coupled with chemometric analysis. We found that the position and intensity of characteristic peaks at 3600–3100 cm−1 in IR spectra allowed discrimination of G. mangostana from different locations. Further principal component analysis (PCA of all the accessions suggests the two main clusters were formed: samples from Johor, Melaka, and Negeri Sembilan (South were clustered together in one group while samples from Perak, Kedah, Penang, Selangor, Kelantan, and Terengganu (North and East Coast were in another clustered group. Keywords: Apomictic, Mangosteen, Fourier Transformed-Infrared, Peninsular Malaysia

A Run-Length Encoding Approach for Path Analysis of C. elegans Search Behavior

Directory of Open Access Journals (Sweden)

Li Huang

2016-01-01

Full Text Available The nematode Caenorhabditis elegans explores the environment using a combination of different movement patterns, which include straight movement, reversal, and turns. We propose to quantify C. elegans movement behavior using a computer vision approach based on run-length encoding of step-length data. In this approach, the path of C. elegans is encoded as a string of characters, where each character represents a path segment of a specific type of movement. With these encoded string data, we perform k-means cluster analysis to distinguish movement behaviors resulting from different genotypes and food availability. We found that shallow and sharp turns are the most critical factors in distinguishing the differences among the movement behaviors. To validate our approach, we examined the movement behavior of tph-1 mutants that lack an enzyme responsible for serotonin biosynthesis. A k-means cluster analysis with the path string-encoded data showed that tph-1 movement behavior on food is similar to that of wild-type animals off food. We suggest that this run-length encoding approach is applicable to trajectory data in animal or human mobility data.

Application of group analysis to the spatially homogeneous and isotropic Boltzmann equation with source using its Fourier image

International Nuclear Information System (INIS)

Grigoriev, Yurii N; Meleshko, Sergey V; Suriyawichitseranee, Amornrat

2015-01-01

Group analysis of the spatially homogeneous and molecular energy dependent Boltzmann equations with source term is carried out. The Fourier transform of the Boltzmann equation with respect to the molecular velocity variable is considered. The correspondent determining equation of the admitted Lie group is reduced to a partial differential equation for the admitted source. The latter equation is analyzed by an algebraic method. A complete group classification of the Fourier transform of the Boltzmann equation with respect to a source function is given. The representation of invariant solutions and corresponding reduced equations for all obtained source functions are also presented. (paper)

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.

Deconvolution, differentiation and Fourier transformation algorithms for noise-containing data based on splines and global approximation

NARCIS (Netherlands)

Wormeester, Herbert; Sasse, A.G.B.M.; van Silfhout, Arend

1988-01-01

One of the main problems in the analysis of measured spectra is how to reduce the influence of noise in data processing. We show a deconvolution, a differentiation and a Fourier Transform algorithm that can be run on a small computer (64 K RAM) and suffer less from noise than commonly used routines.

A unified Fourier theory for time-of-flight PET data.

Science.gov (United States)

Li, Yusheng; Matej, Samuel; Metzler, Scott D

2016-01-21

Fully 3D time-of-flight (TOF) PET scanners offer the potential of previously unachievable image quality in clinical PET imaging. TOF measurements add another degree of redundancy for cylindrical PET scanners and make photon-limited TOF-PET imaging more robust than non-TOF PET imaging. The data space for 3D TOF-PET data is five-dimensional with two degrees of redundancy. Previously, consistency equations were used to characterize the redundancy of TOF-PET data. In this paper, we first derive two Fourier consistency equations and Fourier-John equation for 3D TOF PET based on the generalized projection-slice theorem; the three partial differential equations (PDEs) are the dual of the sinogram consistency equations and John's equation. We then solve the three PDEs using the method of characteristics. The two degrees of entangled redundancy of the TOF-PET data can be explicitly elicited and exploited by the solutions of the PDEs along the characteristic curves, which gives a complete understanding of the rich structure of the 3D x-ray transform with TOF measurement. Fourier rebinning equations and other mapping equations among different types of PET data are special cases of the general solutions. We also obtain new Fourier rebinning and consistency equations (FORCEs) from other special cases of the general solutions, and thus we obtain a complete scheme to convert among different types of PET data: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF data. The new FORCEs can be used as new Fourier-based rebinning algorithms for TOF-PET data reduction, inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. Further, we give a geometric interpretation of the general solutions--the two families of characteristic curves can be obtained by respectively changing the azimuthal and co-polar angles of the biorthogonal coordinates in Fourier space. We conclude the unified Fourier theory by showing that the Fourier consistency equations are

Alleviating Border Effects in Wavelet Transforms for Nonlinear Time-varying Signal Analysis

Directory of Open Access Journals (Sweden)

SU, H.

2011-08-01

Full Text Available Border effects are very common in many finite signals analysis and processing approaches using convolution operation. Alleviating the border effects that can occur in the processing of finite-length signals using wavelet transform is considered in this paper. Traditional methods for alleviating the border effects are suitable to compression or coding applications. We propose an algorithm based on Fourier series which is proved to be appropriate to the application of time-frequency analysis of nonlinear signals. Fourier series extension method preserves the time-varying characteristics of the signals. A modified signal duration expression for measuring the extent of border effects region is presented. The proposed algorithm is confirmed to be efficient to alleviate the border effects in comparison to the current methods through the numerical examples.

Fourier rebinning and consistency equations for time-of-flight PET planograms.

Science.gov (United States)

Li, Yusheng; Defrise, Michel; Matej, Samuel; Metzler, Scott D

2016-01-01

Due to the unique geometry, dual-panel PET scanners have many advantages in dedicated breast imaging and on-board imaging applications since the compact scanners can be combined with other imaging and treatment modalities. The major challenges of dual-panel PET imaging are the limited-angle problem and data truncation, which can cause artifacts due to incomplete data sampling. The time-of-flight (TOF) information can be a promising solution to reduce these artifacts. The TOF planogram is the native data format for dual-panel TOF PET scanners, and the non-TOF planogram is the 3D extension of linogram. The TOF planograms is five-dimensional while the objects are three-dimensional, and there are two degrees of redundancy. In this paper, we derive consistency equations and Fourier-based rebinning algorithms to provide a complete understanding of the rich structure of the fully 3D TOF planograms. We first derive two consistency equations and John's equation for 3D TOF planograms. By taking the Fourier transforms, we obtain two Fourier consistency equations and the Fourier-John equation, which are the duals of the consistency equations and John's equation, respectively. We then solve the Fourier consistency equations and Fourier-John equation using the method of characteristics. The two degrees of entangled redundancy of the 3D TOF data can be explicitly elicited and exploited by the solutions along the characteristic curves. As the special cases of the general solutions, we obtain Fourier rebinning and consistency equations (FORCEs), and thus we obtain a complete scheme to convert among different types of PET planograms: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF planograms. The FORCEs can be used as Fourier-based rebinning algorithms for TOF-PET data reduction, inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. As a byproduct, we show the two consistency equations are necessary and sufficient for 3D TOF planograms

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.

Application of linear discriminant analysis and Attenuated Total Reflectance Fourier Transform Infrared microspectroscopy for diagnosis of colon cancer.

Science.gov (United States)

Khanmohammadi, Mohammadreza; Bagheri Garmarudi, Amir; Samani, Simin; Ghasemi, Keyvan; Ashuri, Ahmad

2011-06-01

Attenuated Total Reflectance Fourier Transform Infrared (ATR-FTIR) microspectroscopy was applied for detection of colon cancer according to the spectral features of colon tissues. Supervised classification models can be trained to identify the tissue type based on the spectroscopic fingerprint. A total of 78 colon tissues were used in spectroscopy studies. Major spectral differences were observed in 1,740-900 cm(-1) spectral region. Several chemometric methods such as analysis of variance (ANOVA), cluster analysis (CA) and linear discriminate analysis (LDA) were applied for classification of IR spectra. Utilizing the chemometric techniques, clear and reproducible differences were observed between the spectra of normal and cancer cases, suggesting that infrared microspectroscopy in conjunction with spectral data processing would be useful for diagnostic classification. Using LDA technique, the spectra were classified into cancer and normal tissue classes with an accuracy of 95.8%. The sensitivity and specificity was 100 and 93.1%, respectively.

Mathematical Methods for Engineers and Scientists 3 Fourier Analysis, Partial Differential Equations and Variational Methods

CERN Document Server

Tang, Kwong-Tin

2007-01-01

Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to make students comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.

A Fourier-series-based kernel-independent fast multipole method

International Nuclear Information System (INIS)

Zhang Bo; Huang Jingfang; Pitsianis, Nikos P.; Sun Xiaobai

2011-01-01

We present in this paper a new kernel-independent fast multipole method (FMM), named as FKI-FMM, for pairwise particle interactions with translation-invariant kernel functions. FKI-FMM creates, using numerical techniques, sufficiently accurate and compressive representations of a given kernel function over multi-scale interaction regions in the form of a truncated Fourier series. It provides also economic operators for the multipole-to-multipole, multipole-to-local, and local-to-local translations that are typical and essential in the FMM algorithms. The multipole-to-local translation operator, in particular, is readily diagonal and does not dominate in arithmetic operations. FKI-FMM provides an alternative and competitive option, among other kernel-independent FMM algorithms, for an efficient application of the FMM, especially for applications where the kernel function consists of multi-physics and multi-scale components as those arising in recent studies of biological systems. We present the complexity analysis and demonstrate with experimental results the FKI-FMM performance in accuracy and efficiency.

Fourier-based quantification of renal glomeruli size using Hough transform and shape descriptors.

Science.gov (United States)

Najafian, Sohrab; Beigzadeh, Borhan; Riahi, Mohammad; Khadir Chamazkoti, Fatemeh; Pouramir, Mahdi

2017-11-01

Analysis of glomeruli geometry is important in histopathological evaluation of renal microscopic images. Due to the shape and size disparity of even glomeruli of same kidney, automatic detection of these renal objects is not an easy task. Although manual measurements are time consuming and at times are not very accurate, it is commonly used in medical centers. In this paper, a new method based on Fourier transform following usage of some shape descriptors is proposed to detect these objects and their geometrical parameters. Reaching the goal, a database of 400 regions are selected randomly. 200 regions of which are part of glomeruli and the other 200 regions are not belong to renal corpuscles. ROC curve is used to decide which descriptor could classify two groups better. f_measure, which is a combination of both tpr (true positive rate) and fpr (false positive rate), is also proposed to select optimal threshold for descriptors. Combination of three parameters (solidity, eccentricity, and also mean squared error of fitted ellipse) provided better result in terms of f_measure to distinguish desired regions. Then, Fourier transform of outer edges is calculated to form a complete curve out of separated region(s). The generality of proposed model is verified by use of cross validation method, which resulted tpr of 94%, and fpr of 5%. Calculation of glomerulus' and Bowman's space with use of the algorithm are also compared with a non-automatic measurement done by a renal pathologist, and errors of 5.9%, 5.4%, and 6.26% are resulted in calculation of Capsule area, Bowman space, and glomeruli area, respectively. Having tested different glomeruli with various shapes, the experimental consequences show robustness and reliability of our method. Therefore, it could be used to illustrate renal diseases and glomerular disorders by measuring the morphological changes accurately and expeditiously. Copyright © 2017 Elsevier B.V. All rights reserved.

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.

Partial Fourier analysis of time-harmonic Maxwell's equations in axisymmetric domains

International Nuclear Information System (INIS)

Nkemzi, Boniface

2003-01-01

We analyze the Fourier method for treating time-harmonic Maxwell's equations in three-dimensional axisymmetric domains with non-axisymmetric data. The Fourier method reduces the three-dimensional boundary value problem to a system of decoupled two-dimensional boundary value problems on the plane meridian domain of the axisymmetric domain. The reduction process is fully described and suitable weighted spaces are introduced on the meridian domain to characterize the two-dimensional solutions. In particular, existence and uniqueness of solutions of the two-dimensional problems is proved and a priori estimates for the solutions are given. (author)

Fourier analysis of a new P1 synthetic acceleration for Sn transport equations

International Nuclear Information System (INIS)

Turcksin, B.; Ragusa, J. C.

