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

Directory of Open Access Journals (Sweden)

Ludwig Kohaupt

2015-12-01

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

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

Science.gov (United States)

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

2015-03-01

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

Accounting for the Spatial Observation Window in the 2-D Fourier Transform Analysis of Shear Wave Attenuation.

Science.gov (United States)

Rouze, Ned C; Deng, Yufeng; Palmeri, Mark L; Nightingale, Kathryn R

2017-10-01

Recent measurements of shear wave propagation in viscoelastic materials have been analyzed by constructing the 2-D Fourier transform (2DFT) of the shear wave signal and measuring the phase velocity c(ω) and attenuation α(ω) from the peak location and full width at half-maximum (FWHM) of the 2DFT signal at discrete frequencies. However, when the shear wave is observed over a finite spatial range, the 2DFT signal is a convolution of the true signal and the observation window, and measurements using the FWHM can yield biased results. In this study, we describe a method to account for the size of the spatial observation window using a model of the 2DFT signal and a non-linear, least-squares fitting procedure to determine c(ω) and α(ω). Results from the analysis of finite-element simulation data agree with c(ω) and α(ω) calculated from the material parameters used in the simulation. Results obtained in a viscoelastic phantom indicate that the measured attenuation is independent of the observation window and agree with measurements of c(ω) and α(ω) obtained using the previously described progressive phase and exponential decay analysis. Copyright © 2017 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

The short time Fourier transform and local signals

Science.gov (United States)

Okumura, Shuhei

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

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.

The quantum state vector in phase space and Gabor's windowed Fourier transform

International Nuclear Information System (INIS)

Bracken, A J; Watson, P

2010-01-01

Representations of quantum state vectors by complex phase space amplitudes, complementing the description of the density operator by the Wigner function, have been defined by applying the Weyl-Wigner transform to dyadic operators, linear in the state vector and anti-linear in a fixed 'window state vector'. Here aspects of this construction are explored, and a connection is established with Gabor's 'windowed Fourier transform'. The amplitudes that arise for simple quantum states from various choices of windows are presented as illustrations. Generalized Bargmann representations of the state vector appear as special cases, associated with Gaussian windows. For every choice of window, amplitudes lie in a corresponding linear subspace of square-integrable functions on phase space. A generalized Born interpretation of amplitudes is described, with both the Wigner function and a generalized Husimi function appearing as quantities linear in an amplitude and anti-linear in its complex conjugate. Schroedinger's time-dependent and time-independent equations are represented on phase space amplitudes, and their solutions described in simple cases.

Time dependent and asymptotic neutron number probability distribution calculation using discrete Fourier transform

International Nuclear Information System (INIS)

Humbert, Ph.

2005-01-01

In this paper we consider the probability distribution of neutrons in a multiplying assembly. The problem is studied using a space independent one group neutron point reactor model without delayed neutrons. We recall the generating function methodology and analytical results obtained by G.I. Bell when the c 2 approximation is used and we present numerical solutions in the general case, without this approximation. The neutron source induced distribution is calculated using the single initial neutron distribution which satisfies a master (Kolmogorov backward) equation. This equation is solved using the generating function method. The generating function satisfies a differential equation and the probability distribution is derived by inversion of the generating function. Numerical results are obtained using the same methodology where the generating function is the Fourier transform of the probability distribution. Discrete Fourier transforms are used to calculate the discrete time dependent distributions and continuous Fourier transforms are used to calculate the asymptotic continuous probability distributions. Numerical applications are presented to illustrate the method. (author)

The Pegg–Barnett phase operator and the discrete Fourier transform

International Nuclear Information System (INIS)

Perez-Leija, Armando; Szameit, Alexander; Andrade-Morales, Luis A; Soto-Eguibar, Francisco; Moya-Cessa, Héctor M

2016-01-01

In quantum mechanics the position and momentum operators are related to each other via the Fourier transform. In the same way, here we show that the so-called Pegg–Barnett phase operator can be obtained by the application of the discrete Fourier transform to the number operators defined in a finite-dimensional Hilbert space. Furthermore, we show that the structure of the London–Susskind–Glogower phase operator, whose natural logarithm gives rise to the Pegg–Barnett phase operator, is contained in the Hamiltonian of circular waveguide arrays. Our results may find applications in the development of new finite-dimensional photonic systems with interesting phase-dependent properties. (invited comment)

The discrete Fourier transform theory, algorithms and applications

CERN Document Server

Sundaraajan, D

2001-01-01

This authoritative book provides comprehensive coverage of practical Fourier analysis. It develops the concepts right from the basics and gradually guides the reader to the advanced topics. It presents the latest and practically efficient DFT algorithms, as well as the computation of discrete cosine and Walsh-Hadamard transforms. The large number of visual aids such as figures, flow graphs and flow charts makes the mathematical topic easy to understand. In addition, the numerous examples and the set of C-language programs (a supplement to the book) help greatly in understanding the theory and

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.

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....

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.

The Fourier U(2 Group and Separation of Discrete Variables

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Kurt Bernardo Wolf

2011-06-01

Full Text Available The linear canonical transformations of geometric optics on two-dimensional screens form the group Sp(4,R, whose maximal compact subgroup is the Fourier group U(2_F; this includes isotropic and anisotropic Fourier transforms, screen rotations and gyrations in the phase space of ray positions and optical momenta. Deforming classical optics into a Hamiltonian system whose positions and momenta range over a finite set of values, leads us to the finite oscillator model, which is ruled by the Lie algebra so(4. Two distinct subalgebra chains are used to model arrays of N^2 points placed along Cartesian or polar (radius and angle coordinates, thus realizing one case of separation in two discrete coordinates. The N^2-vectors in this space are digital (pixellated images on either of these two grids, related by a unitary transformation. Here we examine the unitary action of the analogue Fourier group on such images, whose rotations are particularly visible.

3-D discrete analytical ridgelet transform.

Science.gov (United States)

Helbert, David; Carré, Philippe; Andres, Eric

2006-12-01

In this paper, we propose an implementation of the 3-D Ridgelet transform: the 3-D discrete analytical Ridgelet transform (3-D DART). This transform uses the Fourier strategy for the computation of the associated 3-D discrete Radon transform. The innovative step is the definition of a discrete 3-D transform with the discrete analytical geometry theory by the construction of 3-D discrete analytical lines in the Fourier domain. We propose two types of 3-D discrete lines: 3-D discrete radial lines going through the origin defined from their orthogonal projections and 3-D planes covered with 2-D discrete line segments. These discrete analytical lines have a parameter called arithmetical thickness, allowing us to define a 3-D DART adapted to a specific application. Indeed, the 3-D DART representation is not orthogonal, It is associated with a flexible redundancy factor. The 3-D DART has a very simple forward/inverse algorithm that provides an exact reconstruction without any iterative method. In order to illustrate the potentiality of this new discrete transform, we apply the 3-D DART and its extension to the Local-DART (with smooth windowing) to the denoising of 3-D image and color video. These experimental results show that the simple thresholding of the 3-D DART coefficients is efficient.

Discrete quantum Fourier transform in coupled semiconductor double quantum dot molecules

International Nuclear Information System (INIS)

Dong Ping; Yang Ming; Cao Zhuoliang

2008-01-01

In this Letter, we present a physical scheme for implementing the discrete quantum Fourier transform in a coupled semiconductor double quantum dot system. The main controlled-R gate operation can be decomposed into many simple and feasible unitary transformations. The current scheme would be a useful step towards the realization of complex quantum algorithms in the quantum dot system

Mechanical model for steel frames with discretely connected precast concrete infill panels with window openings

NARCIS (Netherlands)

Teeuwen, P.A.; Kleinman, C.S.; Snijder, H.H.

2012-01-01

This paper presents a mechanical model for a structure comprising of steel frames with discretely connected precast concrete infill panels having window openings, termed semi-integral infilled frames. The discrete panel-to-frame connections are realized by structural bolts acting under compression.

Discrete Fourier Transform in a Complex Vector Space

Science.gov (United States)

Dean, Bruce H. (Inventor)

2015-01-01

An image-based phase retrieval technique has been developed that can be used on board a space based iterative transformation system. Image-based wavefront sensing is computationally demanding due to the floating-point nature of the process. The discrete Fourier transform (DFT) calculation is presented in "diagonal" form. By diagonal we mean that a transformation of basis is introduced by an application of the similarity transform of linear algebra. The current method exploits the diagonal structure of the DFT in a special way, particularly when parts of the calculation do not have to be repeated at each iteration to converge to an acceptable solution in order to focus an image.

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.

A novel method for computation of the discrete Fourier transform over characteristic two finite field of even extension degree

OpenAIRE

Fedorenko, Sergei V.

2011-01-01

A novel method for computation of the discrete Fourier transform over a finite field with reduced multiplicative complexity is described. If the number of multiplications is to be minimized, then the novel method for the finite field of even extension degree is the best known method of the discrete Fourier transform computation. A constructive method of constructing for a cyclic convolution over a finite field is introduced.

Radial artery pulse waveform analysis based on curve fitting using discrete Fourier series.

Science.gov (United States)

Jiang, Zhixing; Zhang, David; Lu, Guangming

2018-04-19

Radial artery pulse diagnosis has been playing an important role in traditional Chinese medicine (TCM). For its non-invasion and convenience, the pulse diagnosis has great significance in diseases analysis of modern medicine. The practitioners sense the pulse waveforms in patients' wrist to make diagnoses based on their non-objective personal experience. With the researches of pulse acquisition platforms and computerized analysis methods, the objective study on pulse diagnosis can help the TCM to keep up with the development of modern medicine. In this paper, we propose a new method to extract feature from pulse waveform based on discrete Fourier series (DFS). It regards the waveform as one kind of signal that consists of a series of sub-components represented by sine and cosine (SC) signals with different frequencies and amplitudes. After the pulse signals are collected and preprocessed, we fit the average waveform for each sample using discrete Fourier series by least squares. The feature vector is comprised by the coefficients of discrete Fourier series function. Compared with the fitting method using Gaussian mixture function, the fitting errors of proposed method are smaller, which indicate that our method can represent the original signal better. The classification performance of proposed feature is superior to the other features extracted from waveform, liking auto-regression model and Gaussian mixture model. The coefficients of optimized DFS function, who is used to fit the arterial pressure waveforms, can obtain better performance in modeling the waveforms and holds more potential information for distinguishing different psychological states. Copyright © 2018 Elsevier B.V. All rights reserved.

Discrete fourier transform (DFT) analysis for applications using iterative transform methods

Science.gov (United States)

Dean, Bruce H. (Inventor)

2012-01-01

According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.

A Parallel Framework with Block Matrices of a Discrete Fourier Transform for Vector-Valued Discrete-Time Signals

Directory of Open Access Journals (Sweden)

Pablo Soto-Quiros

2015-01-01

Full Text Available This paper presents a parallel implementation of a kind of discrete Fourier transform (DFT: the vector-valued DFT. The vector-valued DFT is a novel tool to analyze the spectra of vector-valued discrete-time signals. This parallel implementation is developed in terms of a mathematical framework with a set of block matrix operations. These block matrix operations contribute to analysis, design, and implementation of parallel algorithms in multicore processors. In this work, an implementation and experimental investigation of the mathematical framework are performed using MATLAB with the Parallel Computing Toolbox. We found that there is advantage to use multicore processors and a parallel computing environment to minimize the high execution time. Additionally, speedup increases when the number of logical processors and length of the signal increase.

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)

Review of finite fields: Applications to discrete Fourier, transforms and Reed-Solomon coding

Science.gov (United States)

Wong, J. S. L.; Truong, T. K.; Benjauthrit, B.; Mulhall, B. D. L.; Reed, I. S.

1977-01-01

An attempt is made to provide a step-by-step approach to the subject of finite fields. Rigorous proofs and highly theoretical materials are avoided. The simple concepts of groups, rings, and fields are discussed and developed more or less heuristically. Examples are used liberally to illustrate the meaning of definitions and theories. Applications include discrete Fourier transforms and Reed-Solomon coding.

Effect of window function for measurement of ultrasonic nonlinear parameter using fast fourier transform of tone-burst signal

Energy Technology Data Exchange (ETDEWEB)

Lee, Kyoung Jun; Kim, Jong Beom; Song, Dong Gil; Jhang, Kyung Young [Dept. of Mechanical Engineering, Hanyang University, Seoul (Korea, Republic of)

2015-08-15

In ultrasonic nonlinear parameter measurement using the fast Fourier transform(FFT) of tone-burst signals, the side lobe and leakage on spectrum because of finite time and non-periodicity of signals makes it difficult to measure the harmonic magnitudes accurately. The window function made it possible to resolve this problem. In this study, the effect of the Hanning and Turkey window functions on the experimental measurement of nonlinear parameters was analyzed. In addition, the effect of changes in tone burst signal number with changes in the window function on the experimental measurement was analyzed. The result for both window functions were similar and showed that they enabled reliable nonlinear parameter measurement. However, in order to restore original signal amplitude, the amplitude compensation coefficient should be considered for each window function. On a separate note, the larger number of tone bursts was advantageous for stable nonlinear parameter measurement, but this effect was more advantageous in the case of the Hanning window than the Tukey window.

A novel least-square Fourier algorithm for decomposition of discrete, non-equidistant acquisition data

CERN Document Server

Bouthéon, M; Potier, J P

1977-01-01

A novel procedure for evaluating directly the Fourier series coefficients of a function described by unequally spaced but symmetrically disposed interval discrete points is given and an example illustrated. The procedure's simplicity enables it to be used for harmonic analyses of non-equidistant interval data without using the intermediate curve-fitting techniques. (2 refs).

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.

Multidimensional digital image representations using generalized Kaiser-Bessel window functions.

Science.gov (United States)

Lewitt, R M

1990-10-01

Inverse problems that require the solution of integral equations are inherent in a number of indirect imaging applications, such as computerized tomography. Numerical solutions based on discretization of the mathematical model of the imaging process, or on discretization of analytic formulas for iterative inversion of the integral equations, require a discrete representation of an underlying continuous image. This paper describes discrete image representations, in n-dimensional space, that are constructed by the superposition of shifted copies of a rotationally symmetric basis function. The basis function is constructed using a generalization of the Kaiser-Bessel window function of digital signal processing. The generalization of the window function involves going from one dimension to a rotationally symmetric function in n dimensions and going from the zero-order modified Bessel function of the standard window to a function involving the modified Bessel function of order m. Three methods are given for the construction, in n-dimensional space, of basis functions having a specified (finite) number of continuous derivatives, and formulas are derived for the Fourier transform, the x-ray transform, the gradient, and the Laplacian of these basis functions. Properties of the new image representations using these basis functions are discussed, primarily in the context of two-dimensional and three-dimensional image reconstruction from line-integral data by iterative inversion of the x-ray transform. Potential applications to three-dimensional image display are also mentioned.

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.

Application of Discrete Fourier Transform in solving the inverse problem in gamma-ray logging

International Nuclear Information System (INIS)

Zorski, T.

1980-01-01

A new approach to the solution of inverse problem in gamma-ray logging is presented. The equation: I(z) = ∫sup(+infinite)sub(-infinite) phi (z-z')Isub(infinite)(z')dz', which relates the measured intensity I(z) with the intensity Isub(infinite)(z) not disturbed by finite thickness of an elementary layer, is solved for Isub(infinite)(z). Discrete Fourier Transform and convolution theorem are used. As a result of our solution discrete values of Isub(infinite)(z) given at a step of Δh are obtained. Examples of application of this method for Δh <= 4.5 cm and for the curves I(z) theoretically calculated are also discussed. (author)

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.

Introduction to the Discrete Fourier Series Considering Both Mathematical and Engineering Aspects--A Linear Algebra Approach

Science.gov (United States)

Kohaupt, Ludwig

2015-01-01

The discrete Fourier series is a valuable tool developed and used by mathematicians and engineers alike. One of the most prominent applications is signal processing. Usually, it is important that the signals be transmitted fast, for example, when transmitting images over large distances such as between the moon and the earth or when generating…

Comparison between the accuracies of a new discretization method and an improved Fourier method to evaluate heat transfers between soil and atmosphere

International Nuclear Information System (INIS)

Hechinger, E.; Raffy, M.; Becker, F.

1982-01-01

To improve and evaluate the accuracy of Fourier methods for the analysis of the energy exchanges between soil and atmosphere, we have developed first a Fourier method that takes into account the nonneutrality corrections and the time variation of the air temperature and which improves the linearization procedures and, second a new discretization method that does not imply any linearization. The Fourier method, which gives the exact solution of an approximated problem, turns out to have the same order of accuracy as the discretization method, which gives an approximate solution of the exact problem. These methods reproduce the temperatures and fluxes predicted by the Tergra model as well as another set of experimental surface temperatures. In its present form, the Fourier method leads to results that become less accurate (mainly for low wind speeds) under certain conditions, namely, as the amplitude of the daily variation of the air and surface temperatures and their differences increase and as the relative humidities of the air at about 2 m and at the soil surface differ. Nevertheless, the results may be considered as generally satisfactory. Possible improvements of the Fourier model are discussed

A simple approach to Fourier aliasing

International Nuclear Information System (INIS)

Foadi, James

2007-01-01

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

Numerical computation of the discrete Fourier transform and its applications in the statistic processing of experimental data

International Nuclear Information System (INIS)

Marinescu, D.C.; Radulescu, T.G.

1977-06-01

The Integral Fourier Transform has a large range of applications in such areas as communication theory, circuit theory, physics, etc. In order to perform discrete Fourier Transform the Finite Fourier Transform is defined; it operates upon N samples of a uniformely sampled continuous function. All the properties known in the continuous case can be found in the discrete case also. The first part of the paper presents the relationship between the Finite Fourier Transform and the Integral one. The computing of a Finite Fourier Transform is a problem in itself since in order to transform a set of N data we have to perform N 2 ''operations'' if the transformation relations are used directly. An algorithm known as the Fast Fourier Transform (FFT) reduces this figure from N 2 to a more reasonable Nlog 2 N, when N is a power of two. The original Cooley and Tuckey algorithm for FFT can be further improved when higher basis are used. The price to be paid in this case is the increase in complexity of such algorithms. The recurrence relations and a comparation among such algorithms are presented. The key point in understanding the application of FFT resides in the convolution theorem which states that the convolution (an N 2 type procedure) of the primitive functions is equivalent to the ordinar multiplication of their transforms. Since filtering is actually a convolution process we present several procedures to perform digital filtering by means of FFT. The best is the one using the segmentation of records and the transformation of pairs of records. In the digital processing of signals, besides digital filtering a special attention is paid to the estimation of various statistical characteristics of a signal as: autocorrelation and correlation functions, periodiograms, density power sepctrum, etc. We give several algorithms for the consistent and unbiased estimation of such functions, by means of FFT. (author)

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.

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.

Post-processing of EPR spectrum from dosimetric substances through filtering of Discrete Fourier Transform

International Nuclear Information System (INIS)

Vieira, Fabio P.B.; Bevilacqua, Joyce S.

2014-01-01

The use of electron paramagnetic resonance spectrometers - EPR - in radiation dosimetry is known for more than four decades. It is an important tool in the retrospective determination of doses absorbed. To estimate the dose absorbed by the sample, it is necessary to know the amplitude of the peak to peak signature of the substance in its EPR spectrum. This information can be compromised by the presence of spurious information: noise - of random and low intensity nature; and the behavior of the baseline - coming from the coupling between the resonator tube and the sample analyzed. Due to the intrinsic characteristics of the three main components of the signal, i.e. signature, noise, and baseline - the analysis in the frequency domain allows, through post-processing techniques to filter spurious information. In this work, an algorithm that retrieves the signature of a substance has been implemented. The Discrete Fourier Transform is applied to the signal and without user intervention, the noise is filtered. From the filtered signal, recovers the signature by Inverse Discrete Fourier Transform. The peak to peak amplitude, and the absorbed dose is calculated with an error of less than 1% for signals wherein the base line is linearized. Some more general cases are under investigation and with little user intervention, you can get the same error

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.

Discrete Gabor transform and discrete Zak transform

NARCIS (Netherlands)

Bastiaans, M.J.; Namazi, N.M.; Matthews, K.

1996-01-01

Gabor's expansion of a discrete-time signal into a set of shifted and modulated versions of an elementary signal or synthesis window is introduced, along with the inverse operation, i.e. the Gabor transform, which uses an analysis window that is related to the synthesis window and with the help of

Generalized fiber Fourier optics.

Science.gov (United States)

Cincotti, Gabriella

2011-06-15

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

Secure Hashing of Dynamic Hand Signatures Using Wavelet-Fourier Compression with BioPhasor Mixing and Discretization

Directory of Open Access Journals (Sweden)

Wai Kuan Yip

2007-01-01

Full Text Available We introduce a novel method for secure computation of biometric hash on dynamic hand signatures using BioPhasor mixing and discretization. The use of BioPhasor as the mixing process provides a one-way transformation that precludes exact recovery of the biometric vector from compromised hashes and stolen tokens. In addition, our user-specific discretization acts both as an error correction step as well as a real-to-binary space converter. We also propose a new method of extracting compressed representation of dynamic hand signatures using discrete wavelet transform (DWT and discrete fourier transform (DFT. Without the conventional use of dynamic time warping, the proposed method avoids storage of user's hand signature template. This is an important consideration for protecting the privacy of the biometric owner. Our results show that the proposed method could produce stable and distinguishable bit strings with equal error rates (EERs of and for random and skilled forgeries for stolen token (worst case scenario, and for both forgeries in the genuine token (optimal scenario.

3-D Discrete Analytical Ridgelet Transform

OpenAIRE

Helbert , David; Carré , Philippe; Andrès , Éric

2006-01-01

International audience; In this paper, we propose an implementation of the 3-D Ridgelet transform: the 3-D discrete analytical Ridgelet transform (3-D DART). This transform uses the Fourier strategy for the computation of the associated 3-D discrete Radon transform. The innovative step is the definition of a discrete 3-D transform with the discrete analytical geometry theory by the construction of 3-D discrete analytical lines in the Fourier domain. We propose two types of 3-D discrete lines:...

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.

The gridding method for image reconstruction by Fourier transformation

International Nuclear Information System (INIS)

Schomberg, H.; Timmer, J.

1995-01-01

This paper explores a computational method for reconstructing an n-dimensional signal f from a sampled version of its Fourier transform f. The method involves a window function w and proceeds in three steps. First, the convolution g = w * f is computed numerically on a Cartesian grid, using the available samples of f. Then, g = wf is computed via the inverse discrete Fourier transform, and finally f is obtained as g/w. Due to the smoothing effect of the convolution, evaluating w * f is much less error prone than merely interpolating f. The method was originally devised for image reconstruction in radio astronomy, but is actually applicable to a broad range of reconstructive imaging methods, including magnetic resonance imaging and computed tomography. In particular, it provides a fast and accurate alternative to the filtered backprojection. The basic method has several variants with other applications, such as the equidistant resampling of arbitrarily sampled signals or the fast computation of the Radon (Hough) transform

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...

Cone-beam tomography with discrete data sets

International Nuclear Information System (INIS)

Barrett, H.H.

1994-01-01

Sufficiently conditions for cone-beam data are well known for the case of continuous data collection along a cone-vortex curve with continuous detectors. These continuous conditions are inadequate for real-world data where discrete vertex geometries and discrete detector arrays are used. In this paper we present a theoretical formulation of cone-beam tomography with arbitrary discrete arrays of detectors and vertices. The theory models the imaging system as a linear continuous-to-discrete mapping and represents the continuous object exactly as a Fourier series. The reconstruction problem is posed as the estimation of some subset of the Fourier coefficients. The main goal of the theory is to determine which Fourier coefficients can be reliably determined from the data delivered by a specific discrete design. A fourier component will be well determined by the data if it satisfies two conditions: it makes a strong contribution to the data, and this contribution is relatively independent of the contribution of other Fourier components. To make these considerations precise, we introduce a concept called the cross-talk matrix. A diagonal element of this matrix measures the strength of a Fourier component in the data, while an off-diagonal element quantifies the dependence or aliasing of two different components. (Author)

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)

An optical Fourier transform coprocessor with direct phase determination.

Science.gov (United States)

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

2017-10-20

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

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

Directory of Open Access Journals (Sweden)

Farhad A. Namin

2016-08-01

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

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.

On frame properties for Fourier-like systems

DEFF Research Database (Denmark)

Christensen, Ole; Osgooei, Elnaz

2013-01-01

Fourier-like systems are formed by multiplying a class of exponentials with a set of window functions. Via the Fourier transform they are equivalent to shift-invariant systems. We present sufficient and easily verifiable conditions for such systems to form a frame with a dual frame having the same...... structure. An attractive class of frames is formed by letting the window functions be trigonometric polynomials, restricted to compact intervals. We prove, under weak conditions, that such systems generate a frame with a dual that is also generated by a trigonometric polynomial. For polynomial windows......, a result of this type does not hold. Throughout the paper the results are related to the well established theory for Gabor systems....

Approximation for discrete Fourier transform and application in study of three-dimensional interacting electron gas.

Science.gov (United States)

Yan, Xin-Zhong

2011-07-01

The discrete Fourier transform is approximated by summing over part of the terms with corresponding weights. The approximation reduces significantly the requirement for computer memory storage and enhances the numerical computation efficiency with several orders without losing accuracy. As an example, we apply the algorithm to study the three-dimensional interacting electron gas under the renormalized-ring-diagram approximation where the Green's function needs to be self-consistently solved. We present the results for the chemical potential, compressibility, free energy, entropy, and specific heat of the system. The ground-state energy obtained by the present calculation is compared with the existing results of Monte Carlo simulation and random-phase approximation.

Discretization of four types of Weyl group orbit functions

International Nuclear Information System (INIS)

Hrivnák, Jiří

2013-01-01

The discrete Fourier calculus of the four families of special functions, called C–, S–, S s – and S l -functions, is summarized. Functions from each of the four families of special functions are discretely orthogonal over a certain finite set of points. The generalizations of discrete cosine and sine transforms of one variable — the discrete S s – and S l -transforms of the group F 4 — are considered in detail required for their exploitation in discrete Fourier spectral methods. The continuous interpolations, induced by the discrete expansions, are presented

Iterative normalization technique for reference sequence generation for zero-tail discrete fourier transform spread orthogonal frequency division multiplexing

DEFF Research Database (Denmark)

2017-01-01

Systems, methods, apparatuses, and computer program products for generating sequences for zero-tail discrete fourier transform (DFT)-spread-orthogonal frequency division multiplexing (OFDM) (ZT DFT-s-OFDM) reference signals. One method includes adding a zero vector to an input sequence...... of each of the elements, converting the sequence to time domain, generating a zero-padded sequence by forcing a zero head and tail of the sequence, and repeating the steps until a final sequence with zero-tail and flat frequency response is obtained....

Principles of Fourier analysis

CERN Document Server

Howell, Kenneth B

2001-01-01

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

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.

A new twist to fourier transforms

CERN Document Server

Meikle, Hamish D

2004-01-01

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

Techniques for computing the discrete Fourier transform using the quadratic residue Fermat number systems

Science.gov (United States)

Truong, T. K.; Chang, J. J.; Hsu, I. S.; Pei, D. Y.; Reed, I. S.

1986-01-01

The complex integer multiplier and adder over the direct sum of two copies of finite field developed by Cozzens and Finkelstein (1985) is specialized to the direct sum of the rings of integers modulo Fermat numbers. Such multiplication over the rings of integers modulo Fermat numbers can be performed by means of two integer multiplications, whereas the complex integer multiplication requires three integer multiplications. Such multiplications and additions can be used in the implementation of a discrete Fourier transform (DFT) of a sequence of complex numbers. The advantage of the present approach is that the number of multiplications needed to compute a systolic array of the DFT can be reduced substantially. The architectural designs using this approach are regular, simple, expandable and, therefore, naturally suitable for VLSI implementation.