2010-10-01

In this work, is derived a new P1 synthetic acceleration scheme (P1SA) for the S N transport equation and analyze its convergence properties through the means of a Fourier analysis. The Fourier analysis is carried out for both continuous (i.e., not spatially discretized) S N equations and linear discontinuous Fem discretization. We show, thanks to the continuous analysis, that the scheme is unstable when the anisotropy is important (μ - >0.5). However, the discrete analysis shows that when cells are large in comparison to the mean free path, the spectral radius decreases and the acceleration scheme becomes effective, even for highly anisotropic scattering. In charged particles transport, scattering is highly anisotropic and mean free paths are very small and, thus, this scheme could be of interest. To use the P1SA when cells are small and anisotropy is important, the scheme is modified by altering the update of the accelerated flux or by using either K transport sweeps before the application of P1SA. The update scheme performs well as long as μ - - ≥0.9, the modified update scheme is unstable. The multiple transport sweeps scheme is convergent with an arbitrary μ - but the spectral radius increases when scattering is isotropic. When anisotropic increases, the frequency of use of the acceleration scheme needs to be decreased. Even if the P1SA is used less often, the spectral radius is significantly smaller when compared with a method that does not use it for high anisotropy (μ - ≥0.5). It is interesting to notice that using P1SA every two iterations gives the same spectral radius than the update method when μ - ≥0.5 but it is much less efficient when μ - <0.5. (Author)

Segment density profiles of polyelectrolyte brushes determined by Fourier transform ellipsometry

Science.gov (United States)

Biesalski, Markus; Rühe, Jürgen; Johannsmann, Diethelm

1999-10-01

We describe a method for the explicit determination of the segment density profile φ(z) of surface-attached polymer brushes with multiple angle of incidence null-ellipsometry. Because the refractive index contrast between the brush layer and the solvent is weak, multiple reflections are of minor influence and the ellipsometric spectrum is closely related to the Fourier transform of the refractive index profile, thereby allowing for explicit inversion of the ellipsometric data. We chose surface-attached monolayers of polymethacrylic acid (PMAA), a weak polyelectrolyte, as a model system and determined the segment density profile of this system as a function of the pH value of the surrounding medium by the Fourier method. Complementary to the Fourier analysis, fits with error functions are given as well. The brushes were prepared on the bases of high refractive index prisms with the "grafting-from" technique. In water, the brushes swell by more than a factor of 30. The swelling increases with increasing pH because of a growing fraction of dissociated acidic groups leading to a larger electrostatic repulsion.

A symplectic Poisson solver based on Fast Fourier Transformation. The first trial

International Nuclear Information System (INIS)

Vorobiev, L.G.; Hirata, Kohji.

1995-11-01

A symplectic Poisson solver calculates numerically a potential and fields due to a 2D distribution of particles in a way that the symplecticity and smoothness are assured automatically. Such a code, based on Fast Fourier Transformation combined with Bicubic Interpolation, is developed for the use in multi-turn particle simulation in circular accelerators. Beside that, it may have a number of applications, where computations of space charge forces should obey a symplecticity criterion. Detailed computational schemes of all algorithms will be outlined to facilitate practical programming. (author)

A Fourier-based textural feature extraction procedure

Science.gov (United States)

Stromberg, W. D.; Farr, T. G.

1986-01-01

A procedure is presented to discriminate and characterize regions of uniform image texture. The procedure utilizes textural features consisting of pixel-by-pixel estimates of the relative emphases of annular regions of the Fourier transform. The utility and derivation of the features are described through presentation of a theoretical justification of the concept followed by a heuristic extension to a real environment. Two examples are provided that validate the technique on synthetic images and demonstrate its applicability to the discrimination of geologic texture in a radar image of a tropical vegetated area.

Maximum length scale in density based topology optimization

DEFF Research Database (Denmark)

Lazarov, Boyan Stefanov; Wang, Fengwen

2017-01-01

The focus of this work is on two new techniques for imposing maximum length scale in topology optimization. Restrictions on the maximum length scale provide designers with full control over the optimized structure and open possibilities to tailor the optimized design for broader range...... of manufacturing processes by fulfilling the associated technological constraints. One of the proposed methods is based on combination of several filters and builds on top of the classical density filtering which can be viewed as a low pass filter applied to the design parametrization. The main idea...

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.

An image hiding method based on cascaded iterative Fourier transform and public-key encryption algorithm

Science.gov (United States)

Zhang, B.; Sang, Jun; Alam, Mohammad S.

2013-03-01

An image hiding method based on cascaded iterative Fourier transform and public-key encryption algorithm was proposed. Firstly, the original secret image was encrypted into two phase-only masks M1 and M2 via cascaded iterative Fourier transform (CIFT) algorithm. Then, the public-key encryption algorithm RSA was adopted to encrypt M2 into M2' . Finally, a host image was enlarged by extending one pixel into 2×2 pixels and each element in M1 and M2' was multiplied with a superimposition coefficient and added to or subtracted from two different elements in the 2×2 pixels of the enlarged host image. To recover the secret image from the stego-image, the two masks were extracted from the stego-image without the original host image. By applying public-key encryption algorithm, the key distribution was facilitated, and also compared with the image hiding method based on optical interference, the proposed method may reach higher robustness by employing the characteristics of the CIFT algorithm. Computer simulations show that this method has good robustness against image processing.

Efficient Fourier-based algorithms for time-periodic unsteady problems

Science.gov (United States)

Gopinath, Arathi Kamath

2007-12-01

This dissertation work proposes two algorithms for the simulation of time-periodic unsteady problems via the solution of Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations. These algorithms use a Fourier representation in time and hence solve for the periodic state directly without resolving transients (which consume most of the resources in a time-accurate scheme). In contrast to conventional Fourier-based techniques which solve the governing equations in frequency space, the new algorithms perform all the calculations in the time domain, and hence require minimal modifications to an existing solver. The complete space-time solution is obtained by iterating in a fifth pseudo-time dimension. Various time-periodic problems such as helicopter rotors, wind turbines, turbomachinery and flapping-wings can be simulated using the Time Spectral method. The algorithm is first validated using pitching airfoil/wing test cases. The method is further extended to turbomachinery problems, and computational results verified by comparison with a time-accurate calculation. The technique can be very memory intensive for large problems, since the solution is computed (and hence stored) simultaneously at all time levels. Often, the blade counts of a turbomachine are rescaled such that a periodic fraction of the annulus can be solved. This approximation enables the solution to be obtained at a fraction of the cost of a full-scale time-accurate solution. For a viscous computation over a three-dimensional single-stage rescaled compressor, an order of magnitude savings is achieved. The second algorithm, the reduced-order Harmonic Balance method is applicable only to turbomachinery flows, and offers even larger computational savings than the Time Spectral method. It simulates the true geometry of the turbomachine using only one blade passage per blade row as the computational domain. In each blade row of the turbomachine, only the dominant frequencies are resolved, namely

Fourier transformations for difference analogs of the harmonic oscillator

International Nuclear Information System (INIS)

Askey, R.; Atakishiyev, N.M.

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

Dual-polarization nonlinear Fourier transform-based optical communication system

DEFF Research Database (Denmark)

Gaiarin, Simone; Perego, A. M.; da Silva, Edson Porto

2018-01-01

communication could potentially overcome these limitations. It relies on a mathematical technique called “nonlinear Fourier transform (NFT)” to exploit the “hidden” linearity of the nonlinear Schrödinger equation as the master model for signal propagation in an optical fiber. We present here the theoretical...

Fourier Hull Fatigue Assessment Method’s Proposing and Software Development

Directory of Open Access Journals (Sweden)

Jing Chen

2014-05-01

Full Text Available In this paper, based on the spectral analysis and the strain energy theory, the systematic errors of Rain-flow Counting Method have been quantitatively analyzed, from which a Fourier Counting Method is put forward. And according to this new method, software has been developed combined with sampling data of the real container ship via rigorous theoretical derivation and compact modular design, which has certain theoretical innovation significance and practical value.

Spectroscopie de Fourier par peignes de fréquences femtosecondes

OpenAIRE

Mandon , Julien

2009-01-01

This work presents results towards the development of a novel frequency-comb based Fourier transform spectroscopy (FTS). Since 1970, due to its exceptional qualities, FTS has offered a simple way for spectral analysis and has assumed a position of dominance for the measurement of broadband well-resolved accurate spectra. However, FTS doesn't satisfy the new requirements in molecular physics. Acquisition time at the limit, extreme resolution, broad spectral extension, high sensitivity, and acc...

Universal discrete Fourier optics RF photonic integrated circuit architecture.

Science.gov (United States)

Hall, Trevor J; Hasan, Mehedi

2016-04-04

This paper describes a coherent electro-optic circuit architecture that generates a frequency comb consisting of N spatially separated orders using a generalised Mach-Zenhder interferometer (MZI) with its N × 1 combiner replaced by an optical N × N Discrete Fourier Transform (DFT). Advantage may be taken of the tight optical path-length control, component and circuit symmetries and emerging trimming algorithms offered by photonic integration in any platform that offers linear electro-optic phase modulation such as LiNbO3, silicon, III-V or hybrid technology. The circuit architecture subsumes all MZI-based RF photonic circuit architectures in the prior art given an appropriate choice of output port(s) and dimension N although the principal application envisaged is phase correlated subcarrier generation for all optical orthogonal frequency division multiplexing. A transfer matrix approach is used to model the operation of the architecture. The predictions of the model are validated by simulations performed using an industry standard software tool. Implementation is found to be practical.

Filtros digitais por transformadas de Fourier aplicados em eletroquímica Digital filters based on Fourier transforms for application in electrochemistry

Directory of Open Access Journals (Sweden)

Ricardo Nantes Liang

2013-01-01

Full Text Available The electrochemical properties of micro and nano-electrodes are widely investigated due to their low faradaic and capacitive currents, leading to a new generation of smart and implantable devices. However, the current signals obtained in low-dimensional devices are strongly influenced by noise sources. In this paper, we show the evaluation of filters based on Fast Fourier Transform (FFT and their implementation in a graphical user interface (GUI in MATLAB®. As a case study, we evaluated an electrochemical reaction process of charge transfer via outer-sphere. Results showed successful removal of most of the noise in signals, thus proving a promising tool for low-scale measurement.

Análise de Fourier para detecção de defeitos localizados na camada de fibras nervosas da retina com a polarimetria a laser Fourier analysis for the detection of localized nerve fiber layer defects using scanning laser polarimetry

Directory of Open Access Journals (Sweden)

Felipe Andrade Medeiros

2003-12-01

this study, we performed Fourier analysis of retinal nerve fiber layer (RNFL thickness measurements obtained with scanning laser polarimetry and evaluated the ability of this method to detect localized nerve fiber layer defects in glaucomatous patients. METHODS: The study included 40 eyes of 40 glaucomatous patients with localized RNFL defects identified by slit-lamp biomicroscopy or RNFL photography and 43 eyes of 43 normal patients. The patients were submitted to RNFL thickness measurements using the GDx® - Nerve Fiber Analyzer. Fourier analysis was applied to the polarimetry data. Fourier coefficients and GDx parameters were compared between the two groups. A linear discriminant function was developed to identify and combine the most useful Fourier coefficients to separate the two groups. ROC curves were obtained for each measurement and sensitivity values (at fixed specificities were calculated. RESULTS: The combination of Fourier coefficients resulted in a sensitivity of 80% for a specificity set at higher than 90%. For the same specificity, the GDx parameters had sensitivities ranging from 15% to 48%. The area under the ROC curve (AUC for the combination of Fourier coefficients was 0.90, significantly higher than the AUC for the parameter The Number (0.76. CONCLUSION: Fourier analysis of RNFL polarimetry data had a better diagnostic performance than standard GDx parameters to identify localized retinal nerve fiber layer defects in glaucomatous patients.

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)

Vibrational analysis of Fourier transform spectrum of the A3Π0–X1Σ ...

Indian Academy of Sciences (India)

Home; Journals; Pramana – Journal of Physics; Volume 73; Issue 5. Vibrational analysis of Fourier transform spectrum of the A 3 0 – X 1 ∑ + and B 3 1 – X 1 ∑ + transitions of indium monobromide. Renu Singh K N Uttam M D Saksena M N Deo. Volume 73 Issue 5 November 2009 pp 889-899 ...

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...

A unified Fourier theory for time-of-flight PET data

International Nuclear Information System (INIS)

Li, Yusheng; Matej, Samuel; Metzler, Scott D

2016-01-01

Fully 3D time-of-flight (TOF) PET scanners offer the potential of previously unachievable image quality in clinical PET imaging. TOF measurements add another degree of redundancy for cylindrical PET scanners and make photon-limited TOF-PET imaging more robust than non-TOF PET imaging. The data space for 3D TOF-PET data is five-dimensional with two degrees of redundancy. Previously, consistency equations were used to characterize the redundancy of TOF-PET data. In this paper, we first derive two Fourier consistency equations and Fourier–John equation for 3D TOF PET based on the generalized projection-slice theorem; the three partial differential equations (PDEs) are the dual of the sinogram consistency equations and John’s equation. We then solve the three PDEs using the method of characteristics. The two degrees of entangled redundancy of the TOF-PET data can be explicitly elicited and exploited by the solutions of the PDEs along the characteristic curves, which gives a complete understanding of the rich structure of the 3D x-ray transform with TOF measurement. Fourier rebinning equations and other mapping equations among different types of PET data are special cases of the general solutions. We also obtain new Fourier rebinning and consistency equations (FORCEs) from other special cases of the general solutions, and thus we obtain a complete scheme to convert among different types of PET data: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF data. The new FORCEs can be used as new Fourier-based rebinning algorithms for TOF-PET data reduction, inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. Further, we give a geometric interpretation of the general solutions—the two families of characteristic curves can be obtained by respectively changing the azimuthal and co-polar angles of the biorthogonal coordinates in Fourier space. We conclude the unified Fourier theory by showing that the Fourier consistency equations

Size distribution of magnetic iron oxide nanoparticles using Warren-Averbach XRD analysis

Science.gov (United States)

Mahadevan, S.; Behera, S. P.; Gnanaprakash, G.; Jayakumar, T.; Philip, J.; Rao, B. P. C.

2012-07-01

We use the Fourier transform based Warren-Averbach (WA) analysis to separate the contributions of X-ray diffraction (XRD) profile broadening due to crystallite size and microstrain for magnetic iron oxide nanoparticles. The profile shape of the column length distribution, obtained from WA analysis, is used to analyze the shape of the magnetic iron oxide nanoparticles. From the column length distribution, the crystallite size and its distribution are estimated for these nanoparticles which are compared with size distribution obtained from dynamic light scattering measurements. The crystallite size and size distribution of crystallites obtained from WA analysis are explained based on the experimental parameters employed in preparation of these magnetic iron oxide nanoparticles. The variation of volume weighted diameter (Dv, from WA analysis) with saturation magnetization (Ms) fits well to a core shell model wherein it is known that Ms=Mbulk(1-6g/Dv) with Mbulk as bulk magnetization of iron oxide and g as magnetic shell disorder thickness.

Fourier optical cryptosystem using complex spatial modulation

International Nuclear Information System (INIS)

Sarkadi, T; Koppa, P

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)

Using Fourier and Taylor series expansion in semi-analytical deformation analysis of thick-walled isotropic and wound composite structures

Directory of Open Access Journals (Sweden)

Jiran L.

2016-06-01

Full Text Available Thick-walled tubes made from isotropic and anisotropic materials are subjected to an internal pressure while the semi-analytical method is employed to investigate their elastic deformations. The contribution and novelty of this method is that it works universally for different loads, different boundary conditions, and different geometry of analyzed structures. Moreover, even when composite material is considered, the method requires no simplistic assumptions. The method uses a curvilinear tensor calculus and it works with the analytical expression of the total potential energy while the unknown displacement functions are approximated by using appropriate series expansion. Fourier and Taylor series expansion are involved into analysis in which they are tested and compared. The main potential of the proposed method is in analyses of wound composite structures when a simple description of the geometry is made in a curvilinear coordinate system while material properties are described in their inherent Cartesian coordinate system. Validations of the introduced semi-analytical method are performed by comparing results with those obtained from three-dimensional finite element analysis (FEA. Calculations with Fourier series expansion show noticeable disagreement with results from the finite element model because Fourier series expansion is not able to capture the course of radial deformation. Therefore, it can be used only for rough estimations of a shape after deformation. On the other hand, the semi-analytical method with Fourier Taylor series expansion works very well for both types of material. Its predictions of deformations are reliable and widely exploitable.

A new method to cluster genomes based on cumulative Fourier power spectrum.

Science.gov (United States)

Dong, Rui; Zhu, Ziyue; Yin, Changchuan; He, Rong L; Yau, Stephen S-T

2018-06-20

Analyzing phylogenetic relationships using mathematical methods has always been of importance in bioinformatics. Quantitative research may interpret the raw biological data in a precise way. Multiple Sequence Alignment (MSA) is used frequently to analyze biological evolutions, but is very time-consuming. When the scale of data is large, alignment methods cannot finish calculation in reasonable time. Therefore, we present a new method using moments of cumulative Fourier power spectrum in clustering the DNA sequences. Each sequence is translated into a vector in Euclidean space. Distances between the vectors can reflect the relationships between sequences. The mapping between the spectra and moment vector is one-to-one, which means that no information is lost in the power spectra during the calculation. We cluster and classify several datasets including Influenza A, primates, and human rhinovirus (HRV) datasets to build up the phylogenetic trees. Results show that the new proposed cumulative Fourier power spectrum is much faster and more accurately than MSA and another alignment-free method known as k-mer. The research provides us new insights in the study of phylogeny, evolution, and efficient DNA comparison algorithms for large genomes. The computer programs of the cumulative Fourier power spectrum are available at GitHub (https://github.com/YaulabTsinghua/cumulative-Fourier-power-spectrum). Copyright © 2018. Published by Elsevier B.V.

Using Dynamic Fourier Analysis to Discriminate Between Seismic Signals from Natural Earthquakes and Mining Explosions

Directory of Open Access Journals (Sweden)

Maria C. Mariani

2017-08-01

Full Text Available A sequence of intraplate earthquakes occurred in Arizona at the same location where miningexplosions were carried out in previous years. The explosions and some of the earthquakes generatedvery similar seismic signals. In this study Dynamic Fourier Analysis is used for discriminating signalsoriginating from natural earthquakes and mining explosions. Frequency analysis of seismogramsrecorded at regional distances shows that compared with the mining explosions the earthquake signalshave larger amplitudes in the frequency interval ~ 6 to 8 Hz and significantly smaller amplitudes inthe frequency interval ~ 2 to 4 Hz. This type of analysis permits identifying characteristics in theseismograms frequency yielding to detect potentially risky seismic events.

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.

Secure multi-party quantum summation based on quantum Fourier transform

Science.gov (United States)

Yang, Hui-Yi; Ye, Tian-Yu

2018-06-01

In this paper, we propose a novel secure multi-party quantum summation protocol based on quantum Fourier transform, where the traveling particles are transmitted in a tree-type mode. The party who prepares the initial quantum states is assumed to be semi-honest, which means that she may misbehave on her own but will not conspire with anyone. The proposed protocol can resist both the outside attacks and the participant attacks. Especially, one party cannot obtain other parties' private integer strings; and it is secure for the colluding attack performed by at most n - 2 parties, where n is the number of parties. In addition, the proposed protocol calculates the addition of modulo d and implements the calculation of addition in a secret-by-secret way rather than a bit-by-bit way.

Classification of fault diagnosis in a gear wheel by used probabilistic neural network, fast Fourier transform and principal component analysis

Directory of Open Access Journals (Sweden)

Piotr CZECH

2007-01-01

Full Text Available This paper presents the results of an experimental application of artificial neural network as a classifier of the degree of cracking of a tooth root in a gear wheel. The neural classifier was based on the artificial neural network of Probabilistic Neural Network type (PNN. The input data for the classifier was in a form of matrix composedof statistical measures, obtained from fast Fourier transform (FFT and principal component analysis (PCA. The identified model of toothed gear transmission, operating in a circulating power system, served for generation of the teaching and testing set applied for the experiment.

Fractional Fourier domain optical image hiding using phase retrieval algorithm based on iterative nonlinear double random phase encoding.

Science.gov (United States)

Wang, Xiaogang; Chen, Wen; Chen, Xudong

2014-09-22

We present a novel image hiding method based on phase retrieval algorithm under the framework of nonlinear double random phase encoding in fractional Fourier domain. Two phase-only masks (POMs) are efficiently determined by using the phase retrieval algorithm, in which two cascaded phase-truncated fractional Fourier transforms (FrFTs) are involved. No undesired information disclosure, post-processing of the POMs or digital inverse computation appears in our proposed method. In order to achieve the reduction in key transmission, a modified image hiding method based on the modified phase retrieval algorithm and logistic map is further proposed in this paper, in which the fractional orders and the parameters with respect to the logistic map are regarded as encryption keys. Numerical results have demonstrated the feasibility and effectiveness of the proposed algorithms.

Measuring Clearance Mechanics Based on Dynamic Leg Length

Science.gov (United States)

Khamis, Sam; Danino, Barry; Hayek, Shlomo; Carmeli, Eli

2018-01-01

The aim of this study was to quantify clearance mechanics during gait. Seventeen children diagnosed with hemiplegic cerebral palsy underwent a three-dimensional gait analysis evaluation. Dynamic leg lengths were measured from the hip joint center to the heel, to the ankle joint center and to the forefoot throughout the gait cycle. Significant…

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.

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.

Fourier-transform infrared spectroscopy as a novel approach to providing effect-based endpoints in duckweed toxicity testing.

Science.gov (United States)

Hu, Li-Xin; Ying, Guang-Guo; Chen, Xiao-Wen; Huang, Guo-Yong; Liu, You-Sheng; Jiang, Yu-Xia; Pan, Chang-Gui; Tian, Fei; Martin, Francis L

2017-02-01

Traditional duckweed toxicity tests only measure plant growth inhibition as an endpoint, with limited effects-based data. The present study aimed to investigate whether Fourier-transform infrared (FTIR) spectroscopy could enhance the duckweed (Lemna minor L.) toxicity test. Four chemicals (Cu, Cd, atrazine, and acetochlor) and 4 metal-containing industrial wastewater samples were tested. After exposure of duckweed to the chemicals, standard toxicity endpoints (frond number and chlorophyll content) were determined; the fronds were also interrogated using FTIR spectroscopy under optimized test conditions. Biochemical alterations associated with each treatment were assessed and further analyzed by multivariate analysis. The results showed that comparable x% of effective concentration (ECx) values could be achieved based on FTIR spectroscopy in comparison with those based on traditional toxicity endpoints. Biochemical alterations associated with different doses of toxicant were mainly attributed to lipid, protein, nucleic acid, and carbohydrate structural changes, which helped to explain toxic mechanisms. With the help of multivariate analysis, separation of clusters related to different exposure doses could be achieved. The present study is the first to show successful application of FTIR spectroscopy in standard duckweed toxicity tests with biochemical alterations as new endpoints. Environ Toxicol Chem 2017;36:346-353. © 2016 SETAC. © 2016 SETAC.

Non-linear adjustment to purchasing power parity: an analysis using Fourier approximations

OpenAIRE

Juan-Ángel Jiménez-Martín; M. Dolores Robles Fernández

2005-01-01

This paper estimates the dynamics of adjustment to long run purchasing power parity (PPP) using data for 18 mayor bilateral US dollar exchange rates, over the post-Bretton Woods period, in a non-linear framework. We use new unit root and cointegration tests that do not assume a specific non-linear adjustment process. Using a first-order Fourier approximation, we find evidence of non-linear mean reversion in deviations from both absolute and relative PPP. This first-order Fourier approximation...

Line width and line shape analysis in the inductively coupled plasma by high resolution Fourier transform spectrometry

International Nuclear Information System (INIS)

Faires, L.M.; Palmer, B.A.; Brault, J.W.