A planar waveguide optical discrete Fourier transformer design for 160 Gb/s all-optical OFDM systems

Science.gov (United States)

Li, Wei; Liang, Xiaojun; Ma, Weidong; Zhou, Tianhong; Huang, Benxiong; Liu, Deming

2010-01-01

A cost-effective all-optical discrete Fourier transformer (ODFT) is designed based on a silicon planar lightwave circuit (PLC), which can be applied to all-optical orthogonal frequency division multiplexing (OFDM) transmission systems and can be achieved by current techniques. It consists of 2 × 2 directional couplers, phase shifters and optical delay lines. Metal-film heaters are used as phase shifters, according to the thermooptic effect of SiO 2. Based on the ODFT, a 160 Gb/s OFDM system is set up. Simulation results show excellent bit error rate (BER) and optical signal-to-noise ratio (OSNR) performances after 400 km transmission.

Application of discrete Fourier inter-coefficient difference for assessing genetic sequence similarity.

Science.gov (United States)

King, Brian R; Aburdene, Maurice; Thompson, Alex; Warres, Zach

2014-01-01

Digital signal processing (DSP) techniques for biological sequence analysis continue to grow in popularity due to the inherent digital nature of these sequences. DSP methods have demonstrated early success for detection of coding regions in a gene. Recently, these methods are being used to establish DNA gene similarity. We present the inter-coefficient difference (ICD) transformation, a novel extension of the discrete Fourier transformation, which can be applied to any DNA sequence. The ICD method is a mathematical, alignment-free DNA comparison method that generates a genetic signature for any DNA sequence that is used to generate relative measures of similarity among DNA sequences. We demonstrate our method on a set of insulin genes obtained from an evolutionarily wide range of species, and on a set of avian influenza viral sequences, which represents a set of highly similar sequences. We compare phylogenetic trees generated using our technique against trees generated using traditional alignment techniques for similarity and demonstrate that the ICD method produces a highly accurate tree without requiring an alignment prior to establishing sequence similarity.

A quantum search algorithm of two entangled registers to realize quantum discrete Fourier transform of signal processing

International Nuclear Information System (INIS)

Pang Chaoyang; Hu Benqiong

2008-01-01

The discrete Fourier transform (DFT) is the base of modern signal processing. 1-dimensional fast Fourier transform (ID FFT) and 2D FFT have time complexity O (N log N) and O (N 2 log N) respectively. Since 1965, there has been no more essential breakthrough for the design of fast DFT algorithm. DFT has two properties. One property is that DFT is energy conservation transform. The other property is that many DFT coefficients are close to zero. The basic idea of this paper is that the generalized Grover's iteration can perform the computation of DFT which acts on the entangled states to search the big DFT coefficients until these big coefficients contain nearly all energy. One-dimensional quantum DFT (ID QDFT) and two-dimensional quantum DFT (2D QDFT) are presented in this paper. The quantum algorithm for convolution estimation is also presented in this paper. Compared with FFT, ID and 2D QDFT have time complexity O(√N) and O (N) respectively. QDFT and quantum convolution demonstrate that quantum computation to process classical signal is possible. (general)

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...

Symmetric, discrete fractional splines and Gabor systems

DEFF Research Database (Denmark)

Søndergaard, Peter Lempel

2006-01-01

In this paper we consider fractional splines as windows for Gabor frames. We introduce two new types of symmetric, fractional splines in addition to one found by Unser and Blu. For the finite, discrete case we present two families of splines: One is created by sampling and periodizing the continu......In this paper we consider fractional splines as windows for Gabor frames. We introduce two new types of symmetric, fractional splines in addition to one found by Unser and Blu. For the finite, discrete case we present two families of splines: One is created by sampling and periodizing...... the continuous splines, and one is a truly finite, discrete construction. We discuss the properties of these splines and their usefulness as windows for Gabor frames and Wilson bases....

Comparison of the Time Domain Windows Specified in the ISO 18431 Standards Used to Estimate Modal Parameters in Steel Plates

Directory of Open Access Journals (Sweden)

Jhonatan Camacho-Navarro

2016-01-01

Full Text Available The procedures used to estimate structural modal parameters as natural frequency, damping ratios, and mode shapes are generally based on frequency methods. However, methods of time-frequency analysis are highly sensible to the parameters used to calculate the discrete Fourier transform: windowing, resolution, and preprocessing. Thus, the uncertainty of the modal parameters is increased if a proper parameter selection is not considered. In this work, the influence of three different time domain windows functions (Hanning, flat-top, and rectangular used to estimate modal parameters are discussed in the framework of ISO 18431 standard. Experimental results are conducted over an AISI 1020 steel plate, which is excited by means of a hammer element. Vibration response is acquired by using acceleration records according to the ISO 7626-5 reference guides. The results are compared with a theoretical method and it is obtained that the flat-top window is the best function for experimental modal analysis.

The fractional Fourier transform and applications

Science.gov (United States)

Bailey, David H.; Swarztrauber, Paul N.

1991-01-01

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

Simultaneous two-wavelength tri-window common-path digital holography

Science.gov (United States)

Liu, Lei; Shan, Mingguang; Zhong, Zhi

2018-06-01

Two-wavelength common-path off-axis digital holography is proposed with a tri-window in a single shot. It is established using a standard 4f optical image system with a 2D Ronchi grating placed outside the Fourier plane. The input plane consists of three windows: one for the object and the other two for reference. Aided by a spatial filter together with two orthogonal linear polarizers in the Fourier plane, the two-wavelength information is encoded into a multiplexed hologram with two orthogonal spatial frequencies that enable full separation of spectral information in the digital Fourier space without resolution loss. Theoretical analysis and experimental results illustrate that our approach can simultaneously perform quantitative phase imaging at two wavelengths.

Digital Fourier analysis fundamentals

CERN Document Server

Kido, Ken'iti

2015-01-01

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

On the Cooley-Turkey Fast Fourier algorithm for arbitrary factors ...

African Journals Online (AJOL)

Atonuje and Okonta in [1] developed the Cooley-Turkey Fast Fourier transform algorithm and its application to the Fourier transform of discretely sampled data points N, expressed in terms of a power y of 2. In this paper, we extend the formalism of [1] Cookey-Turkey Fast Fourier transform algorithm. The method is developed ...

Large quantum Fourier transforms are never exactly realized by braiding conformal blocks

International Nuclear Information System (INIS)

Freedman, Michael H.; Wang, Zhenghan

2007-01-01

Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set {U(2), controlled-NOT}, the discrete Fourier transforms F N =(ω ij ) NxN , i,j=0,1,...,N-1, ω=e 2πi at ∼sol∼ at N , can be realized exactly by quantum circuits of size O(n 2 ), n=ln N, and so can the discrete sine or cosine transforms. In topological quantum computing, the simplest universal topological quantum computer is based on the Fibonacci (2+1)-topological quantum field theory (TQFT), where the standard quantum circuits are replaced by unitary transformations realized by braiding conformal blocks. We report here that the large Fourier transforms F N and the discrete sine or cosine transforms can never be realized exactly by braiding conformal blocks for a fixed TQFT. It follows that an approximation is unavoidable in the implementation of Fourier transforms by braiding conformal blocks

Discrete Fourier transformation processor based on complex radix (−1 + j number system

Directory of Open Access Journals (Sweden)

Anidaphi Shadap

2017-02-01

Full Text Available Complex radix (−1 + j allows the arithmetic operations of complex numbers to be done without treating the divide and conquer rules, which offers the significant speed improvement of complex numbers computation circuitry. Design and hardware implementation of complex radix (−1 + j converter has been introduced in this paper. Extensive simulation results have been incorporated and an application of this converter towards the implementation of discrete Fourier transformation (DFT processor has been presented. The functionality of the DFT processor have been verified in Xilinx ISE design suite version 14.7 and performance parameters like propagation delay and dynamic switching power consumption have been calculated by Virtuoso platform in Cadence. The proposed DFT processor has been implemented through conversion, multiplication and addition. The performance parameter matrix in terms of delay and power consumption offered a significant improvement over other traditional implementation of DFT processor.

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.

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.

Replica Fourier Transform: Properties and applications

International Nuclear Information System (INIS)

Crisanti, A.; De Dominicis, C.

2015-01-01

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

Improvement of the chromatic dispersion tolerance in coherent optical OFDM systems using shifted DFT windows for ultra-long-haul optical transmission systems.

Science.gov (United States)

Sung, Minkyu; Kim, Hoon; Lee, Jaehoon; Jeong, Jichai

2014-09-22

In a high-capacity ultra-long-haul optical coherent orthogonal frequency-division multiplexing (CO-OFDM) system, the dispersion tolerance is determined by the length of cyclic extension (CE). In this paper, we propose a novel scheme to substantially improve the dispersion tolerance of CO-OFDM systems without increasing the CE length. Multiple time-shifted discrete Fourier transform (DFT) windows are exploited at the receiver, each demodulating only a part of the subcarriers. Effectively, the proposed scheme reduces the bandwidth of the OFDM signals under demodulation. Numerical simulations are performed to show the improved dispersion tolerance of the proposed scheme in comparison with the conventional CO-OFDM system. We show that the dispersion tolerance improves by a factor equal to the number of DFT windows. The tradeoff between the improved dispersion tolerance and increased receiver complexity is also presented.

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.

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

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.

CMB in a box: Causal structure and the Fourier-Bessel expansion

International Nuclear Information System (INIS)

Abramo, L. Raul; Reimberg, Paulo H.; Xavier, Henrique S.

2010-01-01

This paper makes two points. First, we show that the line-of-sight solution to cosmic microwave anisotropies in Fourier space, even though formally defined for arbitrarily large wavelengths, leads to position-space solutions which only depend on the sources of anisotropies inside the past light cone of the observer. This foretold manifestation of causality in position (real) space happens order by order in a series expansion in powers of the visibility γ=e -μ , where μ is the optical depth to Thomson scattering. We show that the contributions of order γ N to the cosmic microwave background (CMB) anisotropies are regulated by spacetime window functions which have support only inside the past light cone of the point of observation. Second, we show that the Fourier-Bessel expansion of the physical fields (including the temperature and polarization momenta) is an alternative to the usual Fourier basis as a framework to compute the anisotropies. The viability of the Fourier-Bessel series for treating the CMB is a consequence of the fact that the visibility function becomes exponentially small at redshifts z>>10 3 , effectively cutting off the past light cone and introducing a finite radius inside which initial conditions can affect physical observables measured at our position x-vector=0 and time t 0 . Hence, for each multipole l there is a discrete tower of momenta k il (not a continuum) which can affect physical observables, with the smallest momenta being k 1l ∼l. The Fourier-Bessel modes take into account precisely the information from the sources of anisotropies that propagates from the initial value surface to the point of observation - no more, no less. We also show that the physical observables (the temperature and polarization maps), and hence the angular power spectra, are unaffected by that choice of basis. This implies that the Fourier-Bessel expansion is the optimal scheme with which one can compute CMB anisotropies.

On the discrete Gabor transform and the discrete Zak transform

NARCIS (Netherlands)

Bastiaans, M.J.; Geilen, M.C.W.

1996-01-01

Gabor's expansion of a discrete-time signal into a set of shifted and modulated versions of an elementary signal (or synthesis window) and the inverse operation -- the Gabor transform -- with which Gabor's expansion coefficients can be determined, are introduced. It is shown how, in the case of a

Error analysis and new dual-cosine window for estimating the sensor frequency response function from the step response data

Science.gov (United States)

Yang, Shuang-Long; Liang, Li-Ping; Liu, Hou-De; Xu, Ke-Jun

2018-03-01

Aiming at reducing the estimation error of the sensor frequency response function (FRF) estimated by the commonly used window-based spectral estimation method, the error models of interpolation and transient errors are derived in the form of non-parameter models. Accordingly, window effects on the errors are analyzed and reveal that the commonly used hanning window leads to smaller interpolation error which can also be significantly eliminated by the cubic spline interpolation method when estimating the FRF from the step response data, and window with smaller front-end value can restrain more transient error. Thus, a new dual-cosine window with its non-zero discrete Fourier transform bins at -3, -1, 0, 1, and 3 is constructed for FRF estimation. Compared with the hanning window, the new dual-cosine window has the equivalent interpolation error suppression capability and better transient error suppression capability when estimating the FRF from the step response; specifically, it reduces the asymptotic property of the transient error from O(N-2) of the hanning window method to O(N-4) while only increases the uncertainty slightly (about 0.4 dB). Then, one direction of a wind tunnel strain gauge balance which is a high order, small damping, and non-minimum phase system is employed as the example for verifying the new dual-cosine window-based spectral estimation method. The model simulation result shows that the new dual-cosine window method is better than the hanning window method for FRF estimation, and compared with the Gans method and LPM method, it has the advantages of simple computation, less time consumption, and short data requirement; the actual data calculation result of the balance FRF is consistent to the simulation result. Thus, the new dual-cosine window is effective and practical for FRF estimation.

Cell shape characterization and classification with discrete Fourier transforms and self-organizing maps.

Science.gov (United States)

Kriegel, Fabian L; Köhler, Ralf; Bayat-Sarmadi, Jannike; Bayerl, Simon; Hauser, Anja E; Niesner, Raluca; Luch, Andreas; Cseresnyes, Zoltan

2018-03-01

Cells in their natural environment often exhibit complex kinetic behavior and radical adjustments of their shapes. This enables them to accommodate to short- and long-term changes in their surroundings under physiological and pathological conditions. Intravital multi-photon microscopy is a powerful tool to record this complex behavior. Traditionally, cell behavior is characterized by tracking the cells' movements, which yields numerous parameters describing the spatiotemporal characteristics of cells. Cells can be classified according to their tracking behavior using all or a subset of these kinetic parameters. This categorization can be supported by the a priori knowledge of experts. While such an approach provides an excellent starting point for analyzing complex intravital imaging data, faster methods are required for automated and unbiased characterization. In addition to their kinetic behavior, the 3D shape of these cells also provide essential clues about the cells' status and functionality. New approaches that include the study of cell shapes as well may also allow the discovery of correlations amongst the track- and shape-describing parameters. In the current study, we examine the applicability of a set of Fourier components produced by Discrete Fourier Transform (DFT) as a tool for more efficient and less biased classification of complex cell shapes. By carrying out a number of 3D-to-2D projections of surface-rendered cells, the applied method reduces the more complex 3D shape characterization to a series of 2D DFTs. The resulting shape factors are used to train a Self-Organizing Map (SOM), which provides an unbiased estimate for the best clustering of the data, thereby characterizing groups of cells according to their shape. We propose and demonstrate that such shape characterization is a powerful addition to, or a replacement for kinetic analysis. This would make it especially useful in situations where live kinetic imaging is less practical or not

Double Fourier analysis for Emotion Identification in Voiced Speech

International Nuclear Information System (INIS)

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

2016-01-01

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

Pipeline Analyzer using the Fractional Fourier Transform for Engine Control and Satellites Data

Directory of Open Access Journals (Sweden)

Darian M. Onchiș

2011-09-01

Full Text Available The aim of this paper is to present an algorithm for computing the fractional Fourier transform integrated into the pipeline of processing multi-variate and distributed data recorded by the engine control unit (ECU of a car and its satellites. The role of this transform is vital in establishing a time-variant filter and therefore it must be computed in a fast way. But for large scale time series, the application of the discrete fractional Fourier transform involves the computations of a large number of Hermite polynomials of increasingly order. The parallel algorithm presented will optimally compute the discrete Fourier-type transform for any given angle.

Exponential Form of Discrete Fourier Series from Geometric View%从几何角度看指数形式的傅里叶级数

Institute of Scientific and Technical Information of China (English)

滕建辅; 白煜; 关欣

2012-01-01

In this paper, decomposition and representation of periodic sequences is investigated from geometric view based on orthogonal vectors. In addition, discrete Fourier series formulas are derived by inner product. Com- pared with the traditional teaching methods, the new geometric methods avoid analyzing complete orthogonal func- tions set and minimum mean square error criterion for linear approximation, which make students understand the meaning of the decomposition method for periodic sequences and discrete Fourier series more intuitively.%本文利用正交向量，从几何视角研究周期序列的分解和表示。通过内积运算，推导离散傅里叶级数公式。与传统教学方法相比，本文提出的授课方法避免了对完备正交函数集和最小均方误差准则下线性逼近的分析，使学生更为直观地理解周期序列的分解方法和指数形式的傅立叶级数的含义。

High-order modulation on a single discrete eigenvalue for optical communications based on nonlinear Fourier transform.

Science.gov (United States)

Gui, Tao; Lu, Chao; Lau, Alan Pak Tao; Wai, P K A

2017-08-21

In this paper, we experimentally investigate high-order modulation over a single discrete eigenvalue under the nonlinear Fourier transform (NFT) framework and exploit all degrees of freedom for encoding information. For a fixed eigenvalue, we compare different 4 bit/symbol modulation formats on the spectral amplitude and show that a 2-ring 16-APSK constellation achieves optimal performance. We then study joint spectral phase, spectral magnitude and eigenvalue modulation and found that while modulation on the real part of the eigenvalue induces pulse timing drift and leads to neighboring pulse interactions and nonlinear inter-symbol interference (ISI), it is more bandwidth efficient than modulation on the imaginary part of the eigenvalue in practical settings. We propose a spectral amplitude scaling method to mitigate such nonlinear ISI and demonstrate a record 4 GBaud 16-APSK on the spectral amplitude plus 2-bit eigenvalue modulation (total 6 bit/symbol at 24 Gb/s) transmission over 1000 km.

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.

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

Science.gov (United States)

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

2014-09-01

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

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)

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

Combining the Hanning windowed interpolated FFT in both directions

Science.gov (United States)

Chen, Kui Fu; Li, Yan Feng

2008-06-01

The interpolated fast Fourier transform (IFFT) has been proposed as a way to eliminate the picket fence effect (PFE) of the fast Fourier transform. The modulus based IFFT, cited in most relevant references, makes use of only the 1st and 2nd highest spectral lines. An approach using three principal spectral lines is proposed. This new approach combines both directions of the complex spectrum based IFFT with the Hanning window. The optimal weight to minimize the estimation variance is established on the first order Taylor series expansion of noise interference. A numerical simulation is carried out, and the results are compared with the Cramer-Rao bound. It is demonstrated that the proposed approach has a lower estimation variance than the two-spectral-line approach. The improvement depends on the extent of sampling deviating from the coherent condition, and the best is decreasing variance by 2/7. However, it is also shown that the estimation variance of the windowed IFFT with the Hanning is significantly higher than that of without windowing.

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

Science.gov (United States)

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

2012-01-01

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

The discrete spectrum in azimuthally dependent transport theory

International Nuclear Information System (INIS)

Garcia, R.D.M.; Siewert, C.E.

1989-01-01

The discrete spectrum for each component of a Fourier decomposition of the azimuthally dependent transport equation is analyzed. For a non-multiplying medium described by an L th -order scattering law, the problem of determining the zeros of the dispersion function for the m th Fourier component is formulated in terms of Sturm sequences. In particular, a straightforward application of the Sturm-sequence property is used to compute the number of discrete eigenvalue pairs κ m and to show that either κ m = γ m or κ m = γ m + 1, where γ m denotes the number of zeros of the Chandrasekhar polynomial g m L+1 (ξ) which are greater than unity. It is also shown how Sturm sequences can be used to construct effective algorithms to compute and to refine estimates of the discrete eigenvalues. Results are presented for a test problem. (author) [pt

Finite Discrete Gabor Analysis

DEFF Research Database (Denmark)

Søndergaard, Peter Lempel

2007-01-01

frequency bands at certain times. Gabor theory can be formulated for both functions on the real line and for discrete signals of finite length. The two theories are largely the same because many aspects come from the same underlying theory of locally compact Abelian groups. The two types of Gabor systems...... can also be related by sampling and periodization. This thesis extends on this theory by showing new results for window construction. It also provides a discussion of the problems associated to discrete Gabor bases. The sampling and periodization connection is handy because it allows Gabor systems...... on the real line to be well approximated by finite and discrete Gabor frames. This method of approximation is especially attractive because efficient numerical methods exists for doing computations with finite, discrete Gabor systems. This thesis presents new algorithms for the efficient computation of finite...

Nonuniform sampling and non-Fourier signal processing methods in multidimensional NMR.

Science.gov (United States)

Mobli, Mehdi; Hoch, Jeffrey C

2014-11-01

Beginning with the introduction of Fourier Transform NMR by Ernst and Anderson in 1966, time domain measurement of the impulse response (the free induction decay, FID) consisted of sampling the signal at a series of discrete intervals. For compatibility with the discrete Fourier transform (DFT), the intervals are kept uniform, and the Nyquist theorem dictates the largest value of the interval sufficient to avoid aliasing. With the proposal by Jeener of parametric sampling along an indirect time dimension, extension to multidimensional experiments employed the same sampling techniques used in one dimension, similarly subject to the Nyquist condition and suitable for processing via the discrete Fourier transform. The challenges of obtaining high-resolution spectral estimates from short data records using the DFT were already well understood, however. Despite techniques such as linear prediction extrapolation, the achievable resolution in the indirect dimensions is limited by practical constraints on measuring time. The advent of non-Fourier methods of spectrum analysis capable of processing nonuniformly sampled data has led to an explosion in the development of novel sampling strategies that avoid the limits on resolution and measurement time imposed by uniform sampling. The first part of this review discusses the many approaches to data sampling in multidimensional NMR, the second part highlights commonly used methods for signal processing of such data, and the review concludes with a discussion of other approaches to speeding up data acquisition in NMR. Copyright © 2014 Elsevier B.V. All rights reserved.

Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications

International Nuclear Information System (INIS)

Du, Qiang; Yang, Jiang

2017-01-01

This work is concerned with the Fourier spectral approximation of various integral differential equations associated with some linear nonlocal diffusion and peridynamic operators under periodic boundary conditions. For radially symmetric kernels, the nonlocal operators under consideration are diagonalizable in the Fourier space so that the main computational challenge is on the accurate and fast evaluation of their eigenvalues or Fourier symbols consisting of possibly singular and highly oscillatory integrals. For a large class of fractional power-like kernels, we propose a new approach based on reformulating the Fourier symbols both as coefficients of a series expansion and solutions of some simple ODE models. We then propose a hybrid algorithm that utilizes both truncated series expansions and high order Runge–Kutta ODE solvers to provide fast evaluation of Fourier symbols in both one and higher dimensional spaces. It is shown that this hybrid algorithm is robust, efficient and accurate. As applications, we combine this hybrid spectral discretization in the spatial variables and the fourth-order exponential time differencing Runge–Kutta for temporal discretization to offer high order approximations of some nonlocal gradient dynamics including nonlocal Allen–Cahn equations, nonlocal Cahn–Hilliard equations, and nonlocal phase-field crystal models. Numerical results show the accuracy and effectiveness of the fully discrete scheme and illustrate some interesting phenomena associated with the nonlocal models.

FFT-BM, Code Accuracy Evaluations with the 1D Fast Fourier Transform (FFT) Methodology

International Nuclear Information System (INIS)

D'Auria, F.

2004-01-01

1 - Description of program or function: FFT-BM is an integrated version of the programs package performing code accuracy evaluations with the 1D Fast Fourier Transform (FFT) methodology. It contains two programs: - CASEM: Takes care of the complete manipulation of data in order to evaluate the quantities through which the FFT method quantifies the code accuracy. - AAWFTO completes the evaluation of the average accuracy (AA) and related weighted frequency (WF) values in order to obtain the AAtot and WFtot values characterising the global calculation performance. 2 - Methods: The Fast Fourier Transform, or FFT, which is based on the Fourier analysis method is an optimised method for calculating the amplitude Vs frequency, of functions or experimental or computed data. In order to apply this methodology, after selecting the parameters to be analyzed, it is necessary to choose the following parameters: - number of curves (exp + calc) to be analyzed; - number of time windows to be analyzed; - sampling frequency; - cut frequency; - time begin and time end of each time window. 3 - Restrictions on the complexity of the problem: Up to 30 curves (exp + calc) and 5 time windows may be analyzed

Speed testing of Sliding spectrum analysis

International Nuclear Information System (INIS)

Frenski, Emil; Manolev, Dimitar

2013-01-01

The standard method for spectrum analysis in DSP is the Discrete Fourier transform (DFT), typically implemented using a Fast Fourier transform (FFT) algorithm. The reconstruction of the time-domain signal is then performed by the IFFT (Inverse Fast Fourier transform) algorithm. The FFT calculates the spectral components in a window, on a block-by-block basis. If that window is move by one sample, it is obvious that most of the information will remain the same. This article shows how to measure execution time of scripts realizing SDFT algorithm written for MatLab

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

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

Multi-Beam Radio Frequency (RF) Aperture Arrays Using Multiplierless Approximate Fast Fourier Transform (FFT)

Science.gov (United States)

2017-08-01

Fourier transform, discrete Fourier transform, digital array processing , antenna beamformers 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF...125 3.7 Simulation of 2-D Beams Cross Sections .................................................................... 125 3.7.1 8...unlimited. List of Figures Figure Page Figure 1: N-beam Array Processing System using a Linear Array

Comparison of Fourier transform and continuous wavelet transform to study echo-planar imaging flow maps

Energy Technology Data Exchange (ETDEWEB)

Rodriguez G, A.; Bowtell, R.; Mansfield, P. [Area de Procesamiento Digital de Senales e Imagenes Biomedicas. Universidad Autonoma Metropolitana Iztapalapa. Mexico D.F. 09340 Mexico (Mexico)

1998-12-31

Velocity maps were studied combining Doyle and Mansfield method (1986) with each of the following transforms: Fourier, window Fourier and wavelet (Mexican hat). Continuous wavelet transform was compared against the two Fourier transform to determine which technique is best suited to study blood maps generated by Half Fourier Echo-Planar Imaging. Coefficient images were calculated and plots of the pixel intensity variation are presented. Finally, contour maps are shown to visualize the behavior of the blood flow in the cardiac chambers for the wavelet technique. (Author)

Comparison of Fourier transform and continuous wavelet transform to study echo-planar imaging flow maps

International Nuclear Information System (INIS)

Rodriguez G, A.; Bowtell, R.; Mansfield, P.

1998-01-01

Velocity maps were studied combining Doyle and Mansfield method (1986) with each of the following transforms: Fourier, window Fourier and wavelet (Mexican hat). Continuous wavelet transform was compared against the two Fourier transform to determine which technique is best suited to study blood maps generated by Half Fourier Echo-Planar Imaging. Coefficient images were calculated and plots of the pixel intensity variation are presented. Finally, contour maps are shown to visualize the behavior of the blood flow in the cardiac chambers for the wavelet technique. (Author)

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.

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.

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.

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.

A new discrete dipole kernel for quantitative susceptibility mapping.

Science.gov (United States)

Milovic, Carlos; Acosta-Cabronero, Julio; Pinto, José Miguel; Mattern, Hendrik; Andia, Marcelo; Uribe, Sergio; Tejos, Cristian

2018-09-01

Most approaches for quantitative susceptibility mapping (QSM) are based on a forward model approximation that employs a continuous Fourier transform operator to solve a differential equation system. Such formulation, however, is prone to high-frequency aliasing. The aim of this study was to reduce such errors using an alternative dipole kernel formulation based on the discrete Fourier transform and discrete operators. The impact of such an approach on forward model calculation and susceptibility inversion was evaluated in contrast to the continuous formulation both with synthetic phantoms and in vivo MRI data. The discrete kernel demonstrated systematically better fits to analytic field solutions, and showed less over-oscillations and aliasing artifacts while preserving low- and medium-frequency responses relative to those obtained with the continuous kernel. In the context of QSM estimation, the use of the proposed discrete kernel resulted in error reduction and increased sharpness. This proof-of-concept study demonstrated that discretizing the dipole kernel is advantageous for QSM. The impact on small or narrow structures such as the venous vasculature might by particularly relevant to high-resolution QSM applications with ultra-high field MRI - a topic for future investigations. The proposed dipole kernel has a straightforward implementation to existing QSM routines. Copyright © 2018 Elsevier Inc. All rights reserved.