1984-01-01

High resolution Fourier transform spectrometry has been used to perform line width and line shape analysis of eighty-one iron I emision lines in the spectral range 290 to 390nm originating in the normal analytical zone of an inductively coupled plasma. Computer programs using non-linear least squares fitting techniques for line shape analysis were applied to the fully resolved spectra to determine Gaussian and Lorentzian components of the total observed line width. The effect of noise in the spectrum on the precision of the line fitting technique was assessed, and the importance of signal to noise ratio for line shape analysis is discussed. Translational (Doppler) temperatures were calculated from the Gaussian components of the line width and were found to be on the order of 6300 0 K. The excitation temperature of iron I was also determined from the same spectral data by the spectroscopic slope method based on the Einstein-Boltzmann expression for spectral intensity and was found to be on the order of 4700 0 K. 31 references

Application of Fourier transform infrared spectroscopy with chemometrics on postmortem interval estimation based on pericardial fluids.

Science.gov (United States)

Zhang, Ji; Li, Bing; Wang, Qi; Wei, Xin; Feng, Weibo; Chen, Yijiu; Huang, Ping; Wang, Zhenyuan

2017-12-21

Postmortem interval (PMI) evaluation remains a challenge in the forensic community due to the lack of efficient methods. Studies have focused on chemical analysis of biofluids for PMI estimation; however, no reports using spectroscopic methods in pericardial fluid (PF) are available. In this study, Fourier transform infrared (FTIR) spectroscopy with attenuated total reflectance (ATR) accessory was applied to collect comprehensive biochemical information from rabbit PF at different PMIs. The PMI-dependent spectral signature was determined by two-dimensional (2D) correlation analysis. The partial least square (PLS) and nu-support vector machine (nu-SVM) models were then established based on the acquired spectral dataset. Spectral variables associated with amide I, amide II, COO - , C-H bending, and C-O or C-OH vibrations arising from proteins, polypeptides, amino acids and carbohydrates, respectively, were susceptible to PMI in 2D correlation analysis. Moreover, the nu-SVM model appeared to achieve a more satisfactory prediction than the PLS model in calibration; the reliability of both models was determined in an external validation set. The study shows the possibility of application of ATR-FTIR methods in postmortem interval estimation using PF samples.

Distributed Two-Dimensional Fourier Transforms on DSPs with an Application for Phase Retrieval

Science.gov (United States)

Smith, Jeffrey Scott

2006-01-01

Many applications of two-dimensional Fourier Transforms require fixed timing as defined by system specifications. One example is image-based wavefront sensing. The image-based approach has many benefits, yet it is a computational intensive solution for adaptive optic correction, where optical adjustments are made in real-time to correct for external (atmospheric turbulence) and internal (stability) aberrations, which cause image degradation. For phase retrieval, a type of image-based wavefront sensing, numerous two-dimensional Fast Fourier Transforms (FFTs) are used. To meet the required real-time specifications, a distributed system is needed, and thus, the 2-D FFT necessitates an all-to-all communication among the computational nodes. The 1-D floating point FFT is very efficient on a digital signal processor (DSP). For this study, several architectures and analysis of such are presented which address the all-to-all communication with DSPs. Emphasis of this research is on a 64-node cluster of Analog Devices TigerSharc TS-101 DSPs.

Modelling fourier regression for time series data- a case study: modelling inflation in foods sector in Indonesia

Science.gov (United States)

Prahutama, Alan; Suparti; Wahyu Utami, Tiani

2018-03-01

Regression analysis is an analysis to model the relationship between response variables and predictor variables. The parametric approach to the regression model is very strict with the assumption, but nonparametric regression model isn’t need assumption of model. Time series data is the data of a variable that is observed based on a certain time, so if the time series data wanted to be modeled by regression, then we should determined the response and predictor variables first. Determination of the response variable in time series is variable in t-th (yt), while the predictor variable is a significant lag. In nonparametric regression modeling, one developing approach is to use the Fourier series approach. One of the advantages of nonparametric regression approach using Fourier series is able to overcome data having trigonometric distribution. In modeling using Fourier series needs parameter of K. To determine the number of K can be used Generalized Cross Validation method. In inflation modeling for the transportation sector, communication and financial services using Fourier series yields an optimal K of 120 parameters with R-square 99%. Whereas if it was modeled by multiple linear regression yield R-square 90%.

Techniques for Handling and Removal of Spectral Channels in Fourier Transform Synchrotron-Based Spectra

International Nuclear Information System (INIS)

Ibrahim, Amr; Predoi-Cross, Adriana; Teillet, Philippe M.

2010-01-01

Channel spectra are a big problem for those attempting to use synchrotron-based Fourier transform spectra for spectral lineshape studies. Due to the layout of the optical system at the CLS far-infrared beamline, the synchrotron beam undergoes unavoidable multiple reflections on the steering mirrors, beam splitter, several sets of windows, and filters. We present a method for eliminating channel spectra and compare the results of our technique with other methods available in the literature.

A Fourier Optical Model for the Laser Doppler Velocimeter

DEFF Research Database (Denmark)

Lading, Lars

1972-01-01

The treatment is based on a fourier optical model. It is shown how the various configurations (i.e. ldquodifferential moderdquo and reference beam mode with both one and two incident beams) are incorporated in the model, and how it can be extended to three dimensions. The particles are represented...... filtering ability vanishes as the aperture size converges towards zero. The results based on fourier optics are compared with the rough estimates obtainable by using the "antenna formular" for heterodyning (ArΩr≈λ2)....

Efficient Pricing of European-Style Asian Options under Exponential Lévy Processes Based on Fourier Cosine Expansions

NARCIS (Netherlands)

Zhang, B.; Oosterlee, C.W.

2013-01-01

We propose an efficient pricing method for arithmetic and geometric Asian options under exponential Lévy processes based on Fourier cosine expansions and Clenshaw–Curtis quadrature. The pricing method is developed for both European style and American-style Asian options and for discretely and

Seismic wavefield modeling based on time-domain symplectic and Fourier finite-difference method

Science.gov (United States)

Fang, Gang; Ba, Jing; Liu, Xin-xin; Zhu, Kun; Liu, Guo-Chang

2017-06-01

Seismic wavefield modeling is important for improving seismic data processing and interpretation. Calculations of wavefield propagation are sometimes not stable when forward modeling of seismic wave uses large time steps for long times. Based on the Hamiltonian expression of the acoustic wave equation, we propose a structure-preserving method for seismic wavefield modeling by applying the symplectic finite-difference method on time grids and the Fourier finite-difference method on space grids to solve the acoustic wave equation. The proposed method is called the symplectic Fourier finite-difference (symplectic FFD) method, and offers high computational accuracy and improves the computational stability. Using acoustic approximation, we extend the method to anisotropic media. We discuss the calculations in the symplectic FFD method for seismic wavefield modeling of isotropic and anisotropic media, and use the BP salt model and BP TTI model to test the proposed method. The numerical examples suggest that the proposed method can be used in seismic modeling of strongly variable velocities, offering high computational accuracy and low numerical dispersion. The symplectic FFD method overcomes the residual qSV wave of seismic modeling in anisotropic media and maintains the stability of the wavefield propagation for large time steps.

Comparison between length and velocity gauges in quantum simulations of high-order harmonic generation

DEFF Research Database (Denmark)

Han, Yong-Chang; Madsen, Lars Bojer

2010-01-01

, and acceleration forms, and two gauges, the length and velocity gauges. The relationships among the harmonic phases obtained from the Fourier transform of the three forms are discussed in detail. Although quantum mechanics is gauge invariant and the length and velocity gauges should give identical results, the two...... gauges present different computation efficiencies, which reflects the different behavior in terms of characteristics of the physical couplings acting in the two gauges. In order to obtain convergence, more angular momentum states are required in the length gauge, while more grid points are required...

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

Prediction of solar cycle 24 using fourier series analysis

International Nuclear Information System (INIS)

Khalid, M.; Sultana, M.; Zaidi, F.

2014-01-01

Predicting the behavior of solar activity has become very significant. It is due to its influence on Earth and the surrounding environment. Apt predictions of the amplitude and timing of the next solar cycle will aid in the estimation of the several results of Space Weather. In the past, many prediction procedures have been used and have been successful to various degrees in the field of solar activity forecast. In this study, Solar cycle 24 is forecasted by the Fourier series method. Comparative analysis has been made by auto regressive integrated moving averages method. From sources, January 2008 was the minimum preceding solar cycle 24, the amplitude and shape of solar cycle 24 is approximate on monthly number of sunspots. This forecast framework approximates a mean solar cycle 24, with the maximum appearing during May 2014 (+- 8 months), with most sunspot of 98 +- 10. Solar cycle 24 will be ending in June 2020 (+- 7 months). The difference between two consecutive peak values of solar cycles (i.e. solar cycle 23 and 24 ) is 165 months(+- 6 months). (author)

Fourier Transform Infrared Imaging analysis of dental pulp inflammatory diseases.

Science.gov (United States)

Giorgini, E; Sabbatini, S; Conti, C; Rubini, C; Rocchetti, R; Fioroni, M; Memè, L; Orilisi, G

2017-05-01

Fourier Transform Infrared microspectroscopy let characterize the macromolecular composition and distribution of tissues and cells, by studying the interaction between infrared radiation and matter. Therefore, we hypothesize to exploit this analytical tool in the analysis of inflamed pulps, to detect the different biochemical features related to various degrees of inflammation. IR maps of 13 irreversible and 12 hyperplastic pulpitis, together with 10 normal pulps, were acquired, compared with histological findings and submitted to multivariate (HCA, PCA, SIMCA) and statistical (one-way ANOVA) analysis. The fit of convoluted bands let calculate meaningful band area ratios (means ± s.d., P < 0.05). The infrared imaging analysis pin-pointed higher amounts of water and lower quantities of type I collagen in all inflamed pulps. Specific vibrational markers were defined for irreversible pulpitis (Lipids/Total Biomass, PhII/Total Biomass, CH 2 /CH 3 , and Ty/AII) and hyperplastic ones (OH/Total Biomass, Collagen/Total Biomass, and CH 3 Collagen/Total Biomass). The study confirmed that FTIR microspectroscopy let discriminate tissues' biological features. The infrared imaging analysis evidenced, in inflamed pulps, alterations in tissues' structure and composition. Changes in lipid metabolism, increasing amounts of tyrosine, and the occurrence of phosphorylative processes were highlighted in irreversible pulpitis, while high amounts of water and low quantities of type I collagen were detected in hyperplastic samples. © 2017 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Some Notes on the Use of theWindowed Fourier Transform for Spectral Analysis of Discretely Sampled Data

Directory of Open Access Journals (Sweden)

Robert W. Johnson

2013-06-01

Full Text Available The properties of the Gabor and Morlet transforms are examined with respect to the Fourier analysis of discretely sampled data. Forward and inverse transform pairs based on a fixed window with uniform sampling of the frequency axis can satisfy numerically the energy and reconstruction theorems; however, transform pairs based on a variable window or nonuniform frequency sampling in general do not. Instead of selecting the shape of the window as some function of the central frequency, we propose constructing a single window with unit energy from an arbitrary set of windows that is applied over the entire frequency axis. By virtue of using a fixed window with uniform frequency sampling, such a transform satisfies the energy and reconstruction theorems. The shape of the window can be tailored to meet the requirements of the investigator in terms of time/frequency resolution. The algorithm extends naturally to the case of nonuniform signal sampling without modification beyond identification of the Nyquist interval.

The application of an optical Fourier spectrum analyzer on detecting defects in mass-produced satellite photographs

Science.gov (United States)

Athale, R.; Lee, S. H.

1976-01-01

Various defects in mass-produced pictures transmitted to earth from a satellite are investigated. It is found that the following defects are readily detectable via Fourier spectrum analysis: (1) bit slip, (2) breakup causing loss of image, and (3) disabled track at the top of the imagery. The scratches made on the film during mass production, which are difficult to detect by visual observation, also show themselves readily in Fourier spectrum analysis. A relation is established between the number of scratches, their width and depth and the intensity of their Fourier spectra. Other defects that are found to be equally suitable for Fourier spectrum analysis or visual (image analysis) detection are synchronous loss without blurring of image, and density variation in gray scale. However, the Fourier spectrum analysis is found to be unsuitable for detection of such defects as pin holes, annotation error, synchronous loss with blurring of images, and missing image in the beginning of the work order. The design of an automated, real time system, which will reject defective films, is treated.

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.)

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.

Efficient algorithm for baseline wander and powerline noise removal from ECG signals based on discrete Fourier series.

Science.gov (United States)

Bahaz, Mohamed; Benzid, Redha

2018-03-01

Electrocardiogram (ECG) signals are often contaminated with artefacts and noises which can lead to incorrect diagnosis when they are visually inspected by cardiologists. In this paper, the well-known discrete Fourier series (DFS) is re-explored and an efficient DFS-based method is proposed to reduce contribution of both baseline wander (BW) and powerline interference (PLI) noises in ECG records. In the first step, the determination of the exact number of low frequency harmonics contributing in BW is achieved. Next, the baseline drift is estimated by the sum of all associated Fourier sinusoids components. Then, the baseline shift is discarded efficiently by a subtraction of its approximated version from the original biased ECG signal. Concerning the PLI, the subtraction of the contributing harmonics calculated in the same manner reduces efficiently such type of noise. In addition of visual quality results, the proposed algorithm shows superior performance in terms of higher signal-to-noise ratio and smaller mean square error when faced to the DCT-based algorithm.

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)

Umbilical cord length in singleton gestations: a Finnish population-based retrospective register study.

Science.gov (United States)

Georgiadis, L; Keski-Nisula, L; Harju, M; Räisänen, S; Georgiadis, S; Hannila, M-L; Heinonen, S

2014-04-01

Many complications of pregnancy and delivery are associated with umbilical cord length. It is important to examine the variation in length, in order to identify normal and abnormal conditions. Moreover, the factors influencing cord growth and development are not precisely known. The main objectives were to provide updated reference charts for umbilical cord length in singleton pregnancies and to evaluate potential factors affecting cord length. Birth register data of 47,284 singleton pregnant women delivering in Kuopio University Hospital, Finland was collected prospectively. Gender-specific centile charts for cord length from 22 to 44 gestational weeks were obtained using generalized additive models for location, scale, and shape (GAMLSS). Gestational, fetal, and maternal factors were studied for their potential influence on cord length with single variable analysis and stepwise multiple linear regression analysis. Cord length increased according to gestational age, while the growth decelerated post-term. Birth weight, placental weight, pregravid maternal body mass index, parity, and maternal age correlated to cord length. Gestational diabetes and previous miscarriages were associated with longer cords, while female gender and placental abruption were associated with shorter cords. Girls had shorter cords throughout gestation although there was substantial variation in length in both genders. Cord length associated significantly with birth weight, placental weight, and gestational age. Significantly shorter cords were found in women with placental abruption. This important finding requires further investigation. Copyright © 2014 Elsevier Ltd. All rights reserved.

Response of multiferroic composites inferred from a fast-Fourier-transform-based numerical scheme

International Nuclear Information System (INIS)

Brenner, Renald; Bravo-Castillero, Julián

2010-01-01

The effective response and the local fields within periodic magneto-electric multiferroic composites are investigated by means of a numerical scheme based on fast Fourier transforms. This computational framework relies on the iterative resolution of coupled series expansions for the magnetic, electric and strain fields. By using an augmented Lagrangian formulation, a simple and robust procedure which makes use of the uncoupled Green operators for the elastic, electrostatics and magnetostatics problems is proposed. Its accuracy is assessed in the cases of laminated and fibrous two-phase composites for which analytical solutions exist

Discrete Fourier and wavelet transforms an introduction through linear algebra with applications to signal processing

CERN Document Server

Goodman, Roe W

2016-01-01

This textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, without assuming prior knowledge of signal processing or advanced analysis.It explains how to use the Fourier matrix to extract frequency information from a digital signal and how to use circulant matrices to emphasize selected frequency ranges. It introduces discrete wavelet transforms for digital signals through the lifting method and illustrates through examples and computer explorations how these transforms are used in signal and image processing. Then the general theory of discrete wavelet transforms is developed via the matrix algebra of two-channel filter banks. Finally, wavelet transforms for analog signals are constructed based on filter bank results already presented, and the mathematical framework of multiresolution analysis is examined.

Emotion recognition based on multiple order features using fractional Fourier transform

Science.gov (United States)

Ren, Bo; Liu, Deyin; Qi, Lin

2017-07-01

In order to deal with the insufficiency of recently algorithms based on Two Dimensions Fractional Fourier Transform (2D-FrFT), this paper proposes a multiple order features based method for emotion recognition. Most existing methods utilize the feature of single order or a couple of orders of 2D-FrFT. However, different orders of 2D-FrFT have different contributions on the feature extraction of emotion recognition. Combination of these features can enhance the performance of an emotion recognition system. The proposed approach obtains numerous features that extracted in different orders of 2D-FrFT in the directions of x-axis and y-axis, and uses the statistical magnitudes as the final feature vectors for recognition. The Support Vector Machine (SVM) is utilized for the classification and RML Emotion database and Cohn-Kanade (CK) database are used for the experiment. The experimental results demonstrate the effectiveness of the proposed method.

Modification of the fast fourier transform-based method by signal mirroring for accuracy quantification of thermal-hydraulic system code

Energy Technology Data Exchange (ETDEWEB)

Ha, Tae Wook; Jeong, Jae Jun [School of Mechanical Engineering, Pusan National University, Busan (Korea, Republic of); Choi, Ki Yong [Korea Atomic Energy Research Institute (KAERI), Daejeon (Korea, Republic of)

2017-08-15

A thermal–hydraulic system code is an essential tool for the design and safety analysis of a nuclear power plant, and its accuracy quantification is very important for the code assessment and applications. The fast Fourier transform-based method (FFTBM) by signal mirroring (FFTBM-SM) has been used to quantify the accuracy of a system code by using a comparison of the experimental data and the calculated results. The method is an improved version of the FFTBM, and it is known that the FFTBM-SM judges the code accuracy in a more consistent and unbiased way. However, in some applications, unrealistic results have been obtained. In this study, it was found that accuracy quantification by FFTBM-SM is dependent on the frequency spectrum of the fast Fourier transform of experimental and error signals. The primary objective of this study is to reduce the frequency dependency of FFTBM-SM evaluation. For this, it was proposed to reduce the cut off frequency, which was introduced to cut off spurious contributions, in FFTBM-SM. A method to determine an appropriate cut off frequency was also proposed. The FFTBM-SM with the modified cut off frequency showed a significant improvement of the accuracy quantification.

Modification of the fast fourier transform-based method by signal mirroring for accuracy quantification of thermal-hydraulic system code

International Nuclear Information System (INIS)

Ha, Tae Wook; Jeong, Jae Jun; Choi, Ki Yong

2017-01-01

A thermal–hydraulic system code is an essential tool for the design and safety analysis of a nuclear power plant, and its accuracy quantification is very important for the code assessment and applications. The fast Fourier transform-based method (FFTBM) by signal mirroring (FFTBM-SM) has been used to quantify the accuracy of a system code by using a comparison of the experimental data and the calculated results. The method is an improved version of the FFTBM, and it is known that the FFTBM-SM judges the code accuracy in a more consistent and unbiased way. However, in some applications, unrealistic results have been obtained. In this study, it was found that accuracy quantification by FFTBM-SM is dependent on the frequency spectrum of the fast Fourier transform of experimental and error signals. The primary objective of this study is to reduce the frequency dependency of FFTBM-SM evaluation. For this, it was proposed to reduce the cut off frequency, which was introduced to cut off spurious contributions, in FFTBM-SM. A method to determine an appropriate cut off frequency was also proposed. The FFTBM-SM with the modified cut off frequency showed a significant improvement of the accuracy quantification

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.

Is Fourier analysis performed by the visual system or by the visual investigator.

Science.gov (United States)

Ochs, A L

1979-01-01

A numerical Fourier transform was made of the pincushion grid illusion and the spectral components orthogonal to the illusory lines were isolated. Their inverse transform creates a picture of the illusion. The spatial-frequency response of cortical, simple receptive field neurons similarly filters the grid. A complete set of these neurons thus approximates a two-dimensional Fourier analyzer. One cannot conclude, however, that the brain actually uses frequency-domain information to interpret visual images.

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)

High resolution integral holography using Fourier ptychographic approach.

Science.gov (United States)

Li, Zhaohui; Zhang, Jianqi; Wang, Xiaorui; Liu, Delian

2014-12-29

An innovative approach is proposed for calculating high resolution computer generated integral holograms by using the Fourier Ptychographic (FP) algorithm. The approach initializes a high resolution complex hologram with a random guess, and then stitches together low resolution multi-view images, synthesized from the elemental images captured by integral imaging (II), to recover the high resolution hologram through an iterative retrieval with FP constrains. This paper begins with an analysis of the principle of hologram synthesis from multi-projections, followed by an accurate determination of the constrains required in the Fourier ptychographic integral-holography (FPIH). Next, the procedure of the approach is described in detail. Finally, optical reconstructions are performed and the results are demonstrated. Theoretical analysis and experiments show that our proposed approach can reconstruct 3D scenes with high resolution.

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.

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...

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

Cigarette smoking and telomere length: A systematic review of 84 studies and meta-analysis.

Science.gov (United States)

Astuti, Yuliana; Wardhana, Ardyan; Watkins, Johnathan; Wulaningsih, Wahyu

2017-10-01

Cigarette smoking is a risk factor for ageing-related disease, but its association with biological ageing, indicated by telomere length, is unclear. We systematically reviewed evidence evaluating association between smoking status and telomere length. Searches were performed in MEDLINE (Ovid) and EMBASE (Ovid) databases, combining variation of keywords "smoking" and "telomere". Data was extracted for study characteristics and estimates for association between smoking and telomere length. Quality of studies was assessed with a risk of bias score, and publication bias was assessed with a funnel plot. I 2 test was used to observe heterogeneity. Meta-analysis was carried out to compare mean difference in telomere length by smoking status, and a dose-response approach was carried out for pack-years of smoking and telomere length. A sensitivity analysis was carried out to examine sources of heterogeneity. A total of 84 studies were included in the review, and 30 among them were included in our meta-analysis. Potential bias was addressed in half of included studies, and there was little evidence of small study bias. Telomere length was shorter among ever smokers compared to never smokers (summary standard mean difference [SMD]: -0.11 (95% CI -0.16 to -0.07)). Similarly, shorter telomere length was found among smokers compared to non-smokers, and among current smokers compared to never or former smokers. Dose-response meta-analysis suggested an inverse trend between pack-years of smoking and telomere length. However, heterogeneity among some analyses was observed. Shorter telomeres among ever smokers compared to those who never smoked may imply mechanisms linking tobacco smoke exposure to ageing-related disease. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

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.

Application of model-based spectral analysis to wind-profiler radar observations

Energy Technology Data Exchange (ETDEWEB)

Boyer, E. [ENS, Cachan (France). LESiR; Petitdidier, M.; Corneil, W. [CETP, Velizy (France); Adnet, C. [THALES Air Dfense, Bagneux (France); Larzabal, P. [ENS, Cachan (France). LESiR; IUT, Cachan (France). CRIIP

2001-08-01

A classical way to reduce a radar's data is to compute the spectrum using FFT and then to identify the different peak contributions. But in case an overlapping between the different echoes (atmospheric echo, clutter, hydrometer echo..) exists, Fourier-like techniques provide poor frequency resolution and then sophisticated peak-identification may not be able to detect the different echoes. In order to improve the number of reduced data and their quality relative to Fourier spectrum analysis, three different methods are presented in this paper and applied to actual data. Their approach consists of predicting the main frequency-components, which avoids the development of very sophisticated peak-identification algorithms. The first method is based on cepstrum properties generally used to determine the shift between two close identical echoes. We will see in this paper that this method cannot provide a better estimate than Fourier-like techniques in an operational use. The second method consists of an autoregressive estimation of the spectrum. Since the tests were promising, this method was applied to reduce the radar data obtained during two thunderstorms. The autoregressive method, which is very simple to implement, improved the Doppler-frequency data reduction relative to the FFT spectrum analysis. The third method exploits a MUSIC algorithm, one of the numerous subspace-based methods, which is well adapted to estimate spectra composed of pure lines. A statistical study of performances of this method is presented, and points out the very good resolution of this estimator in comparison with Fourier-like techniques. Application to actual data confirms the good qualities of this estimator for reducing radar's data. (orig.)