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

Science.gov (United States)

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

2017-09-01

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

An Efficient Adaptive Window Size Selection Method for Improving Spectrogram Visualization

Directory of Open Access Journals (Sweden)

Shibli Nisar

2016-01-01

Full Text Available Short Time Fourier Transform (STFT is an important technique for the time-frequency analysis of a time varying signal. The basic approach behind it involves the application of a Fast Fourier Transform (FFT to a signal multiplied with an appropriate window function with fixed resolution. The selection of an appropriate window size is difficult when no background information about the input signal is known. In this paper, a novel empirical model is proposed that adaptively adjusts the window size for a narrow band-signal using spectrum sensing technique. For wide-band signals, where a fixed time-frequency resolution is undesirable, the approach adapts the constant Q transform (CQT. Unlike the STFT, the CQT provides a varying time-frequency resolution. This results in a high spectral resolution at low frequencies and high temporal resolution at high frequencies. In this paper, a simple but effective switching framework is provided between both STFT and CQT. The proposed method also allows for the dynamic construction of a filter bank according to user-defined parameters. This helps in reducing redundant entries in the filter bank. Results obtained from the proposed method not only improve the spectrogram visualization but also reduce the computation cost and achieves 87.71% of the appropriate window length selection.

Online frequency estimation with applications to engine and generator sets

Science.gov (United States)

Manngård, Mikael; Böling, Jari M.

2017-07-01

Frequency and spectral analysis based on the discrete Fourier transform is a fundamental task in signal processing and machine diagnostics. This paper aims at presenting computationally efficient methods for real-time estimation of stationary and time-varying frequency components in signals. A brief survey of the sliding time window discrete Fourier transform and Goertzel filter is presented, and two filter banks consisting of: (i) sliding time window Goertzel filters (ii) infinite impulse response narrow bandpass filters are proposed for estimating instantaneous frequencies. The proposed methods show excellent results on both simulation studies and on a case study using angular speed data measurements of the crankshaft of a marine diesel engine-generator set.

Rectangular-to-quincunx Gabor lattice conversion via fractional Fourier transformation

NARCIS (Netherlands)

Bastiaans, M.J.; Leest, van A.J.

1998-01-01

Transformations of Gabor lattices are associated with operations on the window functions that arise in Gabor theory. In particular it is shown that transformation from a rectangular to a quincunx lattice can be associated with fractional Fourier transformation. Since a Gaussian function, which plays

A Fourier analysis on the maximum acceptable grid size for discrete proton beam dose calculation

International Nuclear Information System (INIS)

Li, Haisen S.; Romeijn, H. Edwin; Dempsey, James F.

2006-01-01

We developed an analytical method for determining the maximum acceptable grid size for discrete dose calculation in proton therapy treatment plan optimization, so that the accuracy of the optimized dose distribution is guaranteed in the phase of dose sampling and the superfluous computational work is avoided. The accuracy of dose sampling was judged by the criterion that the continuous dose distribution could be reconstructed from the discrete dose within a 2% error limit. To keep the error caused by the discrete dose sampling under a 2% limit, the dose grid size cannot exceed a maximum acceptable value. The method was based on Fourier analysis and the Shannon-Nyquist sampling theorem as an extension of our previous analysis for photon beam intensity modulated radiation therapy [J. F. Dempsey, H. E. Romeijn, J. G. Li, D. A. Low, and J. R. Palta, Med. Phys. 32, 380-388 (2005)]. The proton beam model used for the analysis was a near mono-energetic (of width about 1% the incident energy) and monodirectional infinitesimal (nonintegrated) pencil beam in water medium. By monodirection, we mean that the proton particles are in the same direction before entering the water medium and the various scattering prior to entrance to water is not taken into account. In intensity modulated proton therapy, the elementary intensity modulation entity for proton therapy is either an infinitesimal or finite sized beamlet. Since a finite sized beamlet is the superposition of infinitesimal pencil beams, the result of the maximum acceptable grid size obtained with infinitesimal pencil beam also applies to finite sized beamlet. The analytic Bragg curve function proposed by Bortfeld [T. Bortfeld, Med. Phys. 24, 2024-2033 (1997)] was employed. The lateral profile was approximated by a depth dependent Gaussian distribution. The model included the spreads of the Bragg peak and the lateral profiles due to multiple Coulomb scattering. The dependence of the maximum acceptable dose grid size on the

Large-scale chromosome folding versus genomic DNA sequences: A discrete double Fourier transform technique.

Science.gov (United States)

Chechetkin, V R; Lobzin, V V

2017-08-07

Using state-of-the-art techniques combining imaging methods and high-throughput genomic mapping tools leaded to the significant progress in detailing chromosome architecture of various organisms. However, a gap still remains between the rapidly growing structural data on the chromosome folding and the large-scale genome organization. Could a part of information on the chromosome folding be obtained directly from underlying genomic DNA sequences abundantly stored in the databanks? To answer this question, we developed an original discrete double Fourier transform (DDFT). DDFT serves for the detection of large-scale genome regularities associated with domains/units at the different levels of hierarchical chromosome folding. The method is versatile and can be applied to both genomic DNA sequences and corresponding physico-chemical parameters such as base-pairing free energy. The latter characteristic is closely related to the replication and transcription and can also be used for the assessment of temperature or supercoiling effects on the chromosome folding. We tested the method on the genome of E. coli K-12 and found good correspondence with the annotated domains/units established experimentally. As a brief illustration of further abilities of DDFT, the study of large-scale genome organization for bacteriophage PHIX174 and bacterium Caulobacter crescentus was also added. The combined experimental, modeling, and bioinformatic DDFT analysis should yield more complete knowledge on the chromosome architecture and genome organization. Copyright © 2017 Elsevier Ltd. All rights reserved.

On the spectral analysis of iterative solutions of the discretized one-group transport equation

International Nuclear Information System (INIS)

Sanchez, Richard

2004-01-01

We analyze the Fourier-mode technique used for the spectral analysis of iterative solutions of the one-group discretized transport equation. We introduce a direct spectral analysis for the iterative solution of finite difference approximations for finite slabs composed of identical layers, providing thus a complementary analysis that is more appropriate for reactor applications. Numerical calculations for the method of characteristics and with the diamond difference approximation show the appearance of antisymmetric modes generated by the iteration on boundary data. We have also utilized the discrete Fourier transform to compute the spectrum for a periodic slab containing N identical layers and shown that at the limit N → ∞ one obtains the familiar Fourier-mode solution

Primordial black holes and uncertainties in the choice of the window function

Science.gov (United States)

Ando, Kenta; Inomata, Keisuke; Kawasaki, Masahiro

2018-05-01

Primordial black holes (PBHs) can be produced by the perturbations that exit the horizon during the inflationary phase. While inflation models predict the power spectrum of the perturbations in Fourier space, the PBH abundance depends on the probability distribution function of density perturbations in real space. To estimate the PBH abundance in a given inflation model, we must relate the power spectrum in Fourier space to the probability density function in real space by coarse graining the perturbations with a window function. However, there are uncertainties on what window function should be used, which could change the relation between the PBH abundance and the power spectrum. This is particularly important in considering PBHs with mass 30 M⊙, which account for the LIGO events because the required power spectrum is severely constrained by the observations. In this paper, we investigate how large an influence the uncertainties on the choice of a window function has over the power spectrum required for LIGO PBHs. As a result, it is found that the uncertainties significantly affect the prediction for the stochastic gravitational waves induced by the second-order effect of the perturbations. In particular, the pulsar timing array constraints on the produced gravitational waves could disappear for the real-space top-hat window function.

Exact discretization of Schrödinger equation

Energy Technology Data Exchange (ETDEWEB)

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2016-01-08

There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

Exact discretization of Schrödinger equation

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2016-01-01

There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

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

Novel properties of the Fourier decomposition of the sinogram

International Nuclear Information System (INIS)

Edholm, P.R.; Lewitt, R.M.; Lindholm, B.

1986-01-01

The double Fourier decomposition of the sinogram is obtained by first taking the Fourier transform of each parallel-ray projection and then calculating the coefficients of a Fourier series with respect to angle for each frequency component of the transformed projections. The values of these coefficients may be plotted on a two-dimensional map whose coordinates are spatial frequency ω (continuous) and angular harmonic number n (discrete). For absolute value of ω large, the Fourier coefficients on the line n=kω of slope k through the origin of the coefficient space are found to depend strongly on the contributions to the projection data that, for each view, come from a certain distance to the detector plane, where the distance is a linear function of k. The values of these coefficients depend only weakly on contributions from other distances from the detector. The theoretical basis of this property is presented in this paper and a potential application to emission computerized tomography is discussed

On the discrete version of Gabor's signal expansion, the Gabor transform, and the Zak transform

NARCIS (Netherlands)

Bastiaans, M.J.; Veen, J.P.

1996-01-01

Gabors expansion of a discrete-time signal into a set of shifted and modulated versions of an elementary signal or synthesis window is introduced, along with the inverse operation, i.e., the Gabor transform, which uses an analysis window that is related to the synthesis window and with the help of

Fourier Deconvolution Methods for Resolution Enhancement in Continuous-Wave EPR Spectroscopy.

Science.gov (United States)

Reed, George H; Poyner, Russell R

2015-01-01

An overview of resolution enhancement of conventional, field-swept, continuous-wave electron paramagnetic resonance spectra using Fourier transform-based deconvolution methods is presented. Basic steps that are involved in resolution enhancement of calculated spectra using an implementation based on complex discrete Fourier transform algorithms are illustrated. Advantages and limitations of the method are discussed. An application to an experimentally obtained spectrum is provided to illustrate the power of the method for resolving overlapped transitions. © 2015 Elsevier Inc. All rights reserved.

Integrable systems with quadratic nonlinearity in Fourier space

International Nuclear Information System (INIS)

Marikhin, V.G.

2003-01-01

The Lax pair representation in Fourier space is used to obtain a list of integrable scalar evolutionary equations with quadratic nonlinearity. The known systems of this type such as KdV, intermediate long-wave equation (ILW), Camassa-Holm and Degasperis-Procesi systems are represented in this list. Some new systems are obtained as well. Two-dimensional and discrete generalizations are discussed

Manifestly gauge invariant discretizations of the Schrödinger equation

International Nuclear Information System (INIS)

Halvorsen, Tore Gunnar; Kvaal, Simen

2012-01-01

Grid-based discretizations of the time dependent Schrödinger equation coupled to an external magnetic field are converted to manifest gauge invariant discretizations. This is done using generalizations of ideas used in classical lattice gauge theory, and the process defined is applicable to a large class of discretized differential operators. In particular, popular discretizations such as pseudospectral discretizations using the fast Fourier transform can be transformed to gauge invariant schemes. Also generic gauge invariant versions of generic time integration methods are considered, enabling completely gauge invariant calculations of the time dependent Schrödinger equation. Numerical examples illuminating the differences between a gauge invariant discretization and conventional discretization procedures are also presented. -- Highlights: ► We investigate the Schrödinger equation coupled to an external magnetic field. ► Any grid-based discretization is made trivially gauge invariant. ► An extension of classical lattice gauge theory.

TMS320C25 Digital Signal Processor For 2-Dimensional Fast Fourier Transform Computation

International Nuclear Information System (INIS)

Ardisasmita, M. Syamsa

1996-01-01

The Fourier transform is one of the most important mathematical tool in signal processing and analysis, which converts information from the time/spatial domain into the frequency domain. Even with implementation of the Fast Fourier Transform algorithms in imaging data, the discrete Fourier transform execution consume a lot of time. Digital signal processors are designed specifically to perform computation intensive digital signal processing algorithms. By taking advantage of the advanced architecture. parallel processing, and dedicated digital signal processing (DSP) instruction sets. This device can execute million of DSP operations per second. The device architecture, characteristics and feature suitable for fast Fourier transform application and speed-up are discussed

From the rectangular to the quincunx Gabor lattice via fractional Fourier transformation

NARCIS (Netherlands)

Bastiaans, M.J.; Leest, van A.J.

1998-01-01

Transformations of Gabor lattices have been associated with operations on the window functions that arise in Gabor theory. In particular it has been shown that transformation from a rectangular to a quincunx lattice can be associated with fractional Fourier transformation. Since a Gaussian function,

Error analysis in Fourier methods for option pricing for exponential Lévy processes

KAUST Repository

Crocce, Fabian; Hä ppö lä , Juho; Keissling, Jonas; Tempone, Raul

2015-01-01

We derive an error bound for utilising the discrete Fourier transform method for solving Partial Integro-Differential Equations (PIDE) that describe european option prices for exponential Lévy driven asset prices. We give sufficient conditions

Nonparametric volatility density estimation for discrete time models

NARCIS (Netherlands)

Es, van Bert; Spreij, P.J.C.; Zanten, van J.H.

2005-01-01

We consider discrete time models for asset prices with a stationary volatility process. We aim at estimating the multivariate density of this process at a set of consecutive time instants. A Fourier-type deconvolution kernel density estimator based on the logarithm of the squared process is proposed

On the raising and lowering difference operators for eigenvectors of the finite Fourier transform

International Nuclear Information System (INIS)

Atakishiyeva, M K; Atakishiyev, N M

2015-01-01

We construct explicit forms of raising and lowering difference operators that govern eigenvectors of the finite (discrete) Fourier transform. Some of the algebraic properties of these operators are also examined. (paper)

On error estimation in the fourier modal method for diffractive gratings

NARCIS (Netherlands)

Hlod, A.; Maubach, J.M.L.

2010-01-01

The Fourier Modal Method (FMM, also called the Rigorous Coupled Wave Analysis, RCWA) is a numerical discretization method which is often used to calculate a scattered field from a periodic diffraction grating. For 1D periodic gratings in FMM the electromagnetic field is presented by a truncated

Open-geometry Fourier modal method: modeling nanophotonic structures in infinite domains

DEFF Research Database (Denmark)

Häyrynen, Teppo; de Lasson, Jakob Rosenkrantz; Gregersen, Niels

2016-01-01

We present an open-geometry Fourier modal method based on a new combination of open boundary conditions and an efficient k-space discretization. The open boundary of the computational domain is obtained using basis functions that expand the whole space, and the integrals subsequently appearing due...

Fourier two-level analysis for discontinuous Galerkin discretization with linear elements

NARCIS (Netherlands)

P.W. Hemker (Piet); W. Hoffmann; M.H. van Raalte (Marc)

2002-01-01

textabstractIn this paper we study the convergence of a multigrid method for the solution of a linear second order elliptic equation, discretized by discontinuous Galerkin (DG) methods, and we give a detailed analysis of the convergence fordifferent block-relaxation strategies. In addition to an

Simulasi Unjuk Kerja Discrete Wavelet Transform (DWT dan Discrete Cosine Transform (DCT untuk Pengolahan Sinyal Radar di Daerah yang Ber-Noise Tinggi

Directory of Open Access Journals (Sweden)

Raisah Hayati

2014-03-01

Full Text Available Detection of low signal and determination target locations is the basis and important in the system radar. Performance of radar can enhanced with enhancement signal-to-noise ratio in the receiver. In this research, will show a algorithm in radar signal processing, that is for extract the signal target in the place of noise. Discrete Cosine Transform (DCT and Discrete Wavelet Transform (DWT is the success full mathematic function in the signal processing in the last twenty years. In this research will simulate signal with DCT and DWT, analysis his performance in radar signal processing. DWT signal processing will analysis and compare with mother wavelet Haar, Daubechies-12, Coiflet-5 and Symlet-8. DCT signal processing will analysis and compare with same of window function with use in signal restrictions. Window function have influence signal resolution in domain frequency. Window function that use in this research Rectangular, Hamming, Hanning and Dolph-Chebyshev. The result of simulation and analysis Is: mother wavelet with DWT, wavelet Daubechies-12 and Symlet-8 give the best performance and mother wavelet Haar give bad performance. Wavelet Daubechies-12 give the biggest signal to noise ratio that is 32,0603 dB. Mother wavelet Symlet-8 give 32,6589 dB. Mother wavelet Haar give 14,6692 dB. Testing window function DCT, window Dolph-Chebyshev give the best performance, with give the best separation of signal. Analysis of signal reflection that accept of radar give the result that DWT is better performance than DCT in breaking of noise.

New significance test methods for Fourier analysis of geophysical time series

Directory of Open Access Journals (Sweden)

Z. Zhang

2011-09-01

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

Exclusive queueing model including the choice of service windows

Science.gov (United States)

Tanaka, Masahiro; Yanagisawa, Daichi; Nishinari, Katsuhiro

2018-01-01

In a queueing system involving multiple service windows, choice behavior is a significant concern. This paper incorporates the choice of service windows into a queueing model with a floor represented by discrete cells. We contrived a logit-based choice algorithm for agents considering the numbers of agents and the distances to all service windows. Simulations were conducted with various parameters of agent choice preference for these two elements and for different floor configurations, including the floor length and the number of service windows. We investigated the model from the viewpoint of transit times and entrance block rates. The influences of the parameters on these factors were surveyed in detail and we determined that there are optimum floor lengths that minimize the transit times. In addition, we observed that the transit times were determined almost entirely by the entrance block rates. The results of the presented model are relevant to understanding queueing systems including the choice of service windows and can be employed to optimize facility design and floor management.

Semi-Discrete Ingham-Type Inequalities

International Nuclear Information System (INIS)

Komornik, Vilmos; Loreti, Paola

2007-01-01

One of the general methods in linear control theory is based on harmonic and non-harmonic Fourier series. The key of this approach is the establishment of various suitable adaptations and generalizations of the classical Parseval equality. A new and systematic approach was begun in our papers in collaboration with Baiocchi. Many recent results of this kind, obtained through various Ingham-type theorems, were exposed recently. Although this work concentrated on continuous models, in connection with numerical simulations a natural question is whether these results also admit useful discrete versions. The purpose of this paper is to establish discrete versions of various Ingham-type theorems by using our approach. They imply the earlier continuous results by a simple limit process

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

Science.gov (United States)

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

2018-02-01

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

Studying The Effect of Window type On Power Spectrum Based On MATLAB

Directory of Open Access Journals (Sweden)

Soad T. Abed

2012-06-01

Full Text Available The representation that describes signal’s frequency behavior can be divided into two categories: linear representation such as the Fourier-transform and quadratic representation such as power spectrum. Power spectrum characterizes the signal’s energy distribution in the frequency domain, and can answer whether most of the power of the signal resides at low or high frequencies. By performing spectral analysis, some important features of signals can be discovered that are not obvious in the time waveform of the signal. One problem with spectrum analysis is that the duration of the signals is finite, although adjustable. Applying the FFT method to finite duration sequences can produce inadequate results because of “spectral leakage”, to reduce the spectral leakage FFT window function is applied. Power spectrum parameters are window size, window type, window over lap and number of FFT. The aim of this work is to demonstrate the effect of varying window type on the power spectrum using Mat Lab software. Five windows have been compared to study their effect on the spectrum of a typical data.

SU(2 and SU(1,1 Approaches to Phase Operators and Temporally Stable Phase States: Applications to Mutually Unbiased Bases and Discrete Fourier Transforms

Directory of Open Access Journals (Sweden)

Maurice R. Kibler

2010-07-01

Full Text Available We propose a group-theoretical approach to the generalized oscillator algebra Aκ recently investigated in J. Phys. A: Math. Theor. 2010, 43, 115303. The case κ ≥ 0 corresponds to the noncompact group SU(1,1 (as for the harmonic oscillator and the Pöschl-Teller systems while the case κ < 0 is described by the compact group SU(2 (as for the Morse system. We construct the phase operators and the corresponding temporally stable phase eigenstates for Aκ in this group-theoretical context. The SU(2 case is exploited for deriving families of mutually unbiased bases used in quantum information. Along this vein, we examine some characteristics of a quadratic discrete Fourier transform in connection with generalized quadratic Gauss sums and generalized Hadamard matrices.

On E-discretization of tori of compact simple Lie groups. II

Science.gov (United States)

Hrivnák, Jiří; Juránek, Michal

2017-10-01

Ten types of discrete Fourier transforms of Weyl orbit functions are developed. Generalizing one-dimensional cosine, sine, and exponential, each type of the Weyl orbit function represents an exponential symmetrized with respect to a subgroup of the Weyl group. Fundamental domains of even affine and dual even affine Weyl groups, governing the argument and label symmetries of the even orbit functions, are determined. The discrete orthogonality relations are formulated on finite sets of points from the refinements of the dual weight lattices. Explicit counting formulas for the number of points of the discrete transforms are deduced. Real-valued Hartley orbit functions are introduced, and all ten types of the corresponding discrete Hartley transforms are detailed.

Discrete Ramanujan transform for distinguishing the protein coding regions from other regions.

Science.gov (United States)

Hua, Wei; Wang, Jiasong; Zhao, Jian

2014-01-01

Based on the study of Ramanujan sum and Ramanujan coefficient, this paper suggests the concepts of discrete Ramanujan transform and spectrum. Using Voss numerical representation, one maps a symbolic DNA strand as a numerical DNA sequence, and deduces the discrete Ramanujan spectrum of the numerical DNA sequence. It is well known that of discrete Fourier power spectrum of protein coding sequence has an important feature of 3-base periodicity, which is widely used for DNA sequence analysis by the technique of discrete Fourier transform. It is performed by testing the signal-to-noise ratio at frequency N/3 as a criterion for the analysis, where N is the length of the sequence. The results presented in this paper show that the property of 3-base periodicity can be only identified as a prominent spike of the discrete Ramanujan spectrum at period 3 for the protein coding regions. The signal-to-noise ratio for discrete Ramanujan spectrum is defined for numerical measurement. Therefore, the discrete Ramanujan spectrum and the signal-to-noise ratio of a DNA sequence can be used for distinguishing the protein coding regions from the noncoding regions. All the exon and intron sequences in whole chromosomes 1, 2, 3 and 4 of Caenorhabditis elegans have been tested and the histograms and tables from the computational results illustrate the reliability of our method. In addition, we have analyzed theoretically and gotten the conclusion that the algorithm for calculating discrete Ramanujan spectrum owns the lower computational complexity and higher computational accuracy. The computational experiments show that the technique by using discrete Ramanujan spectrum for classifying different DNA sequences is a fast and effective method. Copyright © 2014 Elsevier Ltd. All rights reserved.

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Vehicle Classification Using the Discrete Fourier Transform with Traffic Inductive Sensors.

Science.gov (United States)

Lamas-Seco, José J; Castro, Paula M; Dapena, Adriana; Vazquez-Araujo, Francisco J

2015-10-26

Inductive Loop Detectors (ILDs) are the most commonly used sensors in traffic management systems. This paper shows that some spectral features extracted from the Fourier Transform (FT) of inductive signatures do not depend on the vehicle speed. Such a property is used to propose a novel method for vehicle classification based on only one signature acquired from a sensor single-loop, in contrast to standard methods using two sensor loops. Our proposal will be evaluated by means of real inductive signatures captured with our hardware prototype.

Analog fourier transform channelizer and OFDM receiver

OpenAIRE

2007-01-01

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

Vehicle Classification Using the Discrete Fourier Transform with Traffic Inductive Sensors

Directory of Open Access Journals (Sweden)

José J. Lamas-Seco

2015-10-01

Full Text Available Inductive Loop Detectors (ILDs are the most commonly used sensors in traffic management systems. This paper shows that some spectral features extracted from the Fourier Transform (FT of inductive signatures do not depend on the vehicle speed. Such a property is used to propose a novel method for vehicle classification based on only one signature acquired from a sensor single-loop, in contrast to standard methods using two sensor loops. Our proposal will be evaluated by means of real inductive signatures captured with our hardware prototype.

New design for photonic temporal integration with combined high processing speed and long operation time window.

Science.gov (United States)

Asghari, Mohammad H; Park, Yongwoo; Azaña, José

2011-01-17

We propose and experimentally prove a novel design for implementing photonic temporal integrators simultaneously offering a high processing bandwidth and a long operation time window, namely a large time-bandwidth product. The proposed scheme is based on concatenating in series a time-limited ultrafast photonic temporal integrator, e.g. implemented using a fiber Bragg grating (FBG), with a discrete-time (bandwidth limited) optical integrator, e.g. implemented using an optical resonant cavity. This design combines the advantages of these two previously demonstrated photonic integrator solutions, providing a processing speed as high as that of the time-limited ultrafast integrator and an operation time window fixed by the discrete-time integrator. Proof-of-concept experiments are reported using a uniform fiber Bragg grating (as the original time-limited integrator) connected in series with a bulk-optics coherent interferometers' system (as a passive 4-points discrete-time photonic temporal integrator). Using this setup, we demonstrate accurate temporal integration of complex-field optical signals with time-features as fast as ~6 ps, only limited by the processing bandwidth of the FBG integrator, over time durations as long as ~200 ps, which represents a 4-fold improvement over the operation time window (~50 ps) of the original FBG integrator.

Optimized Kaiser-Bessel Window Functions for Computed Tomography.

Science.gov (United States)

Nilchian, Masih; Ward, John Paul; Vonesch, Cedric; Unser, Michael

2015-11-01

Kaiser-Bessel window functions are frequently used to discretize tomographic problems because they have two desirable properties: 1) their short support leads to a low computational cost and 2) their rotational symmetry makes their imaging transform independent of the direction. In this paper, we aim at optimizing the parameters of these basis functions. We present a formalism based on the theory of approximation and point out the importance of the partition-of-unity condition. While we prove that, for compact-support functions, this condition is incompatible with isotropy, we show that minimizing the deviation from the partition of unity condition is highly beneficial. The numerical results confirm that the proposed tuning of the Kaiser-Bessel window functions yields the best performance.

Formal degrees of unipotent discrete series representations and the exotic Fourier transform

NARCIS (Netherlands)

Ciubotaru, D.; Opdam, E.

2015-01-01

We introduce a notion of elliptic fake degrees for unipotent elliptic representations of a semisimple p-adic group. We conjecture, and verify in some cases, that the relation between the formal degrees of unipotent discrete series representations of a semisimple p-adic group and the elliptic fake

Fourier band-power E/B-mode estimators for cosmic shear

Energy Technology Data Exchange (ETDEWEB)

Becker, Matthew R.; Rozo, Eduardo

2016-01-20

We introduce new Fourier band-power estimators for cosmic shear data analysis and E/B-mode separation. We consider both the case where one performs E/B-mode separation and the case where one does not. The resulting estimators have several nice properties which make them ideal for cosmic shear data analysis. First, they can be written as linear combinations of the binned cosmic shear correlation functions. Secondly, they account for the survey window function in real-space. Thirdly, they are unbiased by shape noise since they do not use correlation function data at zero separation. Fourthly, the band-power window functions in Fourier space are compact and largely non-oscillatory. Fifthly, they can be used to construct band-power estimators with very efficient data compression properties. In particular, we find that all of the information on the parameters Ωm, σ8 and ns in the shear correlation functions in the range of ~10–400 arcmin for single tomographic bin can be compressed into only three band-power estimates. Finally, we can achieve these rates of data compression while excluding small-scale information where the modelling of the shear correlation functions and power spectra is very difficult. Given these desirable properties, these estimators will be very useful for cosmic shear data analysis.

Window Glazing Types | Efficient Windows Collaborative

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Window Frame Types | Efficient Windows Collaborative

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An Efficient Algorithm for the Discrete Gabor Transform using full length Windows

DEFF Research Database (Denmark)

Søndergaard, Peter Lempel

2007-01-01

This paper extends the efficient factorization of the Gabor frame operator developed by Strohmer in [1] to the Gabor analysis/synthesis operator. This provides a fast method for computing the discrete Gabor transform (DGT) and several algorithms associated with it. The algorithm is used...

Efficient Algorithms for the Discrete Gabor Transform with a Long Fir Window

DEFF Research Database (Denmark)

Søndergaard, Peter Lempel

2012-01-01

The Discrete Gabor Transform (DGT) is the most commonly used signal transform for signal analysis and synthesis using a linear frequency scale. The development of the Linear Time-Frequency Analysis Toolbox (LTFAT) has been based on a detailed study of many variants of the relevant algorithms. As ...

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)

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...

On using moving windows in finite element time domain simulation for long accelerator structures

International Nuclear Information System (INIS)

Lee, L.-Q.; Candel, Arno; Ng, Cho; Ko, Kwok

2010-01-01

A finite element moving window technique is developed to simulate the propagation of electromagnetic waves induced by the transit of a charged particle beam inside large and long structures. The window moving along with the beam in the computational domain adopts high-order finite element basis functions through p refinement and/or a high-resolution mesh through h refinement so that a sufficient accuracy is attained with substantially reduced computational costs. Algorithms to transfer discretized fields from one mesh to another, which are the keys to implementing a moving window in a finite element unstructured mesh, are presented. Numerical experiments are carried out using the moving window technique to compute short-range wakefields in long accelerator structures. The results are compared with those obtained from the normal finite element time domain (FETD) method and the advantages of using the moving window technique are discussed.

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

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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…

Proper Installation of Replacement Windows | Efficient Windows

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

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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.

Performance Standards for Windows | Efficient Windows Collaborative

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Assessing Window Replacement Options | Efficient Windows Collaborative

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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.

Symmetrized neutron transport equation and the fast Fourier transform method

International Nuclear Information System (INIS)

Sinh, N.Q.; Kisynski, J.; Mika, J.

1978-01-01

The differential equation obtained from the neutron transport equation by the application of the source iteration method in two-dimensional rectangular geometry is transformed into a symmetrized form with respect to one of the angular variables. The discretization of the symmetrized equation leads to finite difference equations based on the five-point scheme and solved by use of the fast Fourier transform method. Possible advantages of the approach are shown on test calculations

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

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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

Gabor's expansion and the Zak transform for continuous-time and discrete-time signals : critical sampling and rational oversampling

NARCIS (Netherlands)

Bastiaans, M.J.

1995-01-01

Gabor's expansion of a signal into a discrete set of shifted and modulated versions of an elementary signal is introduced and its relation to sampling of the sliding-window spectrum is shown. It is shown how Gabor's expansion coefficients can be found as samples of the sliding-window spectrum, where

Multi-dimensional, fully-implicit, spectral method for the Vlasov-Maxwell equations with exact conservation laws in discrete form

Science.gov (United States)

Delzanno, G. L.

2015-11-01

A spectral method for the numerical solution of the multi-dimensional Vlasov-Maxwell equations is presented. The plasma distribution function is expanded in Fourier (for the spatial part) and Hermite (for the velocity part) basis functions, leading to a truncated system of ordinary differential equations for the expansion coefficients (moments) that is discretized with an implicit, second order accurate Crank-Nicolson time discretization. The discrete non-linear system is solved with a preconditioned Jacobian-Free Newton-Krylov method. It is shown analytically that the Fourier-Hermite method features exact conservation laws for total mass, momentum and energy in discrete form. Standard tests involving plasma waves and the whistler instability confirm the validity of the conservation laws numerically. The whistler instability test also shows that we can step over the fastest time scale in the system without incurring in numerical instabilities. Some preconditioning strategies are presented, showing that the number of linear iterations of the Krylov solver can be drastically reduced and a significant gain in performance can be obtained.

Discrete breathers dynamic in a model for DNA chain with a finite stacking enthalpy

Science.gov (United States)

Gninzanlong, Carlos Lawrence; Ndjomatchoua, Frank Thomas; Tchawoua, Clément

2018-04-01

The nonlinear dynamics of a homogeneous DNA chain based on site-dependent finite stacking and pairing enthalpies is studied. A new variant of extended discrete nonlinear Schrödinger equation describing the dynamics of modulated wave is derived. The regions of discrete modulational instability of plane carrier waves are studied, and it appears that these zones depend strongly on the phonon frequency of Fourier's mode. The staggered/unstaggered discrete breather (SDB/USDB) is obtained straightforwardly without the staggering transformation, and it is demonstrated that SDBs are less unstable than USDB. The instability of discrete multi-humped SDB/USDB solution does not depend on the number of peaks of the discrete breather (DB). By using the concept of Peierls-Nabarro energy barrier, it appears that the low-frequency DBs are more mobile.

Meniscal tears: comparison of half-Fourier technique and conventional MR imaging

International Nuclear Information System (INIS)

Shabana, Wael; Maeseneer, Michel de; Machiels, Freddy; Ridder, Filip de; Osteaux, Michel

2003-01-01

Purpose: To determine whether half-Fourier MR image acquisition technique can provide similar information to that of conventional MR acquisition technique for evaluation of meniscal tears. Materials and methods: We studied 101 menisci in 52 patients who were referred for evaluation of meniscal tears. Sagittal MR images of the knee were obtained for all patients by using proton density and T2-weighted SE sequences on a 1-T clinical system. The half-Fourier technique and conventional technique were used for all patients. All other imaging parameters were identical for both sequences (TR/TE=2400/20,70; 3 mm slice thickness; 200x256 matrix; field of view, 200; one signal acquired). Both sets of images were filmed with standard window and level settings. Images were randomised and interpreted independently by two radiologists for the presence of meniscal tears. Images were also subjectively assessed for image quality using a five-point grading scale. Results: On half-Fourier images, Reader 1 interpreted 23 menisci as torn, compared to 28 for Reader 2. On conventional images, Reader 1 interpreted 24 menisci as torn, compared to 26 for Reader 2. Agreement between interpretation of the conventional and that of the half-Fourier images was 99% for Reader 1, and 98% for Reader 2. Agreement between readers for the half-Fourier images was 95%, and for the conventional images 96%. No statistically significant difference was found in the subjective evaluation of image quality between the conventional and half-Fourier images. Conclusion: The half-Fourier acquisition technique compares favourably with the conventional technique for the evaluation of meniscal tears

Parameter study on infilled steel frames with discretely connected precast concrete panels

NARCIS (Netherlands)

Teeuwen, P.A.; Kleinman, C.S.; Snijder, H.H.; Hofmeyer, H.; Chan, S.L.

2009-01-01

This paper presents a parameter study on infilled steel frames with discretely connected precast concrete infill panels having window openings. In this study, finite element simulations were carried out to study the infilled frame performance by varying several parameters. A recently developed

Universal spectrum data analysis program for microsoft windows

International Nuclear Information System (INIS)

Hao, F.; Cai, Z.; Wang, H.

1993-01-01

We have developed a universal spectrum analysis and characterization program the Microsoft Windows environment. This sophisticated and easy to use software package can be employed in many areas for spectra data analysis, parametrization and line profile recognition. Spectra can for example be smoothed, calibrated and transformed from the laboratory frame to the projectile frame and background can be subtracted by using cubic spline functions or exponential functions. Up to 10 peaks and 40 different parameters can be fitted simultaneously either automatically by least squares routines or manually by system interactive devices. Line profiles include triangular, Gaussian, Lorentzian, Fano, Shore, post collisonal interactions functions etc., and also can be easily expanded to virtually any nonlinear fitting function. In addition, Fast Fourier Transform (FFT) routines allow users to convolute, deconvolute or Fourier analyze complex spectral patterns. Specifically this program has been applied for high resolution electron- and photon emission spectra following electron or ion collision with gaseous targets. Some examples for data evaluation will be presented

Real-time frequency-to-time mapping based on spectrally-discrete chromatic dispersion.

Science.gov (United States)

Dai, Yitang; Li, Jilong; Zhang, Ziping; Yin, Feifei; Li, Wangzhe; Xu, Kun

2017-07-10

Traditional photonics-assisted real-time Fourier transform (RTFT) usually suffers from limited chromatic dispersion, huge volume, or large time delay and attendant loss. In this paper we propose frequency-to-time mapping (FTM) by spectrally-discrete dispersion to increase frequency sensitivity greatly. The novel media has periodic ON/OFF intensity frequency response while quadratic phase distribution along disconnected channels, which de-chirps matched optical input to repeated Fourier-transform-limited output. Real-time FTM is then obtained within each period. Since only discrete phase retardation rather than continuously-changed true time delay is required, huge equivalent dispersion is then available by compact device. Such FTM is theoretically analyzed, and implementation by cascaded optical ring resonators is proposed. After a numerical example, our theory is demonstrated by a proof-of-concept experiment, where a single loop containing 0.5-meters-long fiber is used. FTM under 400-MHz unambiguous bandwidth and 25-MHz resolution is reported. Highly-sensitive and linear mapping is achieved with 6.25 ps/MHz, equivalent to ~4.6 × 10 4 -km standard single mode fiber. Extended instantaneous bandwidth is expected by ring cascading. Our proposal may provide a promising method for real-time, low-latency Fourier transform.

The inverse of winnowing: a FORTRAN subroutine and discussion of unwinnowing discrete data

Science.gov (United States)

Bracken, Robert E.

2004-01-01

This report describes an unwinnowing algorithm that utilizes a discrete Fourier transform, and a resulting Fortran subroutine that winnows or unwinnows a 1-dimensional stream of discrete data; the source code is included. The unwinnowing algorithm effectively increases (by integral factors) the number of available data points while maintaining the original frequency spectrum of a data stream. This has utility when an increased data density is required together with an availability of higher order derivatives that honor the original data.

Interpolation of the discrete logarithm in a finite field of characteristic two by Boolean functions

DEFF Research Database (Denmark)

Brandstaetter, Nina; Lange, Tanja; Winterhof, Arne

2005-01-01

We obtain bounds on degree, weight, and the maximal Fourier coefficient of Boolean functions interpolating the discrete logarithm in finite fields of characteristic two. These bounds complement earlier results for finite fields of odd characteristic....

Intermittent and sustained periodic windows in networked chaotic Rössler oscillators

International Nuclear Information System (INIS)

He, Zhiwei; Sun, Yong; Zhan, Meng

2013-01-01

Route to chaos (or periodicity) in dynamical systems is one of fundamental problems. Here, dynamical behaviors of coupled chaotic Rössler oscillators on complex networks are investigated and two different types of periodic windows with the variation of coupling strength are found. Under a moderate coupling, the periodic window is intermittent, and the attractors within the window extremely sensitively depend on the initial conditions, coupling parameter, and topology of the network. Therefore, after adding or removing one edge of network, the periodic attractor can be destroyed and substituted by a chaotic one, or vice versa. In contrast, under an extremely weak coupling, another type of periodic window appears, which insensitively depends on the initial conditions, coupling parameter, and network. It is sustained and unchanged for different types of network structure. It is also found that the phase differences of the oscillators are almost discrete and randomly distributed except that directly linked oscillators more likely have different phases. These dynamical behaviors have also been generally observed in other networked chaotic oscillators

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.

Unfolding and effective bandstructure calculations as discrete real- and reciprocal-space operations

Energy Technology Data Exchange (ETDEWEB)

Boykin, Timothy B., E-mail: boykin@ece.uah.edu [Department of Electrical and Computer Engineering, The University of Alabama in Huntsville, Huntsville, AL 35899 (United States); Ajoy, Arvind [School of Electrical and Computer Engineering, Cornell University, Ithaca, NY 14853 (United States); Ilatikhameneh, Hesameddin; Povolotskyi, Michael; Klimeck, Gerhard [Network for Computational Nanotechnology, School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907 (United States)

2016-06-15

In recent years, alloy electronic structure calculations based on supercell Brillouin zone unfolding have become popular. There are a number of formulations of the method which on the surface might appear different. Here we show that a discrete real-space description, based on discrete Fourier transforms, is fully general. Furthermore, such an approach can more easily show the effects of alloy scattering. We present such a method for treating the random alloy problem. This treatment features straightforward mathematics and a transparent physical interpretation of the calculated effective (i.e., approximate) energy bands.

Lateral behavior of steel frames with discretely connected precast concrete infill panels

NARCIS (Netherlands)

Teeuwen, P.A.

2009-01-01

As an alternative to the conventional structures for tall buildings, a hybrid lateral load resisting structure has been designed at Eindhoven University of Technology. It consists of discretely connected precast concrete panels with window openings in steel frames, and is a new application in

Windowed Multitaper Correlation Analysis of Multimodal Brain Monitoring Parameters

Directory of Open Access Journals (Sweden)

Rupert Faltermeier

2015-01-01

Full Text Available Although multimodal monitoring sets the standard in daily practice of neurocritical care, problem-oriented analysis tools to interpret the huge amount of data are lacking. Recently a mathematical model was presented that simulates the cerebral perfusion and oxygen supply in case of a severe head trauma, predicting the appearance of distinct correlations between arterial blood pressure and intracranial pressure. In this study we present a set of mathematical tools that reliably detect the predicted correlations in data recorded at a neurocritical care unit. The time resolved correlations will be identified by a windowing technique combined with Fourier-based coherence calculations. The phasing of the data is detected by means of Hilbert phase difference within the above mentioned windows. A statistical testing method is introduced that allows tuning the parameters of the windowing method in such a way that a predefined accuracy is reached. With this method the data of fifteen patients were examined in which we found the predicted correlation in each patient. Additionally it could be shown that the occurrence of a distinct correlation parameter, called scp, represents a predictive value of high quality for the patients outcome.

Windowed multitaper correlation analysis of multimodal brain monitoring parameters.

Science.gov (United States)

Faltermeier, Rupert; Proescholdt, Martin A; Bele, Sylvia; Brawanski, Alexander

2015-01-01

Although multimodal monitoring sets the standard in daily practice of neurocritical care, problem-oriented analysis tools to interpret the huge amount of data are lacking. Recently a mathematical model was presented that simulates the cerebral perfusion and oxygen supply in case of a severe head trauma, predicting the appearance of distinct correlations between arterial blood pressure and intracranial pressure. In this study we present a set of mathematical tools that reliably detect the predicted correlations in data recorded at a neurocritical care unit. The time resolved correlations will be identified by a windowing technique combined with Fourier-based coherence calculations. The phasing of the data is detected by means of Hilbert phase difference within the above mentioned windows. A statistical testing method is introduced that allows tuning the parameters of the windowing method in such a way that a predefined accuracy is reached. With this method the data of fifteen patients were examined in which we found the predicted correlation in each patient. Additionally it could be shown that the occurrence of a distinct correlation parameter, called scp, represents a predictive value of high quality for the patients outcome.

Replacement Windows for Existing Homes Homes | Efficient Windows

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Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Proper Installation of New Windows | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Individua l tree identification in airborne LASER data BY inverse SEARCH window

Directory of Open Access Journals (Sweden)

Eric Bastos Gorgens

2015-03-01

Full Text Available The local maximum filtering performance is highly dependent of the window size definition. This paper proposes that the window size should be determined by an inverse relationship to the canopy height model, and test the hypothesis that a windowsize inversely proportional will have better performance than the window proportional to the canopy height model. The study area is located in the southeastern region of the State of British Columbia, Canada. The natural vegetation is the boreal type and is characterized by the dominance of two species Picea engelmannii Parry ex. Engelmann (Engelmann spruce and Abies lasiocarpa (Hook. Nutt. (sub-alpine fir. The relief is mountainous with altitudes ranging from 650-2400 meters. 62 plots with 256 square meters were measured in the field. The airborne LiDAR had discrete returns, 2 points per square meter density and small-footprint. The performance of the search windows was evaluated based on success percentage, absolute average error and also compared to the observed values of the field plots. The local maximum filter underestimated the number of trees per hectare for both window sizing methods. The use of the inverse proportional window size has resulted in superior results, particularly for regions with highest density of trees.

On the finite Fourier transforms of functions with infinite discontinuities

Directory of Open Access Journals (Sweden)

Branko Saric

2002-01-01

Full Text Available The introductory part of the paper is provided to give a brief review of the stability theory of a matrix pencil for discrete linear time-invariant singular control systems, based on the causal relationship between Jordan's theorem from the theory of Fourier series and Laurent's theorem from the calculus of residues. The main part is concerned with the theory of the integral transforms, which has proved to be a powerful tool in the control systems theory. On the basis of a newly defined notion of the total value of improper integrals, throughout the main part of the paper, an attempt has been made to present the global theory of the integral transforms, which are slightly more general with respect to the Laplace and Fourier transforms. The paper ends with examples by which the results of the theory are verified.

A fast iterative model for discrete velocity calculations on triangular grids

International Nuclear Information System (INIS)

Szalmas, Lajos; Valougeorgis, Dimitris

2010-01-01

A fast synthetic type iterative model is proposed to speed up the slow convergence of discrete velocity algorithms for solving linear kinetic equations on triangular lattices. The efficiency of the scheme is verified both theoretically by a discrete Fourier stability analysis and computationally by solving a rarefied gas flow problem. The stability analysis of the discrete kinetic equations yields the spectral radius of the typical and the proposed iterative algorithms and reveal the drastically improved performance of the latter one for any grid resolution. This is the first time that stability analysis of the full discrete kinetic equations related to rarefied gas theory is formulated, providing the detailed dependency of the iteration scheme on the discretization parameters in the phase space. The corresponding characteristics of the model deduced by solving numerically the rarefied gas flow through a duct with triangular cross section are in complete agreement with the theoretical findings. The proposed approach may open a way for fast computation of rarefied gas flows on complex geometries in the whole range of gas rarefaction including the hydrodynamic regime.

Nonuniform fast Fourier transform method for numerical diffraction simulation on tilted planes.

Science.gov (United States)

Xiao, Yu; Tang, Xiahui; Qin, Yingxiong; Peng, Hao; Wang, Wei; Zhong, Lijing

2016-10-01

The method, based on the rotation of the angular spectrum in the frequency domain, is generally used for the diffraction simulation between the tilted planes. Due to the rotation of the angular spectrum, the interval between the sampling points in the Fourier domain is not even. For the conventional fast Fourier transform (FFT)-based methods, a spectrum interpolation is needed to get the approximate sampling value on the equidistant sampling points. However, due to the numerical error caused by the spectrum interpolation, the calculation accuracy degrades very quickly as the rotation angle increases. Here, the diffraction propagation between the tilted planes is transformed into a problem about the discrete Fourier transform on the uneven sampling points, which can be evaluated effectively and precisely through the nonuniform fast Fourier transform method (NUFFT). The most important advantage of this method is that the conventional spectrum interpolation is avoided and the high calculation accuracy can be guaranteed for different rotation angles, even when the rotation angle is close to π/2. Also, its calculation efficiency is comparable with that of the conventional FFT-based methods. Numerical examples as well as a discussion about the calculation accuracy and the sampling method are presented.

Generating a Square Switching Window for Timing Jitter Tolerant 160 Gb/s Demultiplexing by the Optical Fourier Transform Technique

DEFF Research Database (Denmark)

Oxenløwe, Leif Katsuo; Galili, Michael; Clausen, A. T:

2006-01-01

A square spectrum is optically Fourier transformed into a square pulse in the time domain. This is used to demultiplex a 160 Gb/s data signal with a significant increase in jitter tolerance to 2.6 ps.......A square spectrum is optically Fourier transformed into a square pulse in the time domain. This is used to demultiplex a 160 Gb/s data signal with a significant increase in jitter tolerance to 2.6 ps....

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

Modeling open nanophotonic systems using the Fourier modal method: Generalization to 3D Cartesian coordinates

DEFF Research Database (Denmark)

Häyrynen, Teppo; Østerkryger, Andreas Dyhl; de Lasson, Jakob Rosenkrantz

2017-01-01

Recently, an open geometry Fourier modal method based on a new combination ofan open boundary condition and a non-uniform $k$-space discretization wasintroduced for rotationally symmetric structures providing a more efficientapproach for modeling nanowires and micropillar cavities [J. Opt. Soc. A...... moreaccurate and efficient modeling of open 3D nanophotonic structures....

Application of Fourier transform to MHD flow over an accelerated plate with partial-slippage

Directory of Open Access Journals (Sweden)

Salman Ahmad

2014-06-01

Full Text Available Magneto-Hydrodynamic (MHD flow over an accelerated plate is investigated with partial slip conditions. Generalized Fourier Transform is used to get the exact solution not only for uniform acceleration but also for variable acceleration. The numerical solution is obtained by using linear finite element method in space and One-Step-θ-scheme in time. The resulting discretized algebraic systems are solved by applying geometric-multigrid approach. Numerical solutions are compared with the obtained Fourier transform results. Many interesting results related with slippage and MHD effects are discussed in detail through graphical sketches and tables. Application of Dirac-Delta function is one of the main features of present work.

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

Fault Diagnosis of Induction Machines in a Transient Regime Using Current Sensors with an Optimized Slepian Window.

Science.gov (United States)

Burriel-Valencia, Jordi; Puche-Panadero, Ruben; Martinez-Roman, Javier; Sapena-Bano, Angel; Pineda-Sanchez, Manuel

2018-01-06

The aim of this paper is to introduce a new methodology for the fault diagnosis of induction machines working in the transient regime, when time-frequency analysis tools are used. The proposed method relies on the use of the optimized Slepian window for performing the short time Fourier transform (STFT) of the stator current signal. It is shown that for a given sequence length of finite duration, the Slepian window has the maximum concentration of energy, greater than can be reached with a gated Gaussian window, which is usually used as the analysis window. In this paper, the use and optimization of the Slepian window for fault diagnosis of induction machines is theoretically introduced and experimentally validated through the test of a 3.15-MW induction motor with broken bars during the start-up transient. The theoretical analysis and the experimental results show that the use of the Slepian window can highlight the fault components in the current's spectrogram with a significant reduction of the required computational resources.

Fault Diagnosis of Induction Machines in a Transient Regime Using Current Sensors with an Optimized Slepian Window

Directory of Open Access Journals (Sweden)

Jordi Burriel-Valencia

2018-01-01

Full Text Available The aim of this paper is to introduce a new methodology for the fault diagnosis of induction machines working in the transient regime, when time-frequency analysis tools are used. The proposed method relies on the use of the optimized Slepian window for performing the short time Fourier transform (STFT of the stator current signal. It is shown that for a given sequence length of finite duration, the Slepian window has the maximum concentration of energy, greater than can be reached with a gated Gaussian window, which is usually used as the analysis window. In this paper, the use and optimization of the Slepian window for fault diagnosis of induction machines is theoretically introduced and experimentally validated through the test of a 3.15-MW induction motor with broken bars during the start-up transient. The theoretical analysis and the experimental results show that the use of the Slepian window can highlight the fault components in the current’s spectrogram with a significant reduction of the required computational resources.

Windows

DEFF Research Database (Denmark)

Heiselberg, Per; Svidt, Kjeld; Nielsen, Peter V.

In natural ventilation systems fresh air is often provided through opening of windows. However, the knowledge of the performance of windows is rather limited. Computation of natural ventilation air flow through windows is most commonly made using discharge coefficients, that are regarded as being...... constant. The reported results show that the discharge coefficient for a window opening cannot be regarded as a constant and that it varies considerably with the size of the opening area, the window type and the temperature difference. Therefore, the use of a constant value can lead to serious errors...

Discrete coherent and squeezed states of many-qudit systems

International Nuclear Information System (INIS)

Klimov, Andrei B.; Munoz, Carlos; Sanchez-Soto, Luis L.

2009-01-01

We consider the phase space for n identical qudits (each one of dimension d, with d a primer number) as a grid of d n xd n points and use the finite Galois field GF(d n ) to label the corresponding axes. The associated displacement operators permit to define s-parametrized quasidistributions on this grid, with properties analogous to their continuous counterparts. These displacements allow also for the construction of finite coherent states, once a fiducial state is fixed. We take this reference as one eigenstate of the discrete Fourier transform and study the factorization properties of the resulting coherent states. We extend these ideas to include discrete squeezed states, and show their intriguing relation with entangled states of different qudits.

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.

3-D spherical harmonics code FFT3 by the finite Fourier transformation method

International Nuclear Information System (INIS)

Kobayashi, K.

1997-01-01

In the odd order spherical harmonics method, the rigorous boundary condition at the material interfaces is that the even moments of the angular flux and the normal components of the even order moments of current vectors must be continuous. However, it is difficult to derive spatial discretized equations by the finite difference or finite element methods, which satisfy this material interface condition. It is shown that using the finite Fourier transformation method, space discretized equations which satisfy this interface condition can be easily derived. The discrepancies of the flux distribution near void region between spherical harmonics method codes may be due to the difference of application of the material interface condition. (author)

Structure and isostatic compensation of the Comorin Ridge, north central Indian Ocean

Digital Repository Service at National Institute of Oceanography (India)

Sreejith, K.M.; Krishna, K.S.; Bansal, A.R.

of the ridge. Additionally, ETOPO-5 bathymetric data (3-D image) are used to study the mor- phology of the ridge. Sediment isopachs of this region published by Kahle et al. (1981) are also considered for 2-D forward modelling of gravity anomalies to constrain... admittance. In this method, bathymetry and gravity data are divided into overlapping segments and each of them is detrended, windowed using Hanning window and discrete Fourier transformed. Two more additional parameters, coherence and phase of admittance...

The use of Fourier eigen transform to the boundary element method for transient elastodynamic problems

International Nuclear Information System (INIS)

Ji, X.; Chen, Y.M.

1989-01-01

The boundary element method (BEM) is developed from the boundary integral equation method and the discretization techniques. Compared with other numerical method, BEM has been shown to be a versatile and efficient method for a wide variety of engineering problems, including the wave propagation in elastic media. The first formulation and solution of the transient elastodynamic problem by combining BEM and Laplace transform is due to Cruse. Further improvement was achieved by introducing Durbin's method instead of Papoulis method of numerical Laplace inverse transform. However, a great deal of computer time is still needed for the inverse transformation. The alternative integral transform approach is BEM combining with Fourier transform. The numerical Fourier inverse transformation is also computer time consuming, even if the fast Fourier transform is used. In the present paper, the authors use BEM combining with Fourier transform and Fourier eigen transform (FET). The new approach is very attractive in saving on computer time. This paper illustrates the application of FET to BEM of 2-dimensional transient elastodynamic problem. The example of a half plane subjected to a discontinuous boundary load is solved on ELXSI 6400 computer. The CPU time is less than one minute. If Laplace or Fourier transform is adopted, the CPU time will be more than 10 minutes

Energy window selection for a radiation signal processing system

International Nuclear Information System (INIS)

Knoll, G.F.; Schrader, M.E.

1986-01-01

This invention provides an apparatus and method for selecting only meaningful information from signals produced by Anger-type radioisotope cameras producing positional information. It is an improvement in the means for determining energy threshold values as a function of radiation event positional information. The establishment of an energy threshold table begins by flooding the camera face with a uniform source of radiation and utilizing the pre-established spatial translation table to reposition detected radiation events according to their true spatial element coordinates. A histogram is compiled for each spatial element, the histogram comprising the number of radiation events occurring at several discrete energy levels. A peak centroid value is then determined for each element, and an initial energy window is set. Next, a specified region of the camera field of view is inspected to determine a target sum of radiation events to be accepted by each element, setting a standard for adjusting the energy windows of each element. Using this standard, the energy window for each element is progressively adapted so that each will accept nearly the same number of radiation events or counts in response to a flood or calibration image. Finally the energy window for each true spatial element is translated back to its apparent spatial element and incorporated into an energy threshold table accessible by the apparent spatial coordinates of each radiation event

Full-scale testing of infilled steel frames with precast concrete panels provided with a window opening

NARCIS (Netherlands)

Teeuwen, P.A; Kleinman, C.S.; Snijder, H.H.; Hofmeyer, H.