Distributed ISAR Subimage Fusion of Nonuniform Rotating Target Based on Matching Fourier Transform.

Science.gov (United States)

Li, Yuanyuan; Fu, Yaowen; Zhang, Wenpeng

2018-06-04

In real applications, the image quality of the conventional monostatic Inverse Synthetic Aperture Radar (ISAR) for the maneuvering target is subject to the strong fluctuation of Radar Cross Section (RCS), as the target aspect varies enormously. Meanwhile, the maneuvering target introduces nonuniform rotation after translation motion compensation which degrades the imaging performance of the conventional Fourier Transform (FT)-based method in the cross-range dimension. In this paper, a method which combines the distributed ISAR technique and the Matching Fourier Transform (MFT) is proposed to overcome these problems. Firstly, according to the characteristics of the distributed ISAR, the multiple channel echoes of the nonuniform rotation target from different observation angles can be acquired. Then, by applying the MFT to the echo of each channel, the defocused problem of nonuniform rotation target which is inevitable by using the FT-based imaging method can be avoided. Finally, after preprocessing, scaling and rotation of all subimages, the noncoherent fusion image containing all the RCS information in all channels can be obtained. The accumulation coefficients of all subimages are calculated adaptively according to the their image qualities. Simulation and experimental data are used to validate the effectiveness of the proposed approach, and fusion image with improved recognizability can be obtained. Therefore, by using the distributed ISAR technique and MFT, subimages of high-maneuvering target from different observation angles can be obtained. Meanwhile, by employing the adaptive subimage fusion method, the RCS fluctuation can be alleviated and more recognizable final image can be obtained.

Edge-augmented Fourier partial sums with applications to Magnetic Resonance Imaging (MRI)

Science.gov (United States)

Larriva-Latt, Jade; Morrison, Angela; Radgowski, Alison; Tobin, Joseph; Iwen, Mark; Viswanathan, Aditya

2017-08-01

Certain applications such as Magnetic Resonance Imaging (MRI) require the reconstruction of functions from Fourier spectral data. When the underlying functions are piecewise-smooth, standard Fourier approximation methods suffer from the Gibbs phenomenon - with associated oscillatory artifacts in the vicinity of edges and an overall reduced order of convergence in the approximation. This paper proposes an edge-augmented Fourier reconstruction procedure which uses only the first few Fourier coefficients of an underlying piecewise-smooth function to accurately estimate jump information and then incorporate it into a Fourier partial sum approximation. We provide both theoretical and empirical results showing the improved accuracy of the proposed method, as well as comparisons demonstrating superior performance over existing state-of-the-art sparse optimization-based methods.

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)

New Substrate-Guided Method of Predicting Slow Conducting Isthmuses of Ventricular Tachycardia: Preliminary Analysis to the Combined Use of Voltage Limit Adjustment and Fast-Fourier Transform Analysis.

Science.gov (United States)

Kuroki, Kenji; Nogami, Akihiko; Igarashi, Miyako; Masuda, Keita; Kowase, Shinya; Kurosaki, Kenji; Komatsu, Yuki; Naruse, Yoshihisa; Machino, Takeshi; Yamasaki, Hiro; Xu, Dongzhu; Murakoshi, Nobuyuki; Sekiguchi, Yukio; Aonuma, Kazutaka

2018-04-01

Several conducting channels of ventricular tachycardia (VT) can be identified using voltage limit adjustment (VLA) of substrate mapping. However, the sensitivity or specificity to predict a VT isthmus is not high by using VLA alone. This study aimed to evaluate the efficacy of the combined use of VLA and fast-Fourier transform analysis to predict VT isthmuses. VLA and fast-Fourier transform analyses of local ventricular bipolar electrograms during sinus rhythm were performed in 9 postinfarction patients who underwent catheter ablation for a total of 13 monomorphic VTs. Relatively higher voltage areas on an electroanatomical map were defined as high voltage channels (HVCs), and relatively higher fast-Fourier transform areas were defined as high-frequency channels (HFCs). HVCs were classified into full or partial HVCs (the entire or >30% of HVC can be detectable, respectively). Twelve full HVCs were identified in 7 of 9 patients. HFCs were located on 7 of 12 full HVCs. Five VT isthmuses (71%) were included in the 7 full HVC+/HFC+ sites, whereas no VT isthmus was found in the 5 full HVC+/HFC- sites. HFCs were identical to 9 of 16 partial HVCs. Eight VT isthmuses (89%) were included in the 9 partial HVC+/HFC+ sites, whereas no VT isthmus was found in the 7 partial HVC+/HFC- sites. All HVC+/HFC+ sites predicted VT isthmus with a sensitivity of 100% and a specificity of 80%. Combined use of VLA and fast-Fourier transform analysis may be a useful method to detect VT isthmuses. © 2018 American Heart Association, Inc.

Fourier transform infrared and fluorescence spectroscopy for analysis of vegetable oils

Directory of Open Access Journals (Sweden)

Nigri S.

2013-09-01

Full Text Available Fourier transform infrared (FTIR and fluorescence spectroscopy, combined with chemometric approaches have been developed to analysis of extra virgin olive oil adulterated with pomace olive oil. The measurements were made on pure vegetable oils: extra virgin oil, pomace olive oil and that adulterated with varying concentration of pomace olive oil. Today, the application of FTIR spectroscopy has increased in food studied, and particularly has become a powerful analytical tool in the study of edible oils and fats. The spectral regions where the variations were observed chosen for developing models and cross validation was used. The synchronous fluorescence spectrometry takes advantage of the hardware capability to vary both the excitation and emission wavelengths during the analysis with constant wavelength difference is maintained between the two. The region between 300 and 400 nm is attributed to the tocopherols and phenols, the derivatives of vitamin E are associated with the region 400–600 nm and the bands in the region of 600–700 nm are attributed to the chlorophyll and peophytin pigments. The results presented in this study suggest that FTIR and fluorescence may be a useful tool for analysis and detecting adulteration of extra virgin olive oil with pomace oil.

Numerical model of the influence function of deformable mirrors based on Bessel Fourier orthogonal functions

International Nuclear Information System (INIS)

Li Shun; Zhang Sijiong

2014-01-01

A numerical model is presented to simulate the influence function of deformable mirror actuators. The numerical model is formed by Bessel Fourier orthogonal functions, which are constituted of Bessel orthogonal functions and a Fourier basis. A detailed comparison is presented between the new Bessel Fourier model, the Zernike model, the Gaussian influence function and the modified Gaussian influence function. Numerical experiments indicate that the new numerical model is easy to use and more accurate compared with other numerical models. The new numerical model can be used for describing deformable mirror performances and numerical simulations of adaptive optics systems. (research papers)

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.

Alternatives Generation Analysis Long Length Contaminated Equipment Removal System Storage

International Nuclear Information System (INIS)

BOGER, R.M.

1999-01-01

Major pieces of Characterization sampling equipment are currently stored outdoors. This includes the Long Length Contaminated Equipment receiver trailer and transportation trailer. A decision is required to determine the preferred alternative for facilities to store and maintain this equipment. The Long Length Contaminated Equipment Removal System (LLCERS) consists of many tools, mechanisms, and controllers currently stored in various locations. Much of this equipment should be protected from the elements while being stored. Some of the LLCERS equipment should be protected with some kind of roof cover. This decision analysis is to determine the best alternative for weather protection for the large equipment requiring a cover. Additional details are included in Sections 2.0 and 5.0. Key assumptions used in this analysis are detailed in Section 3.2

A novel ECG data compression method based on adaptive Fourier decomposition

Science.gov (United States)

Tan, Chunyu; Zhang, Liming

2017-12-01

This paper presents a novel electrocardiogram (ECG) compression method based on adaptive Fourier decomposition (AFD). AFD is a newly developed signal decomposition approach, which can decompose a signal with fast convergence, and hence reconstruct ECG signals with high fidelity. Unlike most of the high performance algorithms, our method does not make use of any preprocessing operation before compression. Huffman coding is employed for further compression. Validated with 48 ECG recordings of MIT-BIH arrhythmia database, the proposed method achieves the compression ratio (CR) of 35.53 and the percentage root mean square difference (PRD) of 1.47% on average with N = 8 decomposition times and a robust PRD-CR relationship. The results demonstrate that the proposed method has a good performance compared with the state-of-the-art ECG compressors.

Local structure information by EXAFS analysis using two algorithms for Fourier transform calculation

International Nuclear Information System (INIS)

Aldea, N; Pintea, S; Rednic, V; Matei, F; Hu Tiandou; Xie Yaning

2009-01-01

The present work is a comparison study between different algorithms of Fourier transform for obtaining very accurate local structure results using Extended X-ray Absorption Fine Structure technique. In this paper we focus on the local structural characteristics of supported nickel catalysts and Fe 3 O 4 core-shell nanocomposites. The radial distribution function could be efficiently calculated by the fast Fourier transform when the coordination shells are well separated while the Filon quadrature gave remarkable results for close-shell coordination.

Processing of pulse oximeter data using discrete wavelet analysis.

Science.gov (United States)

Lee, Seungjoon; Ibey, Bennett L; Xu, Weijian; Wilson, Mark A; Ericson, M Nance; Coté, Gerard L

2005-07-01

A wavelet-based signal processing technique was employed to improve an implantable blood perfusion monitoring system. Data was acquired from both in vitro and in vivo sources: a perfusion model and the proximal jejunum of an adult pig. Results showed that wavelet analysis could isolate perfusion signals from raw, periodic, in vitro data as well as fast Fourier transform (FFT) methods. However, for the quasi-periodic in vivo data segments, wavelet analysis provided more consistent results than the FFT analysis for data segments of 50, 10, and 5 s in length. Wavelet analysis has thus been shown to require less data points for quasi-periodic data than FFT analysis making it a good choice for an indwelling perfusion monitor where power consumption and reaction time are paramount.

Digital double random amplitude image encryption method based on the symmetry property of the parametric discrete Fourier transform

Science.gov (United States)

Bekkouche, Toufik; Bouguezel, Saad

2018-03-01

We propose a real-to-real image encryption method. It is a double random amplitude encryption method based on the parametric discrete Fourier transform coupled with chaotic maps to perform the scrambling. The main idea behind this method is the introduction of a complex-to-real conversion by exploiting the inherent symmetry property of the transform in the case of real-valued sequences. This conversion allows the encrypted image to be real-valued instead of being a complex-valued image as in all existing double random phase encryption methods. The advantage is to store or transmit only one image instead of two images (real and imaginary parts). Computer simulation results and comparisons with the existing double random amplitude encryption methods are provided for peak signal-to-noise ratio, correlation coefficient, histogram analysis, and key sensitivity.

Conversion of a DWDM signal to a single Nyquist channel based on a complete optical Fourier transformation

DEFF Research Database (Denmark)

Guan, Pengyu; Røge, Kasper Meldgaard; Mulvad, Hans Christian Hansen

2014-01-01

We propose a DWDM-to-Nyquist channel conversion scheme based on complete Optical Fourier Transformation and optical Nyquist filtering. We demonstrate conversion from 50-GHz-grid 16×10 Gbit/s DPSK DWDM to a 160-Gbit/s Nyquist channel (0.9 symbol/s/Hz spectral efficiency) with 1.4 dB power penalty....