2008-01-01

As an alternative to conventional structures for tall buildings, a hybrid lateral load resisting building system has been designed, enabling the assembly of tall buildings directly from truck. It consists of steel frames with discretely connected precast concrete infill panels provided with a window

Simulating first order optical systems—algorithms for and composition of discrete linear canonical transforms

Science.gov (United States)

Healy, John J.

2018-01-01

The linear canonical transforms (LCTs) are a parameterised group of linear integral transforms. The LCTs encompass a number of well-known transformations as special cases, including the Fourier transform, fractional Fourier transform, and the Fresnel integral. They relate the scalar wave fields at the input and output of systems composed of thin lenses and free space, along with other quadratic phase systems. In this paper, we perform a systematic search of all algorithms based on up to five stages of magnification, chirp multiplication and Fourier transforms. Based on that search, we propose a novel algorithm, for which we present numerical results. We compare the sampling requirements of three algorithms. Finally, we discuss some issues surrounding the composition of discrete LCTs.

The spectral transform as a tool for solving nonlinear discrete evolution equations

International Nuclear Information System (INIS)

Levi, D.

1979-01-01

In this contribution we study nonlinear differential difference equations which became important to the description of an increasing number of problems in natural science. Difference equations arise for instance in the study of electrical networks, in statistical problems, in queueing problems, in ecological problems, as computer models for differential equations and as models for wave excitation in plasma or vibrations of particles in an anharmonic lattice. We shall first review the passages necessary to solve linear discrete evolution equations by the discrete Fourier transfrom, then, starting from the Zakharov-Shabat discretized eigenvalue, problem, we shall introduce the spectral transform. In the following part we obtain the correlation between the evolution of the potentials and scattering data through the Wronskian technique, giving at the same time many other properties as, for example, the Baecklund transformations. Finally we recover some of the important equations belonging to this class of nonlinear discrete evolution equations and extend the method to equations with n-dependent coefficients. (HJ)

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

Discrete mode laser diodes for FTTH/PON applications up to 10 Gbit/s

NARCIS (Netherlands)

O'Carroll, J.; Phelan, R.; Kelly, B.; Byrne, D.; Latkowski, S.; Anandarajah, P.M.; Barry, L.P.

2012-01-01

Discrete Mode Laser Diodes (DMLDs) present an economic approach with a focus on high volume manufacturability of single mode lasers using a single step fabrication process. We report on a DMLD designed for operation in the 1550 nm window with high Side Mode Suppression Ratio (SMSR) over a wide

A novel recursive Fourier transform for nonuniform sampled signals: application to heart rate variability spectrum estimation.

Science.gov (United States)

Holland, Alexander; Aboy, Mateo

2009-07-01

We present a novel method to iteratively calculate discrete Fourier transforms for discrete time signals with sample time intervals that may be widely nonuniform. The proposed recursive Fourier transform (RFT) does not require interpolation of the samples to uniform time intervals, and each iterative transform update of N frequencies has computational order N. Because of the inherent non-uniformity in the time between successive heart beats, an application particularly well suited for this transform is power spectral density (PSD) estimation for heart rate variability. We compare RFT based spectrum estimation with Lomb-Scargle Transform (LST) based estimation. PSD estimation based on the LST also does not require uniform time samples, but the LST has a computational order greater than Nlog(N). We conducted an assessment study involving the analysis of quasi-stationary signals with various levels of randomly missing heart beats. Our results indicate that the RFT leads to comparable estimation performance to the LST with significantly less computational overhead and complexity for applications requiring iterative spectrum estimations.

Discrete transforms

CERN Document Server

Firth, Jean M

1992-01-01

The analysis of signals and systems using transform methods is a very important aspect of the examination of processes and problems in an increasingly wide range of applications. Whereas the initial impetus in the development of methods appropriate for handling discrete sets of data occurred mainly in an electrical engineering context (for example in the design of digital filters), the same techniques are in use in such disciplines as cardiology, optics, speech analysis and management, as well as in other branches of science and engineering. This text is aimed at a readership whose mathematical background includes some acquaintance with complex numbers, linear differen­ tial equations, matrix algebra, and series. Specifically, a familiarity with Fourier series (in trigonometric and exponential forms) is assumed, and an exposure to the concept of a continuous integral transform is desirable. Such a background can be expected, for example, on completion of the first year of a science or engineering degree cour...

Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra

Energy Technology Data Exchange (ETDEWEB)

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R., E-mail: Jeffrey.D.Scargle@nasa.gov, E-mail: Michael.J.Way@nasa.gov, E-mail: PGazis@sbcglobal.net [NASA Ames Research Center, Astrobiology and Space Science Division, Moffett Field, CA 94035 (United States)

2017-04-10

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.

Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra

International Nuclear Information System (INIS)

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R.

2017-01-01

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.

Application of Local Fourier Transform to Mathematical Simulation of Synchronous Machines with Valve Excitation Systems

Directory of Open Access Journals (Sweden)

Fedotov A.

2017-02-01

Full Text Available The article proposes a method of mathematical simulation of electrical machines with thyristor exciters on the basis of the local Fourier transform. The present research demonstrates that this method allows switching from a variable structure model to a constant structure model. Transition from the continuous variables to the discrete variables is used. The numerical example is given in the paper.

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.

Dark discrete gauge symmetries

International Nuclear Information System (INIS)

Batell, Brian

2011-01-01

We investigate scenarios in which dark matter is stabilized by an Abelian Z N discrete gauge symmetry. Models are surveyed according to symmetries and matter content. Multicomponent dark matter arises when N is not prime and Z N contains one or more subgroups. The dark sector interacts with the visible sector through the renormalizable kinetic mixing and Higgs portal operators, and we highlight the basic phenomenology in these scenarios. In particular, multiple species of dark matter can lead to an unconventional nuclear recoil spectrum in direct detection experiments, while the presence of new light states in the dark sector can dramatically affect the decays of the Higgs at the Tevatron and LHC, thus providing a window into the gauge origin of the stability of dark matter.

Windows Azure

CERN Document Server

Johnson, Bruce; Chambers, James; Garber, Danny; Malik, Jamal; Fazio, Adam

2013-01-01

A collection of five must-have Azure titles, from some of the biggest names in the field Available individually, but at a discounted rate for the collection, this bundle of five e-books covers key developer and IT topics of Windows Azure, including ASP.NET, mobile services, web sites, data storage, and the hybrid cloud. A host of Microsoft employees and MPVs come together to cover the biggest challenges that professionals face when working with Windows Azure. The e-books included are as follows: Windows Azure and ASP.NET MVC MigrationWindows Azure Mobile ServicesWindows Azure Web SitesWindows

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.

Learning Windows Azure Mobile Services for Windows 8 and Windows Phone 8

CERN Document Server

Webber-Cross, Geoff

2014-01-01

This book is based around a case study game which was written for the book. This means that the chapters progress in a logical way and build upon lessons learned as we go. Real-world examples are provided for each topic that are practical and not given out-of-context so they can be applied directly to other applications.If you are a developer who wishes to build Windows 8 and Phone 8 applications and integrate them with Windows Azure Mobile Services, this book is for you. Basic C# and JavaScript skills are advantageous, as well as some knowledge of building Windows 8 or Windows Phone 8 applica

DEVS representation of dynamical systems - Event-based intelligent control. [Discrete Event System Specification

Science.gov (United States)

Zeigler, Bernard P.

1989-01-01

It is shown how systems can be advantageously represented as discrete-event models by using DEVS (discrete-event system specification), a set-theoretic formalism. Such DEVS models provide a basis for the design of event-based logic control. In this control paradigm, the controller expects to receive confirming sensor responses to its control commands within definite time windows determined by its DEVS model of the system under control. The event-based contral paradigm is applied in advanced robotic and intelligent automation, showing how classical process control can be readily interfaced with rule-based symbolic reasoning systems.

Diffraction efficiency of photothermoplastic layers for the recording of discrete holograms

Science.gov (United States)

Koreshev, S. N.; Cherkasov, Yu. A.; Kislovskiy, I. L.

1987-01-01

An experimental and theoretical study of the dependence of eta of a digital phase Fourier hologram of a point object on the amount of deformation delta and the discrete-structure parameters representing the hologram is detailed. An expression is given for eta. Experiments were performed on photothermoplastic layers based on polyvinyl carbazole and trinitrofluorenone charge transfer complexes. The maximum eta, 2%, is found at delta = 0.56 micron.

Iterative algorithm of discrete Fourier transform for processing randomly sampled NMR data sets

International Nuclear Information System (INIS)

Stanek, Jan; Kozminski, Wiktor

2010-01-01

Spectra obtained by application of multidimensional Fourier Transformation (MFT) to sparsely sampled nD NMR signals are usually corrupted due to missing data. In the present paper this phenomenon is investigated on simulations and experiments. An effective iterative algorithm for artifact suppression for sparse on-grid NMR data sets is discussed in detail. It includes automated peak recognition based on statistical methods. The results enable one to study NMR spectra of high dynamic range of peak intensities preserving benefits of random sampling, namely the superior resolution in indirectly measured dimensions. Experimental examples include 3D 15 N- and 13 C-edited NOESY-HSQC spectra of human ubiquitin.

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

Discretization and Numerical Solution of a Plane Problem in the Mechanics of Interfacial Cracks

Science.gov (United States)

Khoroshun, L. P.

2017-01-01

The Fourier transform is used to reduce the linear plane problem of the tension of a body with an interfacial crack to a system of dual equations for the transformed stresses and, then, to a system of integro-differential equations for the difference of displacements of the crack faces. After discretization, this latter system transforms into a system of algebraic equations for displacements of the crack faces. The effect of the bielastic constant and the number of discretization points on the half-length of the crack faces and the distribution of stresses at the interface is studied

Preparing the generalized Harvey–Shack rough surface scattering method for use with the discrete ordinates method

DEFF Research Database (Denmark)

Johansen, Villads Egede

2015-01-01

The paper shows how to implement the generalized Harvey–Shack (GHS) method for isotropic rough surfaces discretized in a polar coordinate system and approximated using Fourier series. This is particularly relevant for the use of the GHS method as a boundary condition for radiative transfer proble...

Fourier transforms in NMR, optical, and mass spectrometry

International Nuclear Information System (INIS)

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

1990-01-01

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

Monitoring wine aging with Fourier transform infrared spectroscopy (FT-IR

Directory of Open Access Journals (Sweden)

Basalekou Marianthi

2015-01-01

Full Text Available Oak wood has commonly been used in wine aging but recently other wood types such as Acacia and Chestnut, have attracted the interest of the researchers due to their possible positive contribution to wine quality. However, only the use of oak and chestnut woods is approved by the International Enological Codex of the International Organisation of Vine and Wine. In this study Fourier Transform (FT-mid-infrared spectroscopy combined with Discriminant Analysis was used to differentiate wines aged in barrels made from French oak, American oak, Acacia and Chestnut and in tanks with oak chips, over a period of 12 months. Two red (Mandilaria, Kotsifali and two white (Vilana, Dafni native Greek grape varieties where used to produce four wines. The Fourier Transform Infrared (FT-IR spectra of the samples were recorded on a Zinc Selenide (ZnSe window after incubation at 40 °C for 30 min. A complete differentiation of the samples according to both the type of wood used and the contact time was achieved based on their FT-IR spectra.

Adaptive Filtering to Enhance Noise Immunity of Impedance and Admittance Spectroscopy: Comparison with Fourier Transformation

Science.gov (United States)

Stupin, Daniil D.; Koniakhin, Sergei V.; Verlov, Nikolay A.; Dubina, Michael V.

2017-05-01

The time-domain technique for impedance spectroscopy consists of computing the excitation voltage and current response Fourier images by fast or discrete Fourier transformation and calculating their relation. Here we propose an alternative method for excitation voltage and current response processing for deriving a system impedance spectrum based on a fast and flexible adaptive filtering method. We show the equivalence between the problem of adaptive filter learning and deriving the system impedance spectrum. To be specific, we express the impedance via the adaptive filter weight coefficients. The noise-canceling property of adaptive filtering is also justified. Using the RLC circuit as a model system, we experimentally show that adaptive filtering yields correct admittance spectra and elements ratings in the high-noise conditions when the Fourier-transform technique fails. Providing the additional sensitivity of impedance spectroscopy, adaptive filtering can be applied to otherwise impossible-to-interpret time-domain impedance data. The advantages of adaptive filtering are justified with practical living-cell impedance measurements.

Accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations on rectangular domains

Science.gov (United States)

Ji, Songsong; Yang, Yibo; Pang, Gang; Antoine, Xavier

2018-01-01

The aim of this paper is to design some accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations in rectangular domains. The Laplace transform in time and discrete Fourier transform in space are applied to get Green's functions of the semi-discretized equations in unbounded domains with single-source. An algorithm is given to compute these Green's functions accurately through some recurrence relations. Furthermore, the finite-difference method is used to discretize the reduced problem with accurate boundary conditions. Numerical simulations are presented to illustrate the accuracy of our method in the case of the linear Schrödinger and heat equations. It is shown that the reflection at the corners is correctly eliminated.

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

Windows server cookbook for Windows server 2003 and Windows 2000

CERN Document Server

Allen, Robbie

2005-01-01

This practical reference guide offers hundreds of useful tasks for managing Windows 2000 and Windows Server 2003, Microsoft's latest server. These concise, on-the-job solutions to common problems are certain to save you many hours of time searching through Microsoft documentation. Topics include files, event logs, security, DHCP, DNS, backup/restore, and more

MS Windows domēna darbstaciju migrācija no MS Windows XP uz Windows Vista.

OpenAIRE

Tetere, Agate

2009-01-01

Kvalifikācijas darbā izpētīju darbstaciju migrācijas no Windows XP uz Windows Vista plusus un mīnusus. Darba gaitā tika veikti sekojoši uzdevumi: 1.Veikta Windows XP un Windows Vista darbstaciju instalācija, iestatījumu konfigurēšana un tika pārbaudīta sistēmas darbība 2.Veikta Windows Server 2003 un Windows Server 2008 instalācija, iestatījumu konfigurēšana un tika pārbaudīta sistēmas darbība 3.Izstrādāts migrācijas modelis 4.Veikta migrācijas optimizēšana 5.Veikta datu migrāc...

The Fourier-grid formalism: philosophy and application to scattering problems using R-matrix theory

International Nuclear Information System (INIS)

Layton, E.G.

1993-01-01

The Fourier-grid (FG) method is a recent L 2 variational treatment of the quantum mechanical eigenvalue problem that does not require the use of a set of basis functions; it is rather a discrete variable representation approach. In this article we restate the FG philosophy in more general terms, examine and compare this method with other approaches to the eigenvalue problem, and begin the development of an FG R-matrix method for scattering. The philosophy of the FG method is to use the simplest representation for each of the kinetic and potential energy operators of the Hamiltonian, and use a generalized Fourier transform to put the matrix elements of one of the above operators in the same representation as the other, so the Hamiltonian has a single representation. (author)

Grab Windows training opportunities; check CERN Windows roadmap!

CERN Multimedia

IT Department

2011-01-01

CERN Operating Systems and Information Services group (IT-OIS) actively monitors market trends to check how new software products correspond to CERN needs. In the Windows world, Windows 7 has been a big hit, with over 1500 Windows 7 PCs within less than a year since its support was introduced at CERN. No wonder: Windows XP is nearly 10 years old and is steadily approaching the end of its life-cycle. At CERN, support for Windows XP will stop at the end of December 2012. Compared to Vista, Windows 7 has the same basic hardware requirements, but offers higher performance, so the decision to upgrade is rather straightforward. CERN support for Vista will end in June 2011. In the world of Microsoft Office, version 2007 offers better integration with the central services than the older version 2003. Progressive upgrade from 2003 to 2007 is planned to finish in September 2011, but users are encouraged to pro-actively upgrade at their convenience. Please note that Office 2007 brings an important change in the area of ...

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)

Natural history of Streptococcus sanguinis in the oral cavity of infants: evidence for a discrete window of infectivity.

Science.gov (United States)

Caufield, P W; Dasanayake, A P; Li, Y; Pan, Y; Hsu, J; Hardin, J M

2000-07-01

The heterogeneous group of oral bacteria within the sanguinis (sanguis) streptococci comprise members of the indigenous biota of the human oral cavity. While the association of Streptococcus sanguinis with bacterial endocarditis is well described in the literature, S. sanguinis is thought to play a benign, if not a beneficial, role in the oral cavity. Little is known, however, about the natural history of S. sanguinis and its specific relationship with other oral bacteria. As part of a longitudinal study concerning the transmission and acquisition of oral bacteria within mother-infant pairs, we examined the initial acquisition of S. sanguinis and described its colonization relative to tooth emergence and its proportions in plaque and saliva as a function of other biological events, including subsequent colonization with mutans streptococci. A second cohort of infants was recruited to define the taxonomic affiliation of S. sanguinis. We found that the colonization of the S. sanguinis occurs during a discrete "window of infectivity" at a median age of 9 months in the infants. Its colonization is tooth dependent and correlated to the time of tooth emergence; its proportions in saliva increase as new teeth emerge. In addition, early colonization of S. sanguinis and its elevated levels in the oral cavity were correlated to a significant delay in the colonization of mutans streptococci. Underpinning this apparent antagonism between S. sanguinis and mutans streptococci is the observation that after mutans streptococci colonize the infant, the levels of S. sanguinis decrease. Children who do not harbor detectable levels of mutans streptococci have significantly higher levels of S. sanguinis in their saliva than do children colonized with mutans streptococci. Collectively, these findings suggest that the colonization of S. sanguinis may influence the subsequent colonization of mutans streptococci, and this in turn may suggest several ecological approaches toward controlling

Seismic Shear Energy Reflection By Radon-Fourier Transform

Directory of Open Access Journals (Sweden)

Malik Umairia

2016-01-01

Full Text Available Seismic waves split in an anisotropic medium, instead of rotating horizontal component to principal direction, Radon-Fourier is derived to observe the signature of shear wave reflection. Synthetic model with fracture is built and discretized using finite difference scheme for spatial and time domain. Common depth point (CDP with single shot gives traces and automatic gain is preprocessed before Radon Transform (RT, a filtering technique gives radon domain. It makes easier to observe fractures at specific incidence and improves its quality in some way by removing the noise. A comparison of synthetic data and BF-data is performed on the basis of root means square error (RMS values. The RMS error is minimum at the 10th trace in radon domain.

Fast Algorithm for Computing the Discrete Hartley Transform of Type-II

Directory of Open Access Journals (Sweden)

Mounir Taha Hamood

2016-06-01

Full Text Available The generalized discrete Hartley transforms (GDHTs have proved to be an efficient alternative to the generalized discrete Fourier transforms (GDFTs for real-valued data applications. In this paper, the development of direct computation of radix-2 decimation-in-time (DIT algorithm for the fast calculation of the GDHT of type-II (DHT-II is presented. The mathematical analysis and the implementation of the developed algorithm are derived, showing that this algorithm possesses a regular structure and can be implemented in-place for efficient memory utilization.The performance of the proposed algorithm is analyzed and the computational complexity is calculated for different transform lengths. A comparison between this algorithm and existing DHT-II algorithms shows that it can be considered as a good compromise between the structural and computational complexities.

Search for the periodicity of the prime Indian and American stock exchange indices using date-compensated discrete Fourier transform

International Nuclear Information System (INIS)

Samadder, Swetadri; Ghosh, Koushik; Basu, Tapasendra

2015-01-01

The behaviour of Indian stock markets has a persistent close association with the behaviour of American stock exchange. The present work is an effort in this direction and the purpose of the present work is to investigate the periodicity of the two prime Indian stock market indices viz. SENSEX and NIFTY and the prime American stock market indices viz. DOW-JONES and S&P500. To serve the present purpose we have here used SENSEX logarithmic daily close data during the period from 1st January, 1990 to 31st December, 2013, NIFTY logarithmic daily close data during the period from 3rd July, 1990 to 31st December, 2013, DOW-JONES logarithmic daily close data during the period from 10th January, 1928 to 31st December, 2013 and S&P500 logarithmic daily close data during the period 3rd January, 1950 to 31st December, 2013. For the present analysis we have first used double exponential smoothing on all the four time series in order to remove the trend and next we have generated monthly averages of the smoothed time series in order to remove the irregular fluctuations. At the final stage Ferraz-Mello method of date-compensated discrete Fourier transform (DCDFT) has been applied on the present four double-smoothed monthly averaged time series. Study reveals periods for SENSEX of 11, 53 and 142 months; for NIFTY periods of 22, 38, 52 and 139 months; for DOW-JONES periods of 23, 25, 27, 30, 59, 107, 138, 194 and 494 months and for S&P500 periods of 28, 66, 74, 149 and 384 months. With this specific periodic behaviour we have also observed some pseudo-periods in the present four financial time series which certainly adds to the uncertainty in the process of prediction for the same

Discrete gradients in discrete classical mechanics

International Nuclear Information System (INIS)

Renna, L.

1987-01-01

A simple model of discrete classical mechanics is given where, starting from the continuous Hamilton equations, discrete equations of motion are established together with a proper discrete gradient definition. The conservation laws of the total discrete momentum, angular momentum, and energy are demonstrated

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.

Resolution optimization with irregularly sampled Fourier data

International Nuclear Information System (INIS)

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

2013-01-01

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

Window Stories

DEFF Research Database (Denmark)

Hauge, Bettina

This research project has investigated 17 households in Germany (cities and rural areas). The main aim was to learn about the significance of the window to these people: What they think of their windows, how, when and why they use them in their everyday life, if they have a favorite window and wh...

Windows 10 simplified

CERN Document Server

McFedries, Paul

2015-01-01

Learn Windows 10 quickly and painlessly with this beginner's guide Windows 10 Simplified is your absolute beginner's guide to the ins and outs of Windows. Fully updated to cover Windows 10, this highly visual guide covers all the new features in addition to the basics, giving you a one-stop resource for complete Windows 10 mastery. Every page features step-by-step screen shots and plain-English instructions that walk you through everything you need to know, no matter how new you are to Windows. You'll master the basics as you learn how to navigate the user interface, work with files, create

Windows and doors

Energy Technology Data Exchange (ETDEWEB)

1988-01-01

A complete manual is presented on windows and doors for the housing contractor. In order to understand the role of windows and doors in a house's energy performance, an introduction explains the house as a system of components that can have effects on each other. Further chapters explain in detail the parts of a window, window types and RSI values; window servicing and repair; window replacement; parts of a door, door types and RSI values; door service and repair, including weatherstripping; door replacement; and how to ensure quality, service, and customer satisfaction. A glossary of terms is included. 61 figs., 3 tabs.

Using high-order methods on adaptively refined block-structured meshes - discretizations, interpolations, and filters.

Energy Technology Data Exchange (ETDEWEB)

Ray, Jaideep; Lefantzi, Sophia; Najm, Habib N.; Kennedy, Christopher A.

2006-01-01

Block-structured adaptively refined meshes (SAMR) strive for efficient resolution of partial differential equations (PDEs) solved on large computational domains by clustering mesh points only where required by large gradients. Previous work has indicated that fourth-order convergence can be achieved on such meshes by using a suitable combination of high-order discretizations, interpolations, and filters and can deliver significant computational savings over conventional second-order methods at engineering error tolerances. In this paper, we explore the interactions between the errors introduced by discretizations, interpolations and filters. We develop general expressions for high-order discretizations, interpolations, and filters, in multiple dimensions, using a Fourier approach, facilitating the high-order SAMR implementation. We derive a formulation for the necessary interpolation order for given discretization and derivative orders. We also illustrate this order relationship empirically using one and two-dimensional model problems on refined meshes. We study the observed increase in accuracy with increasing interpolation order. We also examine the empirically observed order of convergence, as the effective resolution of the mesh is increased by successively adding levels of refinement, with different orders of discretization, interpolation, or filtering.

The water vapour continuum in near-infrared windows - Current understanding and prospects for its inclusion in spectroscopic databases

Science.gov (United States)

Shine, Keith P.; Campargue, Alain; Mondelain, Didier; McPheat, Robert A.; Ptashnik, Igor V.; Weidmann, Damien

2016-09-01

Spectroscopic catalogues, such as GEISA and HITRAN, do not yet include information on the water vapour continuum that pervades visible, infrared and microwave spectral regions. This is partly because, in some spectral regions, there are rather few laboratory measurements in conditions close to those in the Earth's atmosphere; hence understanding of the characteristics of the continuum absorption is still emerging. This is particularly so in the near-infrared and visible, where there has been renewed interest and activity in recent years. In this paper we present a critical review focusing on recent laboratory measurements in two near-infrared window regions (centred on 4700 and 6300 cm-1) and include reference to the window centred on 2600 cm-1 where more measurements have been reported. The rather few available measurements, have used Fourier transform spectroscopy (FTS), cavity ring down spectroscopy, optical-feedback - cavity enhanced laser spectroscopy and, in very narrow regions, calorimetric interferometry. These systems have different advantages and disadvantages. Fourier Transform Spectroscopy can measure the continuum across both these and neighbouring windows; by contrast, the cavity laser techniques are limited to fewer wavenumbers, but have a much higher inherent sensitivity. The available results present a diverse view of the characteristics of continuum absorption, with differences in continuum strength exceeding a factor of 10 in the cores of these windows. In individual windows, the temperature dependence of the water vapour self-continuum differs significantly in the few sets of measurements that allow an analysis. The available data also indicate that the temperature dependence differs significantly between different near-infrared windows. These pioneering measurements provide an impetus for further measurements. Improvements and/or extensions in existing techniques would aid progress to a full characterisation of the continuum - as an example, we

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.)

Nonlinear nano-scale localized breather modes in a discrete weak ferromagnetic spin lattice

International Nuclear Information System (INIS)

Kavitha, L.; Parasuraman, E.; Gopi, D.; Prabhu, A.; Vicencio, Rodrigo A.

2016-01-01

We investigate the propagation dynamics of highly localized discrete breather modes in a weak ferromagnetic spin lattice with on-site easy axis anisotropy due to crystal field effect. We derive the discrete nonlinear equation of motion by employing boson mappings and p-representation. We explore the onset of modulational instability both analytically in the framework of linear stability analysis and numerically by means of molecular dynamics (MD) simulations, and a perfect agreement was demonstrated. It is also explored that how the antisymmetric nature of the canted ferromagnetic lattice supports highly localized discrete breather (DBs) modes as shown in the stability/instability windows. The energy exchange between low amplitude discrete breathers favours the growth of higher amplitude DBs, resulting eventually in the formation of few long-lived high amplitude DBs. - Highlights: • The effects of DM and anisotropy interaction on the DB modes are studied. • The antisymmetric nature of the canted ferromagnetic medium supports the DB modes. • Dynamics of ferromagnetic chain is governed by boson mappings and p-representation.

MS Windows domēna darbstacijas migrācijas iespējas no MS Windows XP uz MS Windows 7.

OpenAIRE

Zariņš, Valdis

2009-01-01

Kvalifikācijas darbā tiek aprakstītas MS Windows domēna darbstacijas migrācijas iespējas no MS Windows XP uz MS Windows 7, kā servera operētājsistēmas izmantojot tādus Microsoft produktus, kā Microsoft Windows Server 2003 un Microsoft Windows Server 2008. Kvalifikācijas darba teorētiskaja daļā tiek apskatīti Microsoft Windows 7 priekšrocības un uzlabojumus gan no darbstacijas lietotāja , gan no darbstacijas administratora puses. Ir aprakstītas Microsoft Windows Server 2008 jauninājumu ie...

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.

CROSAT: A digital computer program for statistical-spectral analysis of two discrete time series

International Nuclear Information System (INIS)

Antonopoulos Domis, M.

1978-03-01

The program CROSAT computes directly from two discrete time series auto- and cross-spectra, transfer and coherence functions, using a Fast Fourier Transform subroutine. Statistical analysis of the time series is optional. While of general use the program is constructed to be immediately compatible with the ICL 4-70 and H316 computers at AEE Winfrith, and perhaps with minor modifications, with any other hardware system. (author)

Discrete mKdV and discrete sine-Gordon flows on discrete space curves

International Nuclear Information System (INIS)

Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro

2014-01-01

In this paper, we consider the discrete deformation of the discrete space curves with constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and show that it is formulated as the torsion-preserving equidistant deformation on the osculating plane which satisfies the isoperimetric condition. The curve is reconstructed from the deformation data by using the Sym–Tafel formula. The isoperimetric equidistant deformation of the space curves does not preserve the torsion in general. However, it is possible to construct the torsion-preserving deformation by tuning the deformation parameters. Further, it is also possible to make an arbitrary choice of the deformation described by the discrete mKdV equation or by the discrete sine-Gordon equation at each step. We finally show that the discrete deformation of discrete space curves yields the discrete K-surfaces. (paper)

Comparison of discrete Fourier transform (DFT) and principal component analysis/DFT as forecasting tools for absorbance time series received by UV-visible probes installed in urban sewer systems.

Science.gov (United States)

Plazas-Nossa, Leonardo; Torres, Andrés

2014-01-01

The objective of this work is to introduce a forecasting method for UV-Vis spectrometry time series that combines principal component analysis (PCA) and discrete Fourier transform (DFT), and to compare the results obtained with those obtained by using DFT. Three time series for three different study sites were used: (i) Salitre wastewater treatment plant (WWTP) in Bogotá; (ii) Gibraltar pumping station in Bogotá; and (iii) San Fernando WWTP in Itagüí (in the south part of Medellín). Each of these time series had an equal number of samples (1051). In general terms, the results obtained are hardly generalizable, as they seem to be highly dependent on specific water system dynamics; however, some trends can be outlined: (i) for UV range, DFT and PCA/DFT forecasting accuracy were almost the same; (ii) for visible range, the PCA/DFT forecasting procedure proposed gives systematically lower forecasting errors and variability than those obtained with the DFT procedure; and (iii) for short forecasting times the PCA/DFT procedure proposed is more suitable than the DFT procedure, according to processing times obtained.

Fourier-Based Transmit Beampattern Design Using MIMO Radar

KAUST Repository

Lipor, John

2014-05-01

In multiple-input multiple-output (MIMO) radar settings, it is often desirable to transmit power only to a given location or set of locations defined by a beampattern. Transmit waveform design is a topic that has received much attention recently, involving synthesis of both the signal covariance matrix,, as well as the actual waveforms. Current methods involve a two-step process of designing via iterative solutions and then using to generate waveforms that fulfill practical constraints such as having 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 covariance matrix fulfills the practical constraints such as positive semidefiniteness and the uniformelemental power constraint and provides performance similar to that of iterative methods, which require a much greater computation time. Next, a transmit architecture is presented that exploits the orthogonality of frequencies at discrete DFT values to transmit a sum of orthogonal signals from each antenna. The resulting waveforms provide a lower mean-square error than current methods at a much lower computational cost, and a simulated detection scenario demonstrates the performance advantages achieved.

Resources | Efficient Windows Collaborative

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Links | Efficient Windows Collaborative

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Efficient Windows Collaborative | Home

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FAQ | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Glossary | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Application of fast Fourier transforms to the direct solution of a class of two-dimensional separable elliptic equations on the sphere

Science.gov (United States)

Moorthi, Shrinivas; Higgins, R. W.

1993-01-01

An efficient, direct, second-order solver for the discrete solution of a class of two-dimensional separable elliptic equations on the sphere (which generally arise in implicit and semi-implicit atmospheric models) is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite-difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wave-number and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

Two-dimensional Fourier analysis of the spongy medullary keratin of structurally coloured feather barbs

Science.gov (United States)

Prum, R. O.; Torres, R.; Williamson, S.; Dyck, J.

1999-01-01

We conducted two-dimensional (2D) discrete Fourier analyses of the spatial variation in refractive index of the spongy medullary keratin from four different colours of structurally coloured feather barbs from three species of bird: the rose-faced lovebird, Agapornis roseicollis (Psittacidae), the budgerigar, Melopsittacus undulatus (Psittacidae), and the Gouldian finch, Poephila guttata (Estrildidae). These results indicate that the spongy medullary keratin is a nanostructured tissue that functions as an array of coherent scatterers. The nanostructure of the medullary keratin is nearly uniform in all directions. The largest Fourier components of spatial variation in refractive index in the tissue are of the appropriate size to produce the observed colours by constructive interference alone. The peaks of the predicted reflectance spectra calculated from the 2D Fourier power spectra are congruent with the reflectance spectra measured by using microspectrophotometry. The alternative physical models for the production of these colours, the Rayleigh and Mie theories, hypothesize that medullary keratin is an incoherent array and that scattered waves are independent in phase. This assumption is falsified by the ring-like Fourier power spectra of these feathers, and the spacing of the scattering air vacuoles in the medullary keratin. Structural colours of avian feather barbs are produced by constructive interference of coherently scattered light waves from the optically heterogeneous matrix of keratin and air in the spongy medullary layer.

Windows® Internals

CERN Document Server

Russinovich, Mark E; Ionescu, Alex

2009-01-01

See how the core components of the Windows operating system work behind the scenes-guided by a team of internationally renowned internals experts. Fully updated for Windows Server 2008 and Windows Vista, this classic guide delivers key architectural insights on system design, debugging, performance, and support-along with hands-on experiments to experience Windows internal behavior firsthand.Delve inside Windows architecture and internals:Understand how the core system and management mechanisms work-from the object manager to services to the registryExplore internal system data structures usin

Discrete Curvatures and Discrete Minimal Surfaces

KAUST Repository

Sun, Xiang

2012-06-01

This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.

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.

Global field synchronization in gamma range of the sleep EEG tracks sleep depth: Artifact introduced by a rectangular analysis window.

Science.gov (United States)

Rusterholz, Thomas; Achermann, Peter; Dürr, Roland; Koenig, Thomas; Tarokh, Leila

2017-06-01

Investigating functional connectivity between brain networks has become an area of interest in neuroscience. Several methods for investigating connectivity have recently been developed, however, these techniques need to be applied with care. We demonstrate that global field synchronization (GFS), a global measure of phase alignment in the EEG as a function of frequency, must be applied considering signal processing principles in order to yield valid results. Multichannel EEG (27 derivations) was analyzed for GFS based on the complex spectrum derived by the fast Fourier transform (FFT). We examined the effect of window functions on GFS, in particular of non-rectangular windows. Applying a rectangular window when calculating the FFT revealed high GFS values for high frequencies (>15Hz) that were highly correlated (r=0.9) with spectral power in the lower frequency range (0.75-4.5Hz) and tracked the depth of sleep. This turned out to be spurious synchronization. With a non-rectangular window (Tukey or Hanning window) these high frequency synchronization vanished. Both, GFS and power density spectra significantly differed for rectangular and non-rectangular windows. Previous papers using GFS typically did not specify the applied window and may have used a rectangular window function. However, the demonstrated impact of the window function raises the question of the validity of some previous findings at higher frequencies. We demonstrated that it is crucial to apply an appropriate window function for determining synchronization measures based on a spectral approach to avoid spurious synchronization in the beta/gamma range. Copyright © 2017 Elsevier B.V. All rights reserved.

Closed form fourier-based transmit beamforming for MIMO radar

KAUST Repository

Lipor, John J.

2014-05-01

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

Use of the discriminant Fourier-derived cepstrum with feature-level post-processing for surface electromyographic signal classification

International Nuclear Information System (INIS)

Chen, Xinpu; Zhu, Xiangyang; Zhang, Dingguo

2009-01-01

Myoelectrical pattern classification is a crucial part in multi-functional prosthesis control. This paper investigates a discriminant Fourier-derived cepstrum (DFC) and feature-level post-processing (FLPP) to discriminate hand and wrist motions using the surface electromyographic signal. The Fourier-derived cepstrum takes advantage of the Fourier magnitude or sub-band power energy of signals directly and provides flexible use of spectral information changing with different motions. Appropriate cepstral coefficients are selected by a proposed separability criterion to construct DFC features. For the post-processing, FLPP which combines features from several analysis windows is used to improve the feature performance further. In this work, two classifiers (a linear discriminant classifier and quadratic discriminant classifier) without hyper-parameter optimization are employed to simplify the training procedure and avoid the possible bias of feature evaluation. Experimental results of the 11-motion problem show that the proposed DFC feature outperforms traditional features such as time-domain statistics and autoregressive-derived cepstrum in terms of the classification accuracy, and it is a promising method for the multi-functionality and high-accuracy control of myoelectric prostheses

A spectral approach for discrete dislocation dynamics simulations of nanoindentation

Science.gov (United States)

Bertin, Nicolas; Glavas, Vedran; Datta, Dibakar; Cai, Wei

2018-07-01

We present a spectral approach to perform nanoindentation simulations using three-dimensional nodal discrete dislocation dynamics. The method relies on a two step approach. First, the contact problem between an indenter of arbitrary shape and an isotropic elastic half-space is solved using a spectral iterative algorithm, and the contact pressure is fully determined on the half-space surface. The contact pressure is then used as a boundary condition of the spectral solver to determine the resulting stress field produced in the simulation volume. In both stages, the mechanical fields are decomposed into Fourier modes and are efficiently computed using fast Fourier transforms. To further improve the computational efficiency, the method is coupled with a subcycling integrator and a special approach is devised to approximate the displacement field associated with surface steps. As a benchmark, the method is used to compute the response of an elastic half-space using different types of indenter. An example of a dislocation dynamics nanoindentation simulation with complex initial microstructure is presented.

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.

Windows 2012 Server network security securing your Windows network systems and infrastructure

CERN Document Server

Rountree, Derrick

2013-01-01

Windows 2012 Server Network Security provides the most in-depth guide to deploying and maintaining a secure Windows network. The book drills down into all the new features of Windows 2012 and provides practical, hands-on methods for securing your Windows systems networks, including: Secure remote access Network vulnerabilities and mitigations DHCP installations configuration MAC filtering DNS server security WINS installation configuration Securing wired and wireless connections Windows personal firewall

Windows 8.1 bible

CERN Document Server

Boyce, Jim; Tidrow, Rob

2014-01-01

Windows 8.1 coverage that goes above and beyond all competitors? Serving as an evolutionary update to Windows 8, Windows 8.1 provides critical changes to parts of Windows 8, such as greater customization of the interface and boot operations, return of a 'start button' that reveals apps, greater integration between the two interfaces, and updates to apps. Weighing in at nearly 1000 pages, Windows 8.1 Bible provides deeper Windows insight than any other book on the market. It's valuable for both professionals needing a guide to the nooks and crannies of Windows and regular users wanting a wide

Study of Kerogen Maturity using Transmission Fourier Transform Infrared Spectroscopy (FTIR)

Science.gov (United States)

Dang, S. T.

2014-12-01

Maturity of kerogen in shale governs the productivity and generation hydrocarbon type. There are generally two accepted methods to measure kerogen maturity; one is the measurement of vitrinite reflectance, %Ro, and another is the measurement of Tmax through pyrolysis. However, each of these techniques has its own limits; vitrinite reflectance measurement cannot be applied to marine shale and pre-Silurian shales, which lack plant materials. Furthermore, %Ro, requires the isolation and identification of vitrinite macerals and statistical measurements of at least 50 macerals. Tmax measurement is questionable for mature and post-mature samples. In addition, there are questions involving the effects of solvents on Tmax determinations. Fourier Transmission Infrared Spectroscopy, FTIR, can be applied for both qualitative and quantitative assessment on organics maturity in shale. The technique does not require separating organic matter or identifying macerals. A CH2/CH3 index, RCH, calculated from FTIR spectra is more objective than other measurements. The index increases with maturity (both natural maturation and synthetic maturation through hydrous and dry pyrolysis). The new maturity index RCH can be calibrated to vitrinite reflectance which allows the definition of the following values for levels of maturity: 1) immature—RCH > 1.6±0.2; 2) oil window-- 1.6±0.2 1.3±0.3; 3) wet gas window--1.3±0.3 1.13±0.05; and 4) dry gas window RCH < 1.13±0.05.

Polarization measurement by use of discrete space-variant sub wavelength dielectric gratings

International Nuclear Information System (INIS)

Biener, G.; Niv, A.; Gorodetski, Yu.; Kleiner, V.; Hasman, E.

2004-01-01

Full Text:Polarization measurement has been widely used for a large range of applications such as ellipsometry bio-imaging, imaging polarimetry and optical communications. A commonly used method is measuring of the time-dependent signal once the beam is transmitted through a photoelastic modulator or a rotating quarter-wave plate followed by an analyzer. The polarization state of the beam can be derived by Fourier analysis of the detected signal. This method, however, requires a sequence of consecutive measurements, thus making it impractical for real-time polarization measurement in an application such as adaptive polarization-mode dispersion compensation in optical communications. Recently, we developed a novel method for real-time polarization measurement by use of a discrete space-variant sub wavelength dielectric grating (DSG). The formation of the grating is done by discrete orientation of the local sub wavelength grooves. The complete polarization analysis of the incident beam is determined by spatial Fourier transform of the near-field intensity distribution transmitted through the DSG followed by a sub wavelength metal polarizer. We realized the gratings for CO 2 laser radiation at a wavelength of 10.6 micron on GaAs substrate utilizing advanced photo lithographic and etching techniques. We experimentally demonstrated the ability of our method to measure the polarization state for fully and partially polarized light. Unlike other methods based on Fourier analysis, no active elements are required. It is possible to integrate our polarimeter on a two-dimensional detector array for lab-on chip applications to achieve a high-throughput and low-cost commercial polarimeter for bio sensing. Currently we are investigating the possibility of using far-field measurement of the beam emerging from a DSG for polarization measurement

On the velocity space discretization for the Vlasov-Poisson system: comparison between implicit Hermite spectral and Particle-in-Cell methods

NARCIS (Netherlands)

E. Camporeale (Enrico); G.L. Delzanno; B.K. Bergen; J.D. Moulton

2016-01-01

htmlabstractWe describe a spectral method for the numerical solution of the Vlasov–Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized via a Fourier decomposition. The novelty of our approach is an implicit time

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

Science.gov (United States)

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.

Modeling skin cooling using optical windows and cryogens during laser induced hyperthermia in a multilayer vascularized tissue

International Nuclear Information System (INIS)

Singh, Rupesh; Das, Koushik; Okajima, Junnosuke; Maruyama, Shigenao; Mishra, Subhash C.

2015-01-01

This article deals with the spatial and the temporal evolution of tissue temperature during skin surface cooled laser induced hyperthermia. Three different skin surface cooling methodologies viz., optical window contact cooling, cryogenic spray cooling and cryogen cooled optical window contact cooling are considered. Sapphire, yttrium aluminum garnet, lithium tantalate, and magnesium oxide doped lithium niobate are the considered optical windows. The cryogens considered are liquid CO_2 and R1234yf. Heat transfer in the multilayer skin tissue embedded with thermally significant blood vessels pairs is modeled using the Pennes and Weinbaum–Jiji bioheat equations. Weinbaum–Jiji bioheat equation is used for the vascularized tissue. Laser transport in the tissue is modeled using the radiative transfer equation. Axial and radial (skin surface) temperature distributions for different combinations of optical windows and cryogens are analyzed. Liquid CO_2 cooled yttrium aluminum garnet is found to be the best surface cooling mechanism. - Highlights: • Skin surface cooled laser induced hyperthermia is studied. • A multi-layer 2-D cylindrical tissue geometry is considered. • Both Pennes and Weinbaum–Jiji bioheat models are considered. • Laser transport in the tissue is modeled using discrete ordinate method. • Results for 4 optical windows and 2 cryogens for skin cooling are presented.

Alternatives to the discrete cosine transform for irreversible tomographic image compression

International Nuclear Information System (INIS)

Villasenor, J.D.

1993-01-01

Full-frame irreversible compression of medical images is currently being performed using the discrete cosine transform (DCT). Although the DCT is the optimum fast transform for video compression applications, the authors show here that it is out-performed by the discrete Fourier transform (DFT) and discrete Hartley transform (DHT) for images obtained using positron emission tomography (PET) and magnetic resonance imaging (MRI), and possibly for certain types of digitized radiographs. The difference occurs because PET and MRI images are characterized by a roughly circular region D of non-zero intensity bounded by a region R in which the Image intensity is essentially zero. Clipping R to its minimum extent can reduce the number of low-intensity pixels but the practical requirement that images be stored on a rectangular grid means that a significant region of zero intensity must remain an integral part of the image to be compressed. With this constraint imposed, the DCT loses its advantage over the DFT because neither transform introduces significant artificial discontinuities. The DFT and DHT have the further important advantage of requiring less computation time than the DCT

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.

Efficient Windows Collaborative

Energy Technology Data Exchange (ETDEWEB)

Nils Petermann

2010-02-28

The project goals covered both the residential and commercial windows markets and involved a range of audiences such as window manufacturers, builders, homeowners, design professionals, utilities, and public agencies. Essential goals included: (1) Creation of 'Master Toolkits' of information that integrate diverse tools, rating systems, and incentive programs, customized for key audiences such as window manufacturers, design professionals, and utility programs. (2) Delivery of education and outreach programs to multiple audiences through conference presentations, publication of articles for builders and other industry professionals, and targeted dissemination of efficient window curricula to professionals and students. (3) Design and implementation of mechanisms to encourage and track sales of more efficient products through the existing Window Products Database as an incentive for manufacturers to improve products and participate in programs such as NFRC and ENERGY STAR. (4) Development of utility incentive programs to promote more efficient residential and commercial windows. Partnership with regional and local entities on the development of programs and customized information to move the market toward the highest performing products. An overarching project goal was to ensure that different audiences adopt and use the developed information, design and promotion tools and thus increase the market penetration of energy efficient fenestration products. In particular, a crucial success criterion was to move gas and electric utilities to increase the promotion of energy efficient windows through demand side management programs as an important step toward increasing the market share of energy efficient windows.

Error analysis in Fourier methods for option pricing for exponential Lévy processes

KAUST Repository

Crocce, Fabian

2015-01-07

We derive an error bound for utilising the discrete Fourier transform method for solving Partial Integro-Differential Equations (PIDE) that describe european option prices for exponential Lévy driven asset prices. We give sufficient conditions for the existence of a L? bound that separates the dynamical contribution from that arising from the type of the option n in question. The bound achieved does not rely on information of the asymptotic behaviour of option prices at extreme asset values. In addition, we demonstrate improved numerical performance for select examples of practical relevance when compared to established bounding methods.

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

Science.gov (United States)

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

2015-12-01

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

Windows 10 for dummies

CERN Document Server

Rathbone, Andy

2015-01-01

The fast and easy way to get up and running with Windows 10 Windows 10 For Dummies covers the latest version of Windows and gets you up and running with the changes and new features you'll find in this updated operating system. Packed with time-saving tips to help you get the most out of the software, this helpful Windows 10 guide shows you how to manage Windows tasks like navigating the interface with a mouse or touchscreen, connecting to the web, and troubleshooting problems and making quick fixes. Assuming no prior knowledge of the software, Windows 10 For Dummies addresses the updates to

Provide Views | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Reduced Fading | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

EWC Members | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Visible Transmittance | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Gas Fills | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

EWC Membership | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Reducing Condensation | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Improved Comfort | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Financing & Incentives | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Tools & Resources | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Books & Publications | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Design Considerations | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Windows forensic analysis toolkit advanced analysis techniques for Windows 7

CERN Document Server

Carvey, Harlan

2012-01-01

Now in its third edition, Harlan Carvey has updated "Windows Forensic Analysis Toolkit" to cover Windows 7 systems. The primary focus of this edition is on analyzing Windows 7 systems and on processes using free and open-source tools. The book covers live response, file analysis, malware detection, timeline, and much more. The author presents real-life experiences from the trenches, making the material realistic and showing the why behind the how. New to this edition, the companion and toolkit materials are now hosted online. This material consists of electronic printable checklists, cheat sheets, free custom tools, and walk-through demos. This edition complements "Windows Forensic Analysis Toolkit, 2nd Edition", (ISBN: 9781597494229), which focuses primarily on XP. It includes complete coverage and examples on Windows 7 systems. It contains Lessons from the Field, Case Studies, and War Stories. It features companion online material, including electronic printable checklists, cheat sheets, free custom tools, ...

Advanced energy efficient windows

DEFF Research Database (Denmark)

Thomsen, Kirsten Engelund

2007-01-01

Windows should be paid special attention as they contribute a significant part of the total heat-loss coefficient of the building. Contrary to other parts of the thermal envelope the windows are not only heat loosers, but may gain heat in the day-time. Therefore there are possibilities for large...... energy savings. In terms of energy, windows occupy a special position compared with other thermal envelope structures due to their many functions: 1) windows let daylight into the building and provide occupants with visual contact with their surroundings 2) windows protect against the outdoor climate 3......) windows transmit solar energy that may contribute to a reduction of energy consumption, but which may also lead to unpleasant overheating. In the following paragraphs the current use of windows is reviewed with an emphasis on energy, while special products like solar protection glazing and security...

Windows 8 secrets

CERN Document Server

Thurrott, Paul

2012-01-01

Tips, tricks, treats, and secrets revealed on Windows 8 Microsoft is introducing a major new release of its Windows operating system, Windows 8, and what better way to learn all its ins and outs than from two internationally recognized Windows experts and Microsoft insiders, authors Paul Thurrott and Rafael Rivera? They cut through the hype to get at useful information you'll not find anywhere else, including what role this new OS plays in a mobile and tablet world. Regardless of your level of knowledge, you'll discover little-known facts about how things work, what's new and different, and h

Programming Windows Azure

CERN Document Server

Krishnan, Sriram

2010-01-01

Learn the nuts and bolts of cloud computing with Windows Azure, Microsoft's new Internet services platform. Written by a key member of the product development team, this book shows you how to build, deploy, host, and manage applications using Windows Azure's programming model and essential storage services. Chapters in Programming Windows Azure are organized to reflect the platform's buffet of services. The book's first half focuses on how to write and host application code on Windows Azure, while the second half explains all of the options you have for storing and accessing data on the plat

Beginning Windows 8

CERN Document Server

Halsey, Mike

2012-01-01

Windows 8 has been described by Microsoft as its 'boldest' Windows release ever. Beginning Windows 8 takes you through the new features and helps you get more out of the familiar to reveal the possibilities for this amazing new operating system. You will learn, with non-technical language used throughout, how to get up and running in the new Windows interface, minimize downtime, maximize productivity, and harness the features you never knew existed to take control of your computer and enjoy the peace of mind and excitement that comes with it. From tips and tweaks to easy-to-follow guides and d

Windows 8 tweaks

CERN Document Server

Sinchak, Steve

2013-01-01

Acres of Windows 8 tweaks from a Microsoft MVP and creator of Tweaks.com! From a Microsoft MVP, who is also the savvy creator of Tweaks.com, comes this ultimate collection of Windows 8 workarounds. Steve Sinchak takes you way beyond default system settings, deep under the hood of Windows 8, down to the hidden gems that let you customize your Windows 8 system like you wouldn't believe. From helping you customize the appearance to setting up home networking, sharing media, and squeezing every ounce of performance out of the OS, this book delivers. Get ready to rock and roll with Wind

Discrete imaging models for three-dimensional optoacoustic tomography using radially symmetric expansion functions.

Science.gov (United States)

Wang, Kun; Schoonover, Robert W; Su, Richard; Oraevsky, Alexander; Anastasio, Mark A

2014-05-01

Optoacoustic tomography (OAT), also known as photoacoustic tomography, is an emerging computed biomedical imaging modality that exploits optical contrast and ultrasonic detection principles. Iterative image reconstruction algorithms that are based on discrete imaging models are actively being developed for OAT due to their ability to improve image quality by incorporating accurate models of the imaging physics, instrument response, and measurement noise. In this work, we investigate the use of discrete imaging models based on Kaiser-Bessel window functions for iterative image reconstruction in OAT. A closed-form expression for the pressure produced by a Kaiser-Bessel function is calculated, which facilitates accurate computation of the system matrix. Computer-simulation and experimental studies are employed to demonstrate the potential advantages of Kaiser-Bessel function-based iterative image reconstruction in OAT.

Efficient STFT

International Nuclear Information System (INIS)

Aamir, K.M.; Maud, M.A.

2004-01-01

Small perturbations in signals (or any time series), at some particular instant, affect the whole frequency spectrum due to the global function e/sup j omega t/ in Fourier Transform formulation. However, the Fourier spectrum does not convey the time instant at which the perturbation occurred. Consequently the information on the particular time instance of occurrence of that perturbation is lost when spectrum is observed. Apparently Fourier analysis seems to be inadequate in such situations. This inadequacy is overcome by the use of Short Time Fourier Transform (STFT), which keeps track of time as well as frequency information. In STFT analysis, a fixed length window, say of length N, is moved sample by sample as the data arrives. The Discrete Fourier Transform (DFT) of this fixed window of length N is calculated using Fast Fourier Transform (FFT) algorithm. If the total number of points is M > N, the computational complexity of this scheme works out to be at least ((M-N) N log/sub 2/N). On the other hand, STFT is shown to be of computational complexity 6NM and 8NM in the literature. In this paper, two algorithms are presented which compute the same STFT more efficiently. The computational complexity of the proposed algorithms works out to be MN of one algorithm and even lesser in the other algorithm. This reduction in complexity becomes significant for large data sets. This algorithm also remains valid if a stationary part of signal is skipped. (author)

Fourier photospectroscopy of Xe-C60 through a Xe 4d resonance window: theory versus recent experiment

International Nuclear Information System (INIS)

Patel, Aakash B; Chakraborty, Himadri S

2011-01-01

The photoionization cross section of endohedral Xe-C 60 over a Xe 4d giant resonance energy region, calculated in the time-dependent local density approximation, is compared with recent measurements (Kilcoyne et al 2010 Phys. Rev. Lett. 105 213001). An analysis based on the Fourier transforms of oscillatory cross sections is performed to derive a number of inherent similarities between the prediction and the data, including a large beating-type oscillation and several others of intermediate size. Results stress the need for more accurate measurements to access the wealth of information about the geometry of the system. (fast track communication)

On the computation of molecular surface correlations for protein docking using fourier techniques.

Science.gov (United States)

Sakk, Eric

2007-08-01

The computation of surface correlations using a variety of molecular models has been applied to the unbound protein docking problem. Because of the computational complexity involved in examining all possible molecular orientations, the fast Fourier transform (FFT) (a fast numerical implementation of the discrete Fourier transform (DFT)) is generally applied to minimize the number of calculations. This approach is rooted in the convolution theorem which allows one to inverse transform the product of two DFTs in order to perform the correlation calculation. However, such a DFT calculation results in a cyclic or "circular" correlation which, in general, does not lead to the same result as the linear correlation desired for the docking problem. In this work, we provide computational bounds for constructing molecular models used in the molecular surface correlation problem. The derived bounds are then shown to be consistent with various intuitive guidelines previously reported in the protein docking literature. Finally, these bounds are applied to different molecular models in order to investigate their effect on the correlation calculation.

Window selection for dual photopeak window scatter correction in Tc-99m imaging

International Nuclear Information System (INIS)

Vries, D.J. de; King, M.A.

1994-01-01

The width and placement of the windows for the dual photopeak window (DPW) scatter subtraction method for Tc-99m imaging is investigated in order to obtain a method that is stable on a multihead detector system for single photon emission computed tomography (SPECT) and is capable of providing a good scatter estimate for extended objects. For various window pairs, stability and noise were examined with experiments using a SPECT system, while Monte Carlo simulations were used to predict the accuracy of scatter estimates for a variety of objects and to guide the development of regression relations for various window pairs. The DPW method that resulted from this study was implemented with a symmetric 20% photopeak window composed of a 15% asymmetric photopeak window and a 5% lower window abutted at 7 keV below the peak. A power function regression was used to relate the scatter-to-total ratio to the lower window-to-total ratio at each pixel, from which an estimated scatter image was calculated. DPW demonstrated good stability, achieved by abutting the two windows away from the peak. Performance was assessed and compared with Compton window subtraction (CWS). For simulated extended objects, DPW generally produced a less biased scatter estimate than the commonly used CWS method with k = 0.5. In acquisitions of a clinical SPECT phantom, contrast recovery was comparable for both DPW and CWS; however, DPW showed greater visual contrast in clinical SPECT bone studies

Discrete ordinates transport methods for problems with highly forward-peaked scattering

International Nuclear Information System (INIS)

Pautz, S.D.