Profile inversion of principal diffusivities through the use of a spatially modulated heating and a Fourier analysis; Inversion des profils des diffusivites principales par l'application d'un chauffage spatialement module et une analyse dans le domaine de Fourier

Energy Technology Data Exchange (ETDEWEB)

Krapez, J.C.; Spagnolo, L. [Politechnique di Bari (Italy); Friess, M. [Deutsches Luft- und Raumfahrtzentrum eV (DLR), Stuttgart (Germany); Maier, H.P. [Stuttgart Univ., MPA (Germany); Neuer, G. [Institut fur Kernenergetik und Energiesysteme, Universitat Stuttgart (Germany)

2003-07-01

The through-thickness thermal diffusivity can be evaluated by the classical flash method. If an homogeneous and extended source is used to irradiate the surface and a thermographic camera is used to monitor the temperature evolution of the opposite side, a map of the through-thickness thermal diffusivity can be obtained in a single experiment and without any contact with the sample under inspection. In order to measure the in-plane thermal diffusivity of a plate-like sample or in one of the principal directions of its plane, a thermal gradient across the plane of the material has to be settled. The ratio of the Fourier transform of temperature at two different spatial frequencies is an exponential function of time multiplied by the diffusivity in the considered principal direction. This can be used to evaluate the diffusivity in an homogenous material. In order to maximize the signal-to-noise ratio, it is better if heat is absorbed over a series of periodic parallel strips (grid flash method). When the material presents a transverse gradient of conductivity, we propose, as a first approach, to perform the Fourier analysis over a sliding window corresponding to one period of the grid pattern. This method allowed us to quantify in situ the diffusivity decrease in a tensile composite sample due to the stress-induced density increase of transverse microcracks. We finally analysed a more rigorous method for transverse conductivity profile inversion. It is based on a perturbation method. The analytical expression of the 'transfer function' between the Fourier transform of the temperature contrast and the Fourier transform of conductivity was established. We validated the proposed inverse technique on simulated and noise-corrupted thermograms. The approach is robust and the simulated profiles are very well resolved. (authors)

Differentiation of frog fats from vegetable and marine oils by Fourier Transform Infrared Spectroscopy and chemometric analysis

Directory of Open Access Journals (Sweden)

A. N. Nina Naquiah

2015-01-01

Full Text Available The agro-based production and consumption of frogs coupled with world-wide trading have been increased in the recent years giving rise to the risk of frog fat adulteration in expensive vegetable and marine oils. For the first time, we profiled here frog fats using Fourier Transform Infrared (FTIR Spectroscopy coupled with multivariate principal component analysis (PCA. The comparison of the FTIR spectral absorbance intensities demonstrated linkage of frog fats to other edible fats and oils. Three commercially available marine oils and three vegetables oils were studied with frog fats and clear pattern of clusters with distinctive identifiable features were obtained through PCA modeling. PCA analysis identified 2922.21 cm-1, 2852.88 cm-1, 1745.45 cm-1, 1158.29 cm-1 and 721.51 cm-1 FTIR-frequencies as the most discriminating variables influencing the group separation into different clusters. This fundamental study has clear implications in the identification of frog fat from its marine and vegetable counterparts for the potential detection of frog fat adulteration in various fat and oils.

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

A new BP Fourier algorithm and its application in English teaching evaluation

Science.gov (United States)

Pei, Xuehui; Pei, Guixin

2017-08-01

BP neural network algorithm has wide adaptability and accuracy when used in complicated system evaluation, but its calculation defects such as slow convergence have limited its practical application. The paper tries to speed up the calculation convergence of BP neural network algorithm with Fourier basis functions and presents a new BP Fourier algorithm for complicated system evaluation. First, shortages and working principle of BP algorithm are analyzed for subsequent targeted improvement; Second, the presented BP Fourier algorithm adopts Fourier basis functions to simplify calculation structure, designs new calculation transfer function between input and output layers, and conducts theoretical analysis to prove the efficiency of the presented algorithm; Finally, the presented algorithm is used in evaluating university English teaching and the application results shows that the presented BP Fourier algorithm has better performance in calculation efficiency and evaluation accuracy and can be used in evaluating complicated system practically.

ENHANCING NETWORK SECURITY USING 'LEARNING-FROM-SIGNALS' AND FRACTIONAL FOURIER TRANSFORM BASED RF-DNA FINGERPRINTS

Energy Technology Data Exchange (ETDEWEB)

Buckner, Mark A [ORNL; Bobrek, Miljko [ORNL; Farquhar, Ethan [ORNL; Harmer, Paul K [Air Force Institute of Technology; Temple, Michael A [Air Force Institute of Technology

2011-01-01

Wireless Access Points (WAP) remain one of the top 10 network security threats. This research is part of an effort to develop a physical (PHY) layer aware Radio Frequency (RF) air monitoring system with multi-factor authentication to provide a first-line of defense for network security--stopping attackers before they can gain access to critical infrastructure networks through vulnerable WAPs. This paper presents early results on the identification of OFDM-based 802.11a WiFi devices using RF Distinct Native Attribute (RF-DNA) fingerprints produced by the Fractional Fourier Transform (FRFT). These fingerprints are input to a "Learning from Signals" (LFS) classifier which uses hybrid Differential Evolution/Conjugate Gradient (DECG) optimization to determine the optimal features for a low-rank model to be used for future predictions. Results are presented for devices under the most challenging conditions of intra-manufacturer classification, i.e., same-manufacturer, same-model, differing only in serial number. The results of Fractional Fourier Domain (FRFD) RF-DNA fingerprints demonstrate significant improvement over results based on Time Domain (TD), Spectral Domain (SD) and even Wavelet Domain (WD) fingerprints.

Criteria for confirming sequence periodicity identified by Fourier transform analysis: application to GCR2, a candidate plant GPCR?

Science.gov (United States)

Illingworth, Christopher J R; Parkes, Kevin E; Snell, Christopher R; Mullineaux, Philip M; Reynolds, Christopher A

2008-03-01

Methods to determine periodicity in protein sequences are useful for inferring function. Fourier transformation is one approach but care is required to ensure the periodicity is genuine. Here we have shown that empirically-derived statistical tables can be used as a measure of significance. Genuine protein sequences data rather than randomly generated sequences were used as the statistical backdrop. The method has been applied to G-protein coupled receptor (GPCR) sequences, by Fourier transformation of hydrophobicity values, codon frequencies and the extent of over-representation of codon pairs; the latter being related to translational step times. Genuine periodicity was observed in the hydrophobicity whereas the apparent periodicity (as inferred from previously reported measures) in the translation step times was not validated statistically. GCR2 has recently been proposed as the plant GPCR receptor for the hormone abscisic acid. It has homology to the Lanthionine synthetase C-like family of proteins, an observation confirmed by fold recognition. Application of the Fourier transform algorithm to the GCR2 family revealed strongly predicted seven fold periodicity in hydrophobicity, suggesting why GCR2 has been reported to be a GPCR, despite negative indications in most transmembrane prediction algorithms. The underlying multiple sequence alignment, also required for the Fourier transform analysis of periodicity, indicated that the hydrophobic regions around the 7 GXXG motifs commence near the C-terminal end of each of the 7 inner helices of the alpha-toroid and continue to the N-terminal region of the helix. The results clearly explain why GCR2 has been understandably but erroneously predicted to be a GPCR.

Fourier rebinning and consistency equations for time-of-flight PET planograms

International Nuclear Information System (INIS)

Li, Yusheng; Matej, Samuel; Metzler, Scott D; Defrise, Michel

2016-01-01

Due to the unique geometry, dual-panel PET scanners have many advantages in dedicated breast imaging and on-board imaging applications since the compact scanners can be combined with other imaging and treatment modalities. The major challenges of dual-panel PET imaging are the limited-angle problem and data truncation, which can cause artifacts due to incomplete data sampling. The time-of-flight (TOF) information can be a promising solution to reduce these artifacts. The TOF planogram is the native data format for dual-panel TOF PET scanners, and the non-TOF planogram is the 3D extension of linogram. The TOF planograms is five-dimensional while the objects are three-dimensional, and there are two degrees of redundancy. In this paper, we derive consistency equations and Fourier-based rebinning algorithms to provide a complete understanding of the rich structure of the fully 3D TOF planograms. We first derive two consistency equations and John’s equation for 3D TOF planograms. By taking the Fourier transforms, we obtain two Fourier consistency equations (FCEs) and the Fourier–John equation (FJE), which are the duals of the consistency equations and John’s equation, respectively. We then solve the FCEs and FJE using the method of characteristics. The two degrees of entangled redundancy of the 3D TOF data can be explicitly elicited and exploited by the solutions along the characteristic curves. As the special cases of the general solutions, we obtain Fourier rebinning and consistency equations (FORCEs), and thus we obtain a complete scheme to convert among different types of PET planograms: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF planograms. The FORCEs can be used as Fourier-based rebinning algorithms for TOF-PET data reduction, inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. As a byproduct, we show the two consistency equations are necessary and sufficient for 3D TOF planograms. Finally, we give

Hybrid Fourier pseudospectral/discontinuous Galerkin time-domain method for arbitrary boundary conditions

NARCIS (Netherlands)

Pagan Munoz, R.; Hornikx, M.C.J.

The wave-based Fourier Pseudospectral time-domain (Fourier-PSTD) method was shown to be an effective way of modeling outdoor acoustic propagation problems as described by the linearized Euler equations (LEE), but is limited to real-valued frequency independent boundary conditions and predominantly

Impact of assimilation window length on diurnal features in a Mars atmospheric analysis

Directory of Open Access Journals (Sweden)

Yongjing Zhao

2015-05-01

Full Text Available Effective simulation of diurnal variability is an important aspect of many geophysical data assimilation systems. For the Martian atmosphere, thermal tides are particularly prominent and contribute much to the Martian atmospheric circulation, dynamics and dust transport. To study the Mars diurnal variability and Mars thermal tides, the Geophysical Fluid Dynamics Laboratory Mars Global Climate Model with the 4D-local ensemble transform Kalman filter (4D-LETKF is used to perform an analysis assimilating spacecraft temperature retrievals. We find that the use of a ‘traditional’ 6-hr assimilation cycle induces spurious forcing of a resonantly enhanced semi-diurnal Kelvin waves represented in both surface pressure and mid-level temperature by forming a wave 4 pattern in the diurnal averaged analysis increment that acts as a ‘topographic’ stationary forcing. Different assimilation window lengths in the 4D-LETKF are introduced to remove the artificially induced resonance. It is found that short assimilation window lengths not only remove the spurious resonance, but also push the migrating semi-diurnal temperature variation at 50 Pa closer to the estimated ‘true’ tides even in the absence of a radiatively active water ice cloud parameterisation. In order to compare the performance of different assimilation window lengths, short-term to mid-range forecasts based on the hour 00 and 12 assimilation are evaluated and compared. Results show that during Northern Hemisphere summer, it is not the assimilation window length, but the radiatively active water ice clouds that influence the model prediction. A ‘diurnal bias correction’ that includes bias correction fields dependent on the local time is shown to effectively reduce the forecast root mean square differences between forecasts and observations, compensate for the absence of water ice cloud parameterisation and enhance Martian atmosphere prediction. The implications of these results for

Shock-wave structure based on the Navier-Stokes-Fourier equations

Science.gov (United States)

Uribe, F. J.; Velasco, R. M.

2018-04-01

We use the Navier-Stokes-Fourier constitutive equations to study plane shock waves in dilute gases. It is shown that the experimental information on the normalized density profiles can be fit by using the so-called soft sphere model, in which the viscosity and thermal conductivity are proportional to a power of the temperature.

Disentangling the effects of forage, social rank, and risk on movement autocorrelation of elephants using Fourier and wavelet analyses.

Science.gov (United States)

Wittemyer, George; Polansky, Leo; Douglas-Hamilton, Iain; Getz, Wayne M

2008-12-09

The internal state of an individual-as it relates to thirst, hunger, fear, or reproductive drive-can be inferred by referencing points on its movement path to external environmental and sociological variables. Using time-series approaches to characterize autocorrelative properties of step-length movements collated every 3 h for seven free-ranging African elephants, we examined the influence of social rank, predation risk, and seasonal variation in resource abundance on periodic properties of movement. The frequency domain methods of Fourier and wavelet analyses provide compact summaries of temporal autocorrelation and show both strong diurnal and seasonal based periodicities in the step-length time series. This autocorrelation is weaker during the wet season, indicating random movements are more common when ecological conditions are good. Periodograms of socially dominant individuals are consistent across seasons, whereas subordinate individuals show distinct differences diverging from that of dominants during the dry season. We link temporally localized statistical properties of movement to landscape features and find that diurnal movement correlation is more common within protected wildlife areas, and multiday movement correlations found among lower ranked individuals are typically outside of protected areas where predation risks are greatest. A frequency-related spatial analysis of movement-step lengths reveal that rest cycles related to the spatial distribution of critical resources (i.e., forage and water) are responsible for creating the observed patterns. Our approach generates unique information regarding the spatial-temporal interplay between environmental and individual characteristics, providing an original approach for understanding the movement ecology of individual animals and the spatial organization of animal populations.