1998-04-01

The author examines the solutions of the discrete ordinates (S N ) method for problems with highly forward-peaked scattering kernels. He derives conditions necessary to obtain reasonable solutions in a certain forward-peaked limit, the Fokker-Planck (FP) limit. He also analyzes the acceleration of the iterative solution of such problems and offer improvements to it. He extends the analytic Fokker-Planck limit analysis to the S N equations. This analysis shows that in this asymptotic limit the S N solution satisfies a pseudospectral discretization of the FP equation, provided that the scattering term is handled in a certain way (which he describes) and that the analytic transport solution satisfies an analytic FP equation. Similar analyses of various spatially discretized S N equations reveal that they too produce solutions that satisfy discrete FP equations, given the same provisions. Numerical results agree with these theoretical predictions. He defines a multidimensional angular multigrid (ANMG) method to accelerate the iterative solution of highly forward-peaked problems. The analyses show that a straightforward application of this scheme is subject to high-frequency instabilities. However, by applying a diffusive filter to the ANMG corrections he is able to stabilize this method. Fourier analyses of model problems show that the resulting method is effective at accelerating the convergence rate when the scattering is forward-peaked. The numerical results demonstrate that these analyses are good predictors of the actual performance of the ANMG method

A fractional Fourier transform analysis of the scattering of ultrasonic waves

Science.gov (United States)

Tant, Katherine M.M.; Mulholland, Anthony J.; Langer, Matthias; Gachagan, Anthony

2015-01-01

Many safety critical structures, such as those found in nuclear plants, oil pipelines and in the aerospace industry, rely on key components that are constructed from heterogeneous materials. Ultrasonic non-destructive testing (NDT) uses high-frequency mechanical waves to inspect these parts, ensuring they operate reliably without compromising their integrity. It is possible to employ mathematical models to develop a deeper understanding of the acquired ultrasonic data and enhance defect imaging algorithms. In this paper, a model for the scattering of ultrasonic waves by a crack is derived in the time–frequency domain. The fractional Fourier transform (FrFT) is applied to an inhomogeneous wave equation where the forcing function is prescribed as a linear chirp, modulated by a Gaussian envelope. The homogeneous solution is found via the Born approximation which encapsulates information regarding the flaw geometry. The inhomogeneous solution is obtained via the inverse Fourier transform of a Gaussian-windowed linear chirp excitation. It is observed that, although the scattering profile of the flaw does not change, it is amplified. Thus, the theory demonstrates the enhanced signal-to-noise ratio permitted by the use of coded excitation, as well as establishing a time–frequency domain framework to assist in flaw identification and classification. PMID:25792967

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2011-01-01

The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...

Baecklund transformations for discrete Painleve equations: Discrete PII-PV

International Nuclear Information System (INIS)

Sakka, A.; Mugan, U.

2006-01-01

Transformation properties of discrete Painleve equations are investigated by using an algorithmic method. This method yields explicit transformations which relates the solutions of discrete Painleve equations, discrete P II -P V , with different values of parameters. The particular solutions which are expressible in terms of the discrete analogue of the classical special functions of discrete Painleve equations can also be obtained from these transformations

Sinusoidal Parameter Estimation Using Quadratic Interpolation around Power-Scaled Magnitude Spectrum Peaks

Directory of Open Access Journals (Sweden)

Kurt James Werner

2016-10-01

Full Text Available The magnitude of the Discrete Fourier Transform (DFT of a discrete-time signal has a limited frequency definition. Quadratic interpolation over the three DFT samples surrounding magnitude peaks improves the estimation of parameters (frequency and amplitude of resolved sinusoids beyond that limit. Interpolating on a rescaled magnitude spectrum using a logarithmic scale has been shown to improve those estimates. In this article, we show how to heuristically tune a power scaling parameter to outperform linear and logarithmic scaling at an equivalent computational cost. Although this power scaling factor is computed heuristically rather than analytically, it is shown to depend in a structured way on window parameters. Invariance properties of this family of estimators are studied and the existence of a bias due to noise is shown. Comparing to two state-of-the-art estimators, we show that an optimized power scaling has a lower systematic bias and lower mean-squared-error in noisy conditions for ten out of twelve common windowing functions.

Windows for Intel Macs

CERN Document Server

Ogasawara, Todd

2008-01-01

Even the most devoted Mac OS X user may need to use Windows XP, or may just be curious about XP and its applications. This Short Cut is a concise guide for OS X users who need to quickly get comfortable and become productive with Windows XP basics on their Macs. It covers: Security Networking ApplicationsMac users can easily install and use Windows thanks to Boot Camp and Parallels Desktop for Mac. Boot Camp lets an Intel-based Mac install and boot Windows XP on its own hard drive partition. Parallels Desktop for Mac uses virtualization technology to run Windows XP (or other operating systems

Parameter identification in ODE models with oscillatory dynamics: a Fourier regularization approach

Science.gov (United States)

Chiara D'Autilia, Maria; Sgura, Ivonne; Bozzini, Benedetto

2017-12-01

In this paper we consider a parameter identification problem (PIP) for data oscillating in time, that can be described in terms of the dynamics of some ordinary differential equation (ODE) model, resulting in an optimization problem constrained by the ODEs. In problems with this type of data structure, simple application of the direct method of control theory (discretize-then-optimize) yields a least-squares cost function exhibiting multiple ‘low’ minima. Since in this situation any optimization algorithm is liable to fail in the approximation of a good solution, here we propose a Fourier regularization approach that is able to identify an iso-frequency manifold {{ S}} of codimension-one in the parameter space \

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)

Windows XP ends its life at CERN – register for Windows 7 training!

CERN Multimedia

Michał Kwiatek (IT-OIS)

2012-01-01

Windows XP has been around for over 10 years and it is now time to move on. At CERN, general support for Windows XP will end in December 2012, and before this date users are requested to schedule a migration to the next version of Windows – Windows 7.   Windows 7 is already well established at CERN – it is used by a large majority of users. In fact, there was a considerable user demand even before its official release in October 2009 and its adoption has been smooth. Users praise Windows 7 for its improved stability and a clear advantage on laptops is a much more efficient implementation of offline files. The migration to Windows 7 involves a reinstallation of the operating system. Files stored in user home folders on DFS will be immediately available after the reinstallation. Applications will be upgraded to more recent versions and in certain cases, an application may even be replaced by another application providing the same functionality. Microsoft Office suite is a good ...

Thermal bridges of modern windows

DEFF Research Database (Denmark)

Hansen, Ernst Jan de Place; Møller, Eva B.; Nielsen, Anker

2013-01-01

if the window has an U-factor of 1 W/(m2·K) or lower. This paper describes the development of modern, energy efficient Danish windows with reduced thermal bridges. It focuses on materials, geometry, and sealing of window panes based on a literature review. Examples of modern windows are presented. Experience...... been an important driver for the development of new window solutions in Denmark, increasing the inner-surface temperature at the sealing of window panes. However, it will not stop complaints fromconsumers, as this temperature is calculated under standardized conditions. Increasing requirements...

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

Tokamak physics experiment: Diagnostic windows study

International Nuclear Information System (INIS)

Merrigan, M.; Wurden, G.A.

1995-11-01

We detail the study of diagnostic windows and window thermal stress remediation in the long-pulse, high-power Tokamak Physics Experiment (TPX) operation. The operating environment of the TPX diagnostic windows is reviewed, thermal loads on the windows estimated, and cooling requirements for the windows considered. Applicable window-cooling technology from other fields is reviewed and its application to the TPX windows considered. Methods for TPX window thermal conditioning are recommended, with some discussion of potential implementation problems provided. Recommendations for further research and development work to ensure performance of windows in the TPX system are presented

Sparse-matrix factorizations for fast symmetric Fourier transforms

International Nuclear Information System (INIS)

Sequel, J.

1987-01-01

This work proposes new fast algorithms computing the discrete Fourier transform of certain families of symmetric sequences. Sequences commonly found in problems of structure determination by x-ray crystallography and in numerical solutions of boundary-value problems in partial differential equations are dealt with. In the algorithms presented, the redundancies in the input and output data, due to the presence of symmetries in the input data sequence, were eliminated. Using ring-theoretical methods a matrix representation is obtained for the remaining calculations; which factors as the product of a complex block-diagonal matrix times as integral matrix. A basic two-step algorithm scheme arises from this factorization with a first step consisting of pre-additions and a second step containing the calculations involved in computing with the blocks in the block-diagonal factor. These blocks are structured as block-Hankel matrices, and two sparse-matrix factoring formulas are developed in order to diminish their arithmetic complexity

Mastering Windows 7 Deployment

CERN Document Server

Finn, Aidan; van Surksum, Kenneth

2011-01-01

Get professional-level instruction on Windows 7 deployment tools Enterprise-level operating system deployment is challenging and requires knowledge of specific tools. It is expected that Windows 7 will be extensively deployed in businesses worldwide. This comprehensive Sybex guide provides thorough coverage of the Microsoft deployment tools that were specifically created for Windows 7, preparing system administrators, MIS professionals, and corporate programmers to tackle the task effectively.Companies worldwide are expected to deploy Windows 7 as their enterprise operating system; system admi

Discrete Curvatures and Discrete Minimal Surfaces

KAUST Repository

Sun, Xiang

2012-01-01

This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads

Handbook on Windows and Energy

DEFF Research Database (Denmark)

Thomsen, Kirsten Engelund; Schultz, Jørgen Munthe; Svendsen, Sv Aa Højgaard

The handbook on windows and energy is a general description of windows with the main focus put on the energy performance. Common window products are described by commonly used nomenclature, description of frame and sash conctructions and description of commonly used glazing types.The energy...... transmission through windows is described in detail including radiation, convection and conduction as well as solar transmittance of window glazing. The most used terms related to characterization of window energy performance are defined and calculation methods according to international standards...... flow and detailed calculation of light and solar transmittance is given.Different measurement techniques for characterization of window heat loss coefficient and total solar energy transmittance is described and references to interantional standards are given.Finally, the handbook includes...

SPHARA--a generalized spatial Fourier analysis for multi-sensor systems with non-uniformly arranged sensors: application to EEG.

Science.gov (United States)

Graichen, Uwe; Eichardt, Roland; Fiedler, Patrique; Strohmeier, Daniel; Zanow, Frank; Haueisen, Jens

2015-01-01

Important requirements for the analysis of multichannel EEG data are efficient techniques for signal enhancement, signal decomposition, feature extraction, and dimensionality reduction. We propose a new approach for spatial harmonic analysis (SPHARA) that extends the classical spatial Fourier analysis to EEG sensors positioned non-uniformly on the surface of the head. The proposed method is based on the eigenanalysis of the discrete Laplace-Beltrami operator defined on a triangular mesh. We present several ways to discretize the continuous Laplace-Beltrami operator and compare the properties of the resulting basis functions computed using these discretization methods. We apply SPHARA to somatosensory evoked potential data from eleven volunteers and demonstrate the ability of the method for spatial data decomposition, dimensionality reduction and noise suppression. When employing SPHARA for dimensionality reduction, a significantly more compact representation can be achieved using the FEM approach, compared to the other discretization methods. Using FEM, to recover 95% and 99% of the total energy of the EEG data, on average only 35% and 58% of the coefficients are necessary. The capability of SPHARA for noise suppression is shown using artificial data. We conclude that SPHARA can be used for spatial harmonic analysis of multi-sensor data at arbitrary positions and can be utilized in a variety of other applications.

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.

An environmental friendly electrode and extended cathodic potential window for anodic stripping voltammetry of zinc detection

International Nuclear Information System (INIS)

Dueraning, Anisah; Kanatharana, Proespichaya; Thavarungkul, Panote; Limbut, Warakorn

2016-01-01

This work reports on a novel polyeriochrome black T (poly(EBT) modified electrode for use as an environmentally-friendly electrode material that extends the cathodic potential window and improves the sensitivity and repeatability to detect zinc in industrial wastewater. The poly(EBT) film on the GCE surface was fabricated by electropolymerization. The surface morphology and electrochemical behavior of the modified electrode were characterized by scanning electron microscopy, fourier transform infrared spectroscopy and anodic stripping voltammetry. Under optimal conditions, the poly(EBT)/GCE exhibited a high hydrogen overvoltage (extended cathodic potential window). It provided a high sensitivity, a wide linear range (1.0 to 400.0 μg L −1 ), a low detection limit (0.9 μg L −1 ), had excellent repeatability and good recoveries (95% to 105%). This proposed modified electrode was applied to the determination of zinc in wastewater samples, and the results were consistent with those of an inductively coupled plasma atomic emission spectroscopy analysis.

Lower HVAC Costs | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Increased Light & View | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Condensation Resistance (CR) | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Fact Sheets & Publications | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

State Fact Sheets | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

State Code Guides | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Low Conductance Spacers | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Energy & Cost Savings | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Provide Natural Light | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Provide Fresh Air | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Air Leakage (AL) | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Fourier analysis an introduction

CERN Document Server

Stein, Elias M

2003-01-01

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

Windows 95 Beslutningsguide

DEFF Research Database (Denmark)

Sørensen, Jens Otto

1996-01-01

Mange virksomheder der bruger pc'er står netop nu over for valget: Skal vi fortsætte med DOS/Windows 3.x som operativsystem, eller skal vi skifte til efterfølgeren Windows 95? Skal vi/kan vi skifte successivt, eller skal det være en "alt eller intet beslutning". Hvornår er det rigtige tidspunkt...... at skifte? Denne artikel vil forsøge at give en baggrundsviden om Windows 95, der kan hjælpe virksomhederne igennem denne beslutningsfase....

Gabor windows supported on [-1,1] and compactly supported dual windows

DEFF Research Database (Denmark)

Christensen, Ole; Kim, H. O.; Rae Young, Kim

2010-01-01

window. More precisely, we show that if b window supported on [-N, N]. Under the additional assumption that g is continuous and only has a finite number of zeros on inverted left perpendicular-1, 1inverted right perpendicular, we...... characterize the frame property of {E(mb)T(n)g}(m,n is an element of Z). As a consequence we obtain easily verifiable criteria for a function g to generate a Gabor frame with a dual window having compact support of prescribed size....

Designing for Windows 8 fundamentals of great design in Windows Store apps

CERN Document Server

Schooley, Brent

2013-01-01

Designing for Windows 8 is a fast-paced, 150-page primer on the key design concepts you need to create successful Windows 8 apps. This book will help you design a user interface that is both delightful and effective, feels 'right' to your users, and encapsulates a great Windows 8 experience. In this book, you will: Meet the building blocks of solid Windows 8 UI design in a well-designed sample app. Learn how to incorporate key design elements into your apps, such as the app bar, charms and subtle animations from the animation library. Find out how to deliver the core experience that your users

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.

Fast algorithm of adaptive Fourier series

Science.gov (United States)

Gao, You; Ku, Min; Qian, Tao

2018-05-01

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

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.

Fourier photospectroscopy of Xe-C{sub 60} through a Xe 4d resonance window: theory versus recent experiment

Energy Technology Data Exchange (ETDEWEB)

Patel, Aakash B; Chakraborty, Himadri S, E-mail: himadri@nwmissouri.edu [Center for Innovation and Entrepreneurship, Department of Chemistry and Physics, Northwest Missouri State University, Maryville, Missouri 64468 (United States)

2011-10-14

The photoionization cross section of endohedral Xe-C{sub 60} over a Xe 4d giant resonance energy region, calculated in the time-dependent local density approximation, is compared with recent measurements (Kilcoyne et al 2010 Phys. Rev. Lett. 105 213001). An analysis based on the Fourier transforms of oscillatory cross sections is performed to derive a number of inherent similarities between the prediction and the data, including a large beating-type oscillation and several others of intermediate size. Results stress the need for more accurate measurements to access the wealth of information about the geometry of the system. (fast track communication)

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

Water vapor self-continuum absorption measurements in the 4.0 and 2.1 μm transparency windows

Science.gov (United States)

Richard, L.; Vasilchenko, S.; Mondelain, D.; Ventrillard, I.; Romanini, D.; Campargue, A.

2017-11-01

In a recent contribution [A. Campargue, S. Kassi, D. Mondelain, S. Vasilchenko, D. Romanini, Accurate laboratory determination of the near infrared water vapor self-continuum: A test of the MT_CKD model. J. Geophys. Res. Atmos., 121,13,180-13,203, doi:10.1002/2016JD025531], we reported accurate water vapor absorption continuum measurements by Cavity Ring-down Spectroscopy (CRDS) and Optical-Feedback-Cavity Enhanced Absorption Spectroscopy (OF-CEAS) at selected spectral points of 4 near infrared transparency windows. In the present work, the self-continuum cross-sections, CS, are determined for two new spectral points. The 2491 cm-1 spectral point in the region of maximum transparency of the 4.0 μm window was measured by OF-CEAS in the 23-52 °C temperature range. The 4435 cm-1 spectral point of the 2.1 μm window was measured by CRDS at room temperature. The self-continuum cross-sections were determined from the pressure squared dependence of the continuum absorption. Comparison to the literature shows a reasonable agreement with 1970 s and 1980 s measurements using a grating spectrograph in the 4.0 μm window and a very good consistency with our previous laser measurements in the 2.1 μm window. For both studied spectral points, our values are much smaller than previous room temperature measurements by Fourier Transform Spectroscopy. Significant deviations (up to about a factor 4) are noted compared to the widely used semi empirical MT_CKD model of the absorption continuum. The measured temperature dependence at 2491 cm-1 is consistent with previous high temperature measurements in the 4.0 μm window and follows an exp(D0/kT) law, D0 being the dissociation energy of the water dimer.

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)

A difference tracking algorithm based on discrete sine transform

Science.gov (United States)

Liu, HaoPeng; Yao, Yong; Lei, HeBing; Wu, HaoKun

2018-04-01

Target tracking is an important field of computer vision. The template matching tracking algorithm based on squared difference matching (SSD) and standard correlation coefficient (NCC) matching is very sensitive to the gray change of image. When the brightness or gray change, the tracking algorithm will be affected by high-frequency information. Tracking accuracy is reduced, resulting in loss of tracking target. In this paper, a differential tracking algorithm based on discrete sine transform is proposed to reduce the influence of image gray or brightness change. The algorithm that combines the discrete sine transform and the difference algorithm maps the target image into a image digital sequence. The Kalman filter predicts the target position. Using the Hamming distance determines the degree of similarity between the target and the template. The window closest to the template is determined the target to be tracked. The target to be tracked updates the template. Based on the above achieve target tracking. The algorithm is tested in this paper. Compared with SSD and NCC template matching algorithms, the algorithm tracks target stably when image gray or brightness change. And the tracking speed can meet the read-time requirement.

Windows with improved energy performances

DEFF Research Database (Denmark)

Laustsen, Jacob Birck; Svendsen, Svend

2003-01-01

Heat loss through windows represents a considerable part of the total heat loss from houses. However, apart from providing daylight access and view, windows offer a unique potential for solar gain to be exploited during the heating season. Until now valuation of the energy performance of windows...... has primary focused on the heat loss coefficient, U-value. However, as the U-value, especially for the glazing part, has improved considerably during the last years, the total solar energy transmittance, g-value, has become equally important to the total energy performance of windows. Improved energy...... resulted in a window with a positive net energy gain (in short the Net Gain Window), which means that it contributes to the space heating of the building. All improvements are based on existing technology and manufacturing methods. The results from this work show that the energy performances of windows can...

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...

Beginning Windows 8.1

CERN Document Server

Halsey, Mike

2013-01-01

Windows 8 has been described by Microsoft as its 'boldest' Windows release ever and the 8.1 update enhances the paradigm further. Beginning Windows 8.1 takes you through the new features and helps you get more out of the familiar to reveal the fullest possibilities for this amazing new operating system. You will learn, with non-technical language used throughout, how to get up and running in the new Windows interface, minimize downtime, maximize productivity, and harness the features you never knew existed to take control of your computer and enjoy the peace of mind and excitement that comes w

Visual merchandising window display

Directory of Open Access Journals (Sweden)

Opris (Cas. Stanila M.

2013-12-01

Full Text Available Window display plays a major part in the selling strategies; it does not only include the simple display of goods, nowadays it is a form of art, also having the purpose of sustaining the brand image. This article wants to reveal the tools that are essential in creating a fabulous window display. Being a window designer is not an easy job, you have to always think ahead trends, to have a sense of colour, to know how to use light to attract customers in the store after only one glance at the window. The big store window displays are theatre scenes: with expensive backgrounds, special effects and high fashion mannequins. The final role of the displays is to convince customers to enter the store and trigger the purchasing act which is the final goal of the retail activity.

Mimetic discretization methods

CERN Document Server

Castillo, Jose E

2013-01-01

To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus. Mimetic Discretization Methods focuses on the recent mimetic discretization method co-developed by the first author. Based on the Castillo-Grone operators, this simple mimetic discretization method is invariably valid for spatial dimensions no greater than three. The book also presents a numerical method for obtaining corresponding discrete operators that mimic the continuum differential and

Windows 7 is supported at CERN

CERN Multimedia

IT Department

2010-01-01

The new version of the Windows operating system - Windows 7 - is now officially supported at CERN. Windows 7 32-bit is now the default operating system for the new computers at CERN. What’s new in Windows 7 Users of Windows XP will find many new features and options. Users of Windows Vista will feel very familiar with one major difference: higher performance and better responsiveness of the operating system. Other enhancements include: refined Aero desktop that makes it easier to navigate between your different application windows; new snapping windows that allows user to resize a window simply by dragging it to the edge of the screen and “pin” that allows grouping and arranging often accessed applications on the taskbar. Windows 7 introduces the new concept of libraries – containers for user files that have links to different local or network folders. By default, users can see four libraries: Documents, Music, Pictures and Videos. These libraries point to the cor...

GA microwave window development

International Nuclear Information System (INIS)

Moeller, C.P.; Kasugai, A.; Sakamoto, K.; Takahashi, K.

1994-10-01

The GA prototype distributed window was tested in a 32 mm diam. waveguide system at a power density suitable for a MW gyrotron, using the JAERI/Toshiba 110 GHz long pulse internal converter gyrotron in the JAERI test stand. The presence of the untilted distributed window had no adverse effect on the gyrotron operation. A pulse length of 10 times the calculated thermal equilibrium time (1/e time) of 30 msec was reached, and the window passed at least 750 pulses greater than 30 msec and 343 pulses greater than 60 msec. Beyond 100 msec, the window calorimetry reached steady state, allowing the window dissipation to be measured in a single pulse. The measured loss of 4.0% agrees both with the estimated loss, on which the stress calculations are based, and with the attenuation measured at low power in the HE 11 mode. After the end of the tests, the window was examined; no evidence of arcing air coating was found in the part of the window directly illuminated by the microwaves, although there was discoloration in a recess containing an optical diagnostic which outgassed, causing a local discharge to occur in that recess. Finally, there was no failure of the metal-sapphire joints during a total operating time of 50 seconds consisting of pulses longer than 30 msec

Music@Microsoft.Windows: Composing Ambience

Science.gov (United States)

Rickert, Thomas

2010-01-01

It is well known, of course, that all Windows versions except for 3.1 have a brief (four to six second) piece of music indicating that Windows is booted and ready for use. While the music may indicate Windows has booted, it bears no immediately discernable relation to the various uses we might actually put Windows to--working, gaming,…

Discrete Data Qualification System and Method Comprising Noise Series Fault Detection

Science.gov (United States)

Fulton, Christopher; Wong, Edmond; Melcher, Kevin; Bickford, Randall

2013-01-01

A Sensor Data Qualification (SDQ) function has been developed that allows the onboard flight computers on NASA s launch vehicles to determine the validity of sensor data to ensure that critical safety and operational decisions are not based on faulty sensor data. This SDQ function includes a novel noise series fault detection algorithm for qualification of the output data from LO2 and LH2 low-level liquid sensors. These sensors are positioned in a launch vehicle s propellant tanks in order to detect propellant depletion during a rocket engine s boost operating phase. This detection capability can prevent the catastrophic situation where the engine operates without propellant. The output from each LO2 and LH2 low-level liquid sensor is a discrete valued signal that is expected to be in either of two states, depending on whether the sensor is immersed (wet) or exposed (dry). Conventional methods for sensor data qualification, such as threshold limit checking, are not effective for this type of signal due to its discrete binary-state nature. To address this data qualification challenge, a noise computation and evaluation method, also known as a noise fault detector, was developed to detect unreasonable statistical characteristics in the discrete data stream. The method operates on a time series of discrete data observations over a moving window of data points and performs a continuous examination of the resulting observation stream to identify the presence of anomalous characteristics. If the method determines the existence of anomalous results, the data from the sensor is disqualified for use by other monitoring or control functions.

Suppressing carrier removal error in the Fourier transform method for interferogram analysis

International Nuclear Information System (INIS)

Fan, Qi; Yang, Hongru; Li, Gaoping; Zhao, Jianlin

2010-01-01

A new carrier removal method for interferogram analysis using the Fourier transform is presented. The proposed method can be used to suppress the carrier removal error as well as the spectral leakage error. First, the carrier frequencies are estimated with the spectral centroid of the up sidelobe of the apodized interferogram, and then the up sidelobe can be shifted to the origin in the frequency domain by multiplying the original interferogram by a constructed plane reference wave. The influence of the carrier frequencies without an integer multiple of the frequency interval and the window function for apodization of the interferogram can be avoided in our work. The simulation and experimental results show that this method is effective for phase measurement with a high accuracy from a single interferogram

Windows 8 simplified

CERN Document Server

McFedries, Paul

2012-01-01

The easiest way for visual learners to get started with Windows 8 The popular Simplified series makes visual learning easier than ever, and with more than 360,000 copies sold, previous Windows editions are among the bestselling Visual books. This guide goes straight to the point with easy-to-follow, two-page tutorials for each task. With full-color screen shots and step-by-step directions, it gets beginners up and running on the newest version of Windows right away. Learn to work with the new interface and improved Internet Explorer, manage files, share your computer, and much more. Perfect fo

Rails on Windows

CERN Document Server

Hibbs, Curt

2007-01-01

It's no secret that the entire Ruby onRails core team uses OS X as their preferreddevelopment environment. Becauseof this, it is very easy to findauthoritative information on the webabout using Rails on OS X. But the truthis that Windows developers using Railsprobably outnumber those using otherplatforms. A Windows development environmentcan be just as productive asany other platform. This is a guide to developing with Rubyon Rails under Windows. It won't teachyou how to write Ruby on Rails web applications,but it will show you what toolsto use and how to set them up to createa complete Rail

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)

Windows Home Server users guide

CERN Document Server

Edney, Andrew

2008-01-01

Windows Home Server brings the idea of centralized storage, backup and computer management out of the enterprise and into the home. Windows Home Server is built for people with multiple computers at home and helps to synchronize them, keep them updated, stream media between them, and back them up centrally. Built on a similar foundation as the Microsoft server operating products, it's essentially Small Business Server for the home.This book details how to install, configure, and use Windows Home Server and explains how to connect to and manage different clients such as Windows XP, Windows Vist

Teach yourself visually Windows 10

CERN Document Server

McFedries, Paul

2015-01-01

Learn Windows 10 visually with step-by-step instructions Teach Yourself VISUALLY Windows 10 is the visual learner's guide to the latest Windows upgrade. Completely updated to cover all the latest features, this book walks you step-by-step through over 150 essential Windows tasks. Using full color screen shots and clear instruction, you'll learn your way around the interface, set up user accounts, play media files, download photos from your camera, go online, set up email, and much more. You'll even learn how to customize Windows 10 to suit the way you work best, troubleshoot and repair common

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.