Processing of gamma-ray spectra employing a Fourier deconvolver for the analysis of complex spectra

International Nuclear Information System (INIS)

Madan, V.K.; Rattan, S.S.

1996-01-01

Processing of a nuclear spectrum e.g. gamma ray spectrum is concerned with the estimation of energies and intensities of radiation. The processing involves filtering, peak detection and its significance, baseline delineation, the qualitative and the quantitative analysis of singlets and multiplets present in the spectrum. The methodology for the analysis of singlets is well established. However, the analysis of multiplets provides a challenge and is a extremely difficult problem. This report incorporates a Fourier deconvolver for the quantitative analysis of doublets separated by more than a full width at half maximum. The method is easy to implement. The report discusses the methodology, mathematical analysis, and the results obtained by analyzing both synthetic and observed spectra. A computer program, developed for the analysis of a nuclear spectrum, was verified by analyzing a 152 Eu gamma ray spectrum. The proposed technique compared favourably with SAMPO and MDFT method. (author). 16 refs., 3 tabs

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

Vector Radix 2 × 2 Sliding Fast Fourier Transform

Directory of Open Access Journals (Sweden)

Keun-Yung Byun

2016-01-01

Full Text Available The two-dimensional (2D discrete Fourier transform (DFT in the sliding window scenario has been successfully used for numerous applications requiring consecutive spectrum analysis of input signals. However, the results of conventional sliding DFT algorithms are potentially unstable because of the accumulated numerical errors caused by recursive strategy. In this letter, a stable 2D sliding fast Fourier transform (FFT algorithm based on the vector radix (VR 2 × 2 FFT is presented. In the VR-2 × 2 FFT algorithm, each 2D DFT bin is hierarchically decomposed into four sub-DFT bins until the size of the sub-DFT bins is reduced to 2 × 2; the output DFT bins are calculated using the linear combination of the sub-DFT bins. Because the sub-DFT bins for the overlapped input signals between the previous and current window are the same, the proposed algorithm reduces the computational complexity of the VR-2 × 2 FFT algorithm by reusing previously calculated sub-DFT bins in the sliding window scenario. Moreover, because the resultant DFT bins are identical to those of the VR-2 × 2 FFT algorithm, numerical errors do not arise; therefore, unconditional stability is guaranteed. Theoretical analysis shows that the proposed algorithm has the lowest computational requirements among the existing stable sliding DFT algorithms.

XRLINE, a program to evaluate the crystallite size of supported metal catalysts by single X-ray profile Fourier analysis

International Nuclear Information System (INIS)

Aldea, N.; Indrea, E.

1990-01-01

The computer program presented is based on the Fourier analysis of a singel X-ray diffraction profile. An X-ray diffraction method is presented which is capable of determining the average particle size, microstrain, stacking fault probability as well as the particle size distribution function in crystalline materials. The main numerical methods used are: (i) Smoothing and interpolation by 3rd-order piecewise polynomial functions or by cubic splines with the least squares method; (ii) numerical integration by successive five points formulae and numerical derivative by cubic splines with the least squares method; (iii) estimation of parameters by the weighted least squares method. The results for supported platinum catalysts used in the H/D isotopic exchange reaction are illustrated. (orig.)

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…

FREQUENCY COMPONENT EXTRACTION OF HEARTBEAT CUES WITH SHORT TIME FOURIER TRANSFORM (STFT

Directory of Open Access Journals (Sweden)

Sumarna Sumarna

2017-01-01

  Electro-acoustic human heartbeat detector have been made with the main parts : (a stetoscope (piece chest, (b mic condenser, (c transistor amplifier, and (d cues analysis program with MATLAB. The frequency components that contained in heartbeat. cues have also been extracted with Short Time Fourier Transform (STFT from 9 volunteers. The results of the analysis showed that heart rate appeared in every cue frequency spectrum with their harmony. The steps of the research were including detector instrument design, test and instrument repair, cues heartbeat recording with Sound Forge 10 program and stored in wav file ; cues breaking at the start and the end, and extraction/cues analysis using MATLAB. The MATLAB program included filter (bandpass filter with bandwidth between 0.01 – 110 Hz, cues breaking with hamming window and every part was calculated using Fourier Transform (STFT mechanism and the result were shown in frequency spectrum graph.   Keywords: frequency components extraction, heartbeat cues, Short Time Fourier Transform

Analysis of ureteral length in adult cadavers

Directory of Open Access Journals (Sweden)

Hugo F. F. Novaes

2013-04-01

Full Text Available Introduction In some occasions, correlations between human structures can help planning surgical intra-abdominal interventions. The previous determination of ureteral length helps pre-operatory planning of surgeries, reduces costs of auxiliary exams, the correct choice of double-J catheter with low morbidity and fewer symptoms, and an adequate adhesion to treatment. Objective To evaluate ureteral length in adult cadavers and to analyze its correlation with anthropometric measures. Materials and Methods: From April 2009 to January 2012 we determined ureteral length of adult cadavers submitted to necropsy and obtained the following measures: height, distance from shoulder to wrist, elbow-wrist, xiphoid appendix-umbilicus, umbilicus-pubis, xiphoid appendix-pubis and between iliac spines. We analyzed the correlations between ureteral length and those anthropometric measures. Results We dissected 115 ureters from 115 adult corpses from April 2009 to January 2012. Median ureteral length didn't vary between sexes or according to height. It was observed no correlation among ureteral length and all considered anthropometric measures in all analyzed subgroups and in general population. There were no significant differences between right and left ureteral measures. Conclusions There is no difference of ureteral length in relation to height or gender (male or female. There is no significant correlation among ureteral length and the considered anthropometric measures.

Sample preparation and scanning protocol for computerised analysis of root length and diameter

NARCIS (Netherlands)

Bouma, T.J.; Nielsen, K.F.; Koutstaal, B.P.

2000-01-01

Root length and diameter distribution are important characteristics to be considered when describing and comparing root systems. Root length and root-diameter distribution may be obtained in two ways: by microscopical measurements, which are laborious, or by computerised analysis, which is fast but

Study of lattice strain evolution during biaxial deformation of stainless steel using a finite element and fast Fourier transform based multi-scale approach

International Nuclear Information System (INIS)

Upadhyay, M.V.; Van Petegem, S.; Panzner, T.; Lebensohn, R.A.; Van Swygenhoven, H.

2016-01-01

A multi-scale elastic-plastic finite element and fast Fourier transform based approach is proposed to study lattice strain evolution during uniaxial and biaxial loading of stainless steel cruciform shaped samples. At the macroscale, finite element simulations capture the complex coupling between applied forces in the arms and gauge stresses induced by the cruciform geometry. The predicted gauge stresses are used as macroscopic boundary conditions to drive a mesoscale elasto-viscoplastic fast Fourier transform model, from which lattice strains are calculated for particular grain families. The calculated lattice strain evolution matches well with experimental values from in-situ neutron diffraction measurements and demonstrates that the spread in lattice strain evolution between different grain families decreases with increasing biaxial stress ratio. During equibiaxial loading, the model reveals that the lattice strain evolution in all grain families, and not just the 311 grain family, is representative of the polycrystalline response. A detailed quantitative analysis of the 200 and 220 grain family reveals that the contribution of elastic and plastic anisotropy to the lattice strain evolution significantly depends on the applied stress ratio.

Typing of Human Mycobacterium avium Isolates in Italy by IS1245-Based Restriction Fragment Length Polymorphism Analysis

Science.gov (United States)

Lari, Nicoletta; Cavallini, Michela; Rindi, Laura; Iona, Elisabetta; Fattorini, Lanfranco; Garzelli, Carlo

1998-01-01

All but 2 of 63 Mycobacterium avium isolates from distinct geographic areas of Italy exhibited markedly polymorphic, multibanded IS1245 restriction fragment length polymorphism (RFLP) patterns; 2 isolates showed the low-number banding pattern typical of bird isolates. By computer analysis, 41 distinct IS1245 patterns and 10 clusters of essentially identical strains were detected; 40% of the 63 isolates showed genetic relatedness, suggesting the existence of a predominant AIDS-associated IS1245 RFLP pattern. PMID:9817900

An introduction to non-harmonic Fourier series

CERN Document Server

Young, Robert M

2001-01-01

An Introduction to Non-Harmonic Fourier Series, Revised Edition is an update of a widely known and highly respected classic textbook.Throughout the book, material has also been added on recent developments, including stability theory, the frame radius, and applications to signal analysis and the control of partial differential equations.

Length scale of secondary stresses in fracture and fatigue

International Nuclear Information System (INIS)

Dong, P.

2008-01-01

In an attempt to provide a consistent framework for the analysis and treatment of secondary stresses associated with welding and thermal loading in the context of fracture mechanics, this paper starts with an effective stress characterization procedure by introducing a length-scale concept. With it, a traction-based stress separation procedure is then presented to provide a consistent characterization of stresses from various sources based on their length scale. Their relative contributions to fracture driving force are then quantified in terms of their characteristic length scales. Special attention is given to the implications of the length-scale argument on both analysis and treatment of welding residual stresses in fracture assessment. A series of examples is provided to demonstrate how the present developments can be applied for treating not only secondary stresses but also externally applied stresses, as well as their combined effects on the structural integrity of engineering components

Statistical length of DNA based on AFM image measured by a computer

International Nuclear Information System (INIS)

Chen Xinqing; Qiu Xijun; Zhang Yi; Hu Jun; Wu Shiying; Huang Yibo; Ai Xiaobai; Li Minqian

2001-01-01

Taking advantage of image processing technology, the contour length of DNA molecule was measured automatically by a computer. Based on the AFM image of DNA, the topography of DNA was simulated into a curve. Then the DNA length was measured automatically by inserting mode. It was shown that the experimental length of a naturally deposited DNA (180.4 +- 16.4 nm) was well consistent with the theoretical length (185.0 nm). Comparing to other methods, the present approach had advantages of precision and automatism. The stretched DNA was also measured. It present approach had advantages of precision and automatism. The stretched DNA was also measured. It was shown that the experimental length (343.6 +- 20.7 nm) was much longer than the theoretical length (307.0 nm). This result indicated that the stretching process had a distinct effect on the DNA length. However, the method provided here avoided the DNA-stretching effect

Efficient pricing of Asian options under Lévy processes based on Fourier cosine expansions Part I : European-style products

NARCIS (Netherlands)

Zhang, B.; Oosterlee, C.W.

2011-01-01

We propose an efficient pricing method for arithmetic, and geometric, Asian options under Levy processes, based on Fourier cosine expansions and Clenshaw–Curtis quadrature. The pricing method is developed for both European–style and American–style Asian options, and for discretely and continuously

Evaluation of clay hybrid nanocomposites of different chain length as reinforcing agent for natural and synthetic rubbers

International Nuclear Information System (INIS)

Yehia, A.A.; Akelah, A.M.; Rehab, A.; El-Sabbagh, S.H.; El Nashar, D.E.; Koriem, A.A.

2012-01-01

Highlights: → The modified organo-clay (MMT-ATBN) markedly reinforce natural and synthetic rubbers. → The reinforcing efficiency of the organo-clay is much higher than HAF carbon black. → The reinforcing efficiency of MMT modified with different alkylamines greatly depend on the chain length. → The good compatibility of modified organo-clay with NBR can be attributed to the chemical nature. -- Abstract: Polymer nanocomposites are one of the highly discussed research topics in recent time. It has been reported in the present paper the preparation and the properties of different nanoclays based on sodium montmorillonite (bentonite) and some organic amines of varying chain lengths (dodecylamine, hexadecylamine and octadecylamine) beside amine-terminated butadiene-acrylonitrile copolymer (ATBN). The hybrid clays have been characterized with the help of Fourier Transform Infrared spectroscopy (FTIR). Transmission electron microscopy (TEM), Scanning electron microscopy (SEM), Wide angle X-ray diffractions (WXRD), and Thermogravimetric analysis (TGA). X-ray results showed that the intergallery distance of the clay is increased as a result of the intercalation of the amines and ATBN. The nanocomposite clays were incorporated in natural and synthetic rubbers (NR, SBR and NBR). The physico-mechanical properties are greatly improved with loading low concentrations of the nanocomposite clays compared with carbon black.