Windows registry forensics advanced digital forensic analysis of the Windows registry

CERN Document Server

Carvey, Harlan

2011-01-01

Harlan Carvey brings readers an advanced book on Windows Registry - the most difficult part of Windows to analyze in forensics! Windows Registry Forensics provides the background of the Registry to help develop an understanding of the binary structure of Registry hive files. Approaches to live response and analysis are included, and tools and techniques for postmortem analysis are discussed at length. Tools and techniques will be presented that take the analyst beyond the current use of viewers and into real analysis of data contained in the Registry. This book also has a DVD containing tools, instructions and videos.

Weak signal detection: A discrete window of opportunity for achieving 'Vision 90:90:90'?

Science.gov (United States)

Burman, Christopher J; Aphane, Marota; Delobelle, Peter

2016-01-01

UNAIDS' Vision 90:90:90 is a call to 'end AIDS'. Developing predictive foresight of the unpredictable changes that this journey will entail could contribute to the ambition of 'ending AIDS'. There are few opportunities for managing unpredictable changes. We introduce 'weak signal detection' as a potential opportunity to fill this void. Combining futures and complexity theory, we reflect on two pilot case studies that involved the Archetype Extraction technique and the SenseMaker(®) Collector(™) tool. Both the piloted techniques have the potentials to surface weak signals--but there is room for improvement. A management response to a complex weak signal requires pattern management, rather than an exclusive focus on behaviour management. Weak signal detection is a window of opportunity to improve resilience to unpredictable changes in the HIV/AIDS landscape that can both reduce the risk that emerges from the changes and increase the visibility of opportunities to exploit the unpredictable changes that could contribute to 'ending AIDS'.

Continuous versus discrete structures II -- Discrete Hamiltonian systems and Helmholtz conditions

OpenAIRE

Cresson, Jacky; Pierret, Frédéric

2015-01-01

We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the Hamiltonian setting. Several applications are discussed.

User's guide for ABCI version 9.4 (azimuthal beam cavity interaction) and introducing the ABCI windows application package

International Nuclear Information System (INIS)

Chin, Yong Ho

2005-12-01

ABCI is a computer program which solves the Maxwell equations directly in the time domain when a bunched beam goes through an axi-symmetric structure on or off axis. An arbitrary charge distribution can be defined by the user (default=Gaussian). This document is meant to be a comprehensive user's guide to describe all features of ABCI version 9.4, including also all additions since the release of the guide for version 8.8. All appendixes from the previous two user's guides that contain different important topics are also quoted. The main advantages of ABCI lie in its high speed of execution, the minimum use of computer memory, implementation of Napoly integration method and many elaborate options of Fourier transformations. In the version 9.4, even wake potentials for a counter-rotating beam of opposite charge can be calculated instead of usual ones for a beam trailing the driving beams. Now, the Windows application version of ABCI is available as a package which includes ABCI stand-alone executable modules, the sample input files, the source codes, manuals and the Windows version of TopDrawer, TopDrawW. This package can be downloaded from the ABCI home page: http://abci.kek.jp/abci.htm. Just by drag-and-droping an input file on the icon of ABCI application, all the calculation results pop out. Neither compilation of the source code nor installation of the program to Windows is necessary. Together with the TopDrawer for Windows, all works (computation of wake fields, generation of figures and so on) can be done simply and easily on Windows alone. How to use ABCI on Windows and how to install the program to other computer systems are explained at the end of this manual. (author)

Window observers for linear systems

Directory of Open Access Journals (Sweden)

Utkin Vadim

2000-01-01

Full Text Available Given a linear system x ˙ = A x + B u with output y = C x and a window function ω ( t , i.e., ∀ t , ω ( t ∈ {0,1 }, and assuming that the window function is Lebesgue measurable, we refer to the following observer, x ˆ = A x + B u + ω ( t L C ( x − x ˆ as a window observer. The stability issue is treated in this paper. It is proven that for linear time-invariant systems, the window observer can be stabilized by an appropriate design under a very mild condition on the window functions, albeit for linear time-varying system, some regularity of the window functions is required to achieve observer designs with the asymptotic stability. The corresponding design methods are developed. An example is included to illustrate the possible applications

Window Selection Tool | Efficient Windows Collaborative

Science.gov (United States)

Louisville LA Lake Charles LA New Orleans LA Shreveport MA Boston MD Baltimore ME Portland MI Detroit MI Window Selection Tool will take you through a series of design conditions pertaining to your design and

Color Wheel Windows

Science.gov (United States)

Leonard, Stephanie

2012-01-01

In this article, the author describes a painting and drawing lesson which was inspired by the beautiful circular windows found in cathedrals and churches (also known as "rose windows"). This two-week lesson would reinforce both the concept of symmetry and students' understanding of the color wheel. (Contains 1 online resource.)

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2011-01-01

; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics...... to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties...

Digital Discretion

DEFF Research Database (Denmark)

Busch, Peter Andre; Zinner Henriksen, Helle

2018-01-01

discretion is suggested to reduce this footprint by influencing or replacing their discretionary practices using ICT. What is less researched is whether digital discretion can cause changes in public policy outcomes, and under what conditions such changes can occur. Using the concept of public service values......This study reviews 44 peer-reviewed articles on digital discretion published in the period from 1998 to January 2017. Street-level bureaucrats have traditionally had a wide ability to exercise discretion stirring debate since they can add their personal footprint on public policies. Digital......, we suggest that digital discretion can strengthen ethical and democratic values but weaken professional and relational values. Furthermore, we conclude that contextual factors such as considerations made by policy makers on the macro-level and the degree of professionalization of street...

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.

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…

Classical Fourier analysis

CERN Document Server

Grafakos, Loukas

2014-01-01

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

Fixed Points in Discrete Models for Regulatory Genetic Networks

Directory of Open Access Journals (Sweden)

Orozco Edusmildo

2007-01-01

Full Text Available It is desirable to have efficient mathematical methods to extract information about regulatory iterations between genes from repeated measurements of gene transcript concentrations. One piece of information is of interest when the dynamics reaches a steady state. In this paper we develop tools that enable the detection of steady states that are modeled by fixed points in discrete finite dynamical systems. We discuss two algebraic models, a univariate model and a multivariate model. We show that these two models are equivalent and that one can be converted to the other by means of a discrete Fourier transform. We give a new, more general definition of a linear finite dynamical system and we give a necessary and sufficient condition for such a system to be a fixed point system, that is, all cycles are of length one. We show how this result for generalized linear systems can be used to determine when certain nonlinear systems (monomial dynamical systems over finite fields are fixed point systems. We also show how it is possible to determine in polynomial time when an ordinary linear system (defined over a finite field is a fixed point system. We conclude with a necessary condition for a univariate finite dynamical system to be a fixed point system.

Digital Watermarks Using Discrete Wavelet Transformation and Spectrum Spreading

Directory of Open Access Journals (Sweden)

Ryousuke Takai

2003-12-01

Full Text Available In recent tears, digital media makes rapid progress through the development of digital technology. Digital media normally assures fairly high quality, nevertheless can be easily reproduced in a perfect form. This perfect reproducibility takes and advantage from a certain point of view, while it produces an essential disadvantage, since digital media is frequently copied illegally. Thus the problem of the copyright protection becomes a very important issue. A solution of this problem is to embed digital watermarks that is not perceived clearly by usual people, but represents the proper right of original product. In our method, the images data in the frequency domain are transformed by the Discrete Wavelet Transform and analyzed by the multi resolution approximation, [1]. Further, the spectrum spreading is executed by using PN-sequences. Choi and Aizawa [7] embed watermarks by using block correlation of DCT coefficients. Thus, we apply Discrete Cosine Transformation, abbreviated to DCT, instead of the Fourier transformation in order to embed watermarks.If the value of this variance is high then we decide that the block has bigger magnitude for visual fluctuations. Henceforth, we may embed stronger watermarks, which gives resistance for images processing, such as attacks and/or compressions.

Adaptive Liquid Crystal Windows

Energy Technology Data Exchange (ETDEWEB)

Taheri, Bahman; Bodnar, Volodymyr

2011-12-31

Energy consumption by private and commercial sectors in the U.S. has steadily grown over the last decade. The uncertainty in future availability of imported oil, on which the energy consumption relies strongly, resulted in a dramatic increase in the cost of energy. About 20% of this consumption are used to heat and cool houses and commercial buildings. To reduce dependence on the foreign oil and cut down emission of greenhouse gases, it is necessary to eliminate losses and reduce total energy consumption by buildings. To achieve this goal it is necessary to redefine the role of the conventional windows. At a minimum, windows should stop being a source for energy loss. Ideally, windows should become a source of energy, providing net gain to reduce energy used to heat and cool homes. It is possible to have a net energy gain from a window if its light transmission can be dynamically altered, ideally electronically without the need of operator assistance, providing optimal control of the solar gain that varies with season and climate in the U.S. In addition, the window must not require power from the building for operation. Resolution of this problem is a societal challenge and of national interest and will have a broad global impact. For this purpose, the year-round, allclimate window solution to provide an electronically variable solar heat gain coefficient (SHGC) with a wide dynamic range is needed. AlphaMicron, Inc. (AMI) developed and manufactured 1ft × 1ft prototype panels for the world’s first auto-adjusting Adaptive Liquid Crystal Windows (ALCWs) that can operate from sunlight without the need for external power source and demonstrate an electronically adjustable SHGC. This novel windows are based on AlphaMicron’s patented e-Tint® technology, a guesthost liquid crystal system implemented on flexible, optically clear plastic films. This technology is suitable both for OEM and aftermarket (retro-fitting) lamination to new and existing windows. Low level of

National Fenestration Rating Council (NFRC) | Efficient Windows

Science.gov (United States)

Collaborative Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring

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.

U-Factor (U-value) | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Bifurcation Analysis and Chaos Control in a Discrete Epidemic System

Directory of Open Access Journals (Sweden)

Wei Tan

2015-01-01

Full Text Available The dynamics of discrete SI epidemic model, which has been obtained by the forward Euler scheme, is investigated in detail. By using the center manifold theorem and bifurcation theorem in the interior R+2, the specific conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation have been derived. Numerical simulation not only presents our theoretical analysis but also exhibits rich and complex dynamical behavior existing in the case of the windows of period-1, period-3, period-5, period-6, period-7, period-9, period-11, period-15, period-19, period-23, period-34, period-42, and period-53 orbits. Meanwhile, there appears the cascade of period-doubling 2, 4, 8 bifurcation and chaos sets from the fixed point. These results show the discrete model has more richer dynamics compared with the continuous model. The computations of the largest Lyapunov exponents more than 0 confirm the chaotic behaviors of the system x→x+δ[rN(1-N/K-βxy/N-(μ+mx], y→y+δ[βxy/N-(μ+dy]. Specifically, the chaotic orbits at an unstable fixed point are stabilized by using the feedback control method.

Right-to-left-shunt detected by c-TCD using the orbital window in comparison with temporal bone windows.

Science.gov (United States)

Kobayashi, Kazuto; Kimura, Kazumi; Iguchi, Yasuyuki; Sakai, Kenichirou; Aoki, Junya; Iwanaga, Takeshi; Shibazaki, Kensaku

2012-01-01

There have been some reports on right-to-left shunt as a cause of cryptogenic stroke. Although contrast transcranial Doppler (c-TCD) can detect RLS, an insufficient temporal window has occasionally restricted its applicability. Thus, we compared the rates of detecting RLS among temporal windows for the middle cerebral arteries (MCAs) and the orbital window for the internal carotid artery (ICA) on c-TCD. We used c-TCD to detect RLS in patients with suspected ischemic stroke. We enrolled patients who had both sufficient bilateral temporal windows for MCAs and a right orbital window for ICA and performed c-TCD using all three windows simultaneously. We enrolled 106 consecutive patients and identified microembolic signals (MES) in 30 (28%) of them. Among these 30 patients, 15 had MES from all 3 windows. When these 30 patients were defined as being positive for RLS, the rates of detection were 67%, 73%, and 80% from the right temporal, left temporal, and right orbital windows, respectively (P= .795). The right orbital window as well as the temporal window for c-TCD could detect RLS. Insonation from the orbital window should be useful for patients who lack temporal windows. Copyright © 2010 by the American Society of Neuroimaging.

Streaked x-ray spectrometer having a discrete selection of Bragg geometries for Omega

Energy Technology Data Exchange (ETDEWEB)

Millecchia, M.; Regan, S. P.; Bahr, R. E.; Romanofsky, M.; Sorce, C. [Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623-1299 (United States)

2012-10-15

The streaked x-ray spectrometer (SXS) is used with streak cameras [D. H. Kalantar, P. M. Bell, R. L. Costa, B. A. Hammel, O. L. Landen, T. J. Orzechowski, J. D. Hares, and A. K. L. Dymoke-Bradshaw, in 22nd International Congress on High-Speed Photography and Photonics, edited by D. L. Paisley and A. M. Frank (SPIE, Bellingham, WA, 1997), Vol. 2869, p. 680] positioned with a ten-inch manipulator on OMEGA [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)] and OMEGA EP [L. J. Waxer et al., Presented at CLEO/QELS 2008, San Jose, CA, 4-9 May 2008 (Paper JThB1)] for time-resolved, x-ray spectroscopy of laser-produced plasmas in the 1.4- to 20-keV photon-energy range. These experiments require measuring a portion of this photon-energy range to monitor a particular emission or absorption feature of interest. The SXS relies on a pinned mechanical reference system to create a discrete set of Bragg reflection geometries for a variety of crystals. A wide selection of spectral windows is achieved accurately and efficiently using this technique. It replaces the previous spectrometer designs that had a continuous Bragg angle adjustment and required a tedious alignment calibration procedure. The number of spectral windows needed for the SXS was determined by studying the spectral ranges selected by OMEGA users over the last decade. These selections are easily configured in the SXS using one of the 25 discrete Bragg reflection geometries and one of the six types of Bragg crystals, including two curved crystals.

Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

KAUST Repository

Mohamed, Mamdouh S.

2017-05-23

A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy otherwise. The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of barycentric Hodge star allows the discretization to admit arbitrary simplicial meshes. The discretization scheme is presented along with various numerical test cases demonstrating its main characteristics.

Modeling cavities exhibiting strong lateral confinement using open geometry Fourier modal method

Science.gov (United States)

Häyrynen, Teppo; Gregersen, Niels

2016-04-01

We have developed a computationally efficient Fourier-Bessel expansion based open geometry formalism for modeling the optical properties of rotationally symmetric photonic nanostructures. The lateral computation domain is assumed infinite so that no artificial boundary conditions are needed. Instead, the leakage of the modes due to an imperfect field confinement is taken into account by using a basis functions that expand the whole infinite space. The computational efficiency is obtained by using a non-uniform discretization in the frequency space in which the lateral expansion modes are more densely sampled around a geometry specific dominant transverse wavenumber region. We will use the developed approach to investigate the Q factor and mode confinement in cavities where top DBR mirror has small rectangular defect confining the modes laterally on the defect region.

Fourier and granulometry methods on 3D images of soil surfaces for evaluating soil aggregate size distribution

DEFF Research Database (Denmark)

Jensen, T.; Green, O.; Munkholm, Lars Juhl

2016-01-01

The goal of this research is to present and compare two methods for evaluating soil aggregate size distribution based on high resolution 3D images of the soil surface. The methods for analyzing the images are discrete Fourier transform and granulometry. The results of these methods correlate...... with a measured weight distribution of the soil aggregates. The results have shown that it is possible to distinguish between the cultivated and the uncultivated soil surface. A sensor system suitable for capturing in-situ high resolution 3D images of the soil surface is also described. This sensor system...

Hybrid window layer for photovoltaic cells

Science.gov (United States)

Deng, Xunming

2010-02-23

A novel photovoltaic solar cell and method of making the same are disclosed. The solar cell includes: at least one absorber layer which could either be a lightly doped layer or an undoped layer, and at least a doped window-layers which comprise at least two sub-window-layers. The first sub-window-layer, which is next to the absorber-layer, is deposited to form desirable junction with the absorber-layer. The second sub-window-layer, which is next to the first sub-window-layer, but not in direct contact with the absorber-layer, is deposited in order to have transmission higher than the first-sub-window-layer.

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

X-ray interferometric Fourier holography

International Nuclear Information System (INIS)

Balyan, M.K.

2016-01-01

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

Windows PowerShell 20 Bible

CERN Document Server

Lee, Thomas; Schill, Mark E; Tanasovski, Tome

2011-01-01

Here's the complete guide to Windows PowerShell 2.0 for administrators and developers Windows PowerShell is Microsoft's next-generation scripting and automation language. This comprehensive volume provides the background that IT administrators and developers need in order to start using PowerShell automation in exciting new ways. It explains what PowerShell is, how to use the language, and specific ways to apply PowerShell in various technologies. Windows PowerShell is Microsoft's standard automation tool and something that every Windows administrator will eventually have to understand; this b

Mastering Microsoft Windows Server 2008 R2

CERN Document Server

Minasi, Mark; Finn, Aidan

2010-01-01

The one book you absolutely need to get up and running with Windows Server 2008 R2. One of the world's leading Windows authorities and top-selling author Mark Minasi explores every nook and cranny of the latest version of Microsoft's flagship network operating system, Windows Server 2008 R2, giving you the most in-depth coverage in any book on the market.: Focuses on Windows Windows Server 2008 R2, the newest version of Microsoft's Windows' server line of operating system, and the ideal server for new Windows 7 clients; Author Mark Minasi is one of the world's leading Windows authorities and h

Schematic Window Methodology Project

Data.gov (United States)

National Aeronautics and Space Administration — The aim of this IRAD is to produce a generic launch window analyzer (SWM) that allows for large-scale rapid analysis of a launch window and orbit design trade space....

Windows 7 resource kit

CERN Document Server

Northrup, Tony; Honeycutt, Jerry; Wilson, Ed

2009-01-01

In-depth and comprehensive, this RESOURCE KIT delivers the information you need to administer your Windows 7 system. You get authoritative technical guidance from those who know the technology best-Microsoft Most Valuable Professionals (MVPs) and the Windows 7 product team-along with essential scripts and resources. In addition, "Direct from the Source" sidebars offer deep insights and troubleshooting tips from the Windows 7 team. Get expert guidance on how to: Use Microsoft Deployment Toolkit best practices and tools. Plan user-state migration and test application compatibility.

The Efficient Windows Collaborative

Energy Technology Data Exchange (ETDEWEB)

Petermann, Nils

2006-03-31

The Efficient Windows Collaborative (EWC) is a coalition of manufacturers, component suppliers, government agencies, research institutions, and others who partner to expand the market for energy efficient window products. Funded through a cooperative agreement with the U.S. Department of Energy, the EWC provides education, communication and outreach in order to transform the residential window market to 70% energy efficient products by 2005. Implementation of the EWC is managed by the Alliance to Save Energy, with support from the University of Minnesota and Lawrence Berkeley National Laboratory.

Discrete fourier transformations with weight

International Nuclear Information System (INIS)

Wang Qin; Jiang Yong

1988-01-01

DFT and FFT with weight were considered and their properties were studied. The usual DFT and FFT were modified by reducing the number of sample points within a certain error band and therefore speeded up the computation. Finally, the practical applications of the new method in the fields of spectrum analysis, pulse tracing research and so on were pointed out

A linear multiple balance method for discrete ordinates neutron transport equations

International Nuclear Information System (INIS)

Park, Chang Je; Cho, Nam Zin

2000-01-01

A linear multiple balance method (LMB) is developed to provide more accurate and positive solutions for the discrete ordinates neutron transport equations. In this multiple balance approach, one mesh cell is divided into two subcells with quadratic approximation of angular flux distribution. Four multiple balance equations are used to relate center angular flux with average angular flux by Simpson's rule. From the analysis of spatial truncation error, the accuracy of the linear multiple balance scheme is ο(Δ 4 ) whereas that of diamond differencing is ο(Δ 2 ). To accelerate the linear multiple balance method, we also describe a simplified additive angular dependent rebalance factor scheme which combines a modified boundary projection acceleration scheme and the angular dependent rebalance factor acceleration schme. It is demonstrated, via fourier analysis of a simple model problem as well as numerical calculations, that the additive angular dependent rebalance factor acceleration scheme is unconditionally stable with spectral radius < 0.2069c (c being the scattering ration). The numerical results tested so far on slab-geometry discrete ordinates transport problems show that the solution method of linear multiple balance is effective and sufficiently efficient

Composition of 12-18th century window glass in Belgium: Non-figurative windows in secular buildings and stained-glass windows in religious buildings

International Nuclear Information System (INIS)

Schalm, Olivier; Janssens, Koen; Wouters, Hilde; Caluwe, Danielle

2007-01-01

A set of ca. 500 window glass fragments originating from different historical sites in Belgium and covering the period 12 th -18 th century was analyzed by means of electron probe microanalysis. Most samples are archaeological finds deriving from non-figurative windows in secular buildings. However, the analyzed set also contains glass sampled from still existing non-figurative windows in secular buildings and stained-glass windows in religious buildings. A sudden compositional change at the end of the 14 th century can be noticed among the series of glass compositions that were obtained. These changes could be related to the use of different glassmaker recipes and to the introduction of new raw materials for glass making

Composition of 12-18 th century window glass in Belgium: Non-figurative windows in secular buildings and stained-glass windows in religious buildings

Science.gov (United States)

Schalm, Olivier; Janssens, Koen; Wouters, Hilde; Caluwé, Danielle

2007-07-01

A set of ca. 500 window glass fragments originating from different historical sites in Belgium and covering the period 12 th-18 th century was analyzed by means of electron probe microanalysis. Most samples are archaeological finds deriving from non-figurative windows in secular buildings. However, the analyzed set also contains glass sampled from still existing non-figurative windows in secular buildings and stained-glass windows in religious buildings. A sudden compositional change at the end of the 14 th century can be noticed among the series of glass compositions that were obtained. These changes could be related to the use of different glassmaker recipes and to the introduction of new raw materials for glass making.

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

Comportamiento Accionario según el Análisis de Fourier

Directory of Open Access Journals (Sweden)

Frank Lavagni Bolaños

2013-01-01

Full Text Available Este artículo presenta herramientas muy precisas, enespecial el análisis de Fourier (Carr y Madan, 1999, que seutilizan en otras disciplinas con resultados prácticos, como laingeniería, para analizar el comportamiento del precio de lasacciones en la bolsa, tanto en inversiones a largo plazo como amuy corto plazo. El concepto es aplicable al estudio de señalesdigitalizadas así como al mercado de divisas o a la bolsa devalores. Dada la actual crisis económica, es vital conocer lamayor cantidad de información posible a la hora de tomar unadecisión de inversión. Mucha de esta información se encuentraen el precio mismo y su historial. Se cuestiona, además, laimportancia de la velocidad de muestreo del precio de la accióna la hora de tomar decisiones de inversión de muy corto plazo,así como la de los parámetros calculados sobre estos datos. Coneste fin se emplean técnicas usadas en ingeniería para estudiarseñales, tales como la transformada discreta de Fourier, losfiltros y la teoría de muestreo.   ABSTRACT This article presents very precise tools, specifically a Fourieranalysis (Carr and Madan, 1999 used with practical results inother disciplines such as engineering, to analyze the behavior ofshare prices in stock markets, in long as well as in really shortterms. The concept is applicable to the study of digital signalsas well as in the currency or stock markets. Due to the currenteconomic crisis, it is paramount to know the greatest amountof information in order to make an investment decision. Muchof this information is in the share price and its history. Theimportance of the speed of sampling of share prices at thetime of making very short term investment decisions is alsoquestioned, as well as the parameters calculated from thesedata. To this end techniques used in engineering to studysignals, such as the discrete Fourier transform, filters andsampling theory are used.

High performance sapphire windows

Science.gov (United States)

Bates, Stephen C.; Liou, Larry

1993-02-01

High-quality, wide-aperture optical access is usually required for the advanced laser diagnostics that can now make a wide variety of non-intrusive measurements of combustion processes. Specially processed and mounted sapphire windows are proposed to provide this optical access to extreme environment. Through surface treatments and proper thermal stress design, single crystal sapphire can be a mechanically equivalent replacement for high strength steel. A prototype sapphire window and mounting system have been developed in a successful NASA SBIR Phase 1 project. A large and reliable increase in sapphire design strength (as much as 10x) has been achieved, and the initial specifications necessary for these gains have been defined. Failure testing of small windows has conclusively demonstrated the increased sapphire strength, indicating that a nearly flawless surface polish is the primary cause of strengthening, while an unusual mounting arrangement also significantly contributes to a larger effective strength. Phase 2 work will complete specification and demonstration of these windows, and will fabricate a set for use at NASA. The enhanced capabilities of these high performance sapphire windows will lead to many diagnostic capabilities not previously possible, as well as new applications for sapphire.

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...

Windows 7 The Missing Manual

CERN Document Server

Pogue, David

2010-01-01

In early reviews, geeks raved about Windows 7. But if you're an ordinary mortal, learning what this new system is all about will be challenging. Fear not: David Pogue's Windows 7: The Missing Manual comes to the rescue. Like its predecessors, this book illuminates its subject with reader-friendly insight, plenty of wit, and hardnosed objectivity for beginners as well as veteran PC users. Windows 7 fixes many of Vista's most painful shortcomings. It's speedier, has fewer intrusive and nagging screens, and is more compatible with peripherals. Plus, Windows 7 introduces a slew of new features,

Microsoft Windows Operating System Essentials

CERN Document Server

Carpenter, Tom

2012-01-01

A full-color guide to key Windows 7 administration concepts and topics Windows 7 is the leading desktop software, yet it can be a difficult concept to grasp, especially for those new to the field of IT. Microsoft Windows Operating System Essentials is an ideal resource for anyone new to computer administration and looking for a career in computers. Delving into areas such as fundamental Windows 7 administration concepts and various desktop OS topics, this full-color book addresses the skills necessary for individuals looking to break into a career in IT. Each chapter begins with a list of topi

Improved Windows for Cold Climates

DEFF Research Database (Denmark)

Laustsen, Jacob Birck; Svendsen, Svend

2005-01-01

considerably by reducing the frame width, which results in a larger transparent area causing a larger solar gain but still main-taining a low thermal transmittance. Using three layers of glass with large gaps, using very slim frame profiles, and omitting the edge constructions that normally causes thermal...... windows with improved energy performance. Traditionally evaluation of the energy performance of windows has focused on the thermal transmittance, but as windows differ from the rest of the building envelope by allowing solar energy to enter the building, the total solar energy transmittance is equally...... important. In the heating season in cold climates the solar gain through windows can be utilized for space heating which results in a corresponding reduction in the energy production that is often based on fossil fuels. A suitable quantity for evaluating the energy performance of windows in a simple...

Using the fast fourier transform in binding free energy calculations.

Science.gov (United States)

Nguyen, Trung Hai; Zhou, Huan-Xiang; Minh, David D L

2018-04-30

According to implicit ligand theory, the standard binding free energy is an exponential average of the binding potential of mean force (BPMF), an exponential average of the interaction energy between the unbound ligand ensemble and a rigid receptor. Here, we use the fast Fourier transform (FFT) to efficiently evaluate BPMFs by calculating interaction energies when rigid ligand configurations from the unbound ensemble are discretely translated across rigid receptor conformations. Results for standard binding free energies between T4 lysozyme and 141 small organic molecules are in good agreement with previous alchemical calculations based on (1) a flexible complex ( R≈0.9 for 24 systems) and (2) flexible ligand with multiple rigid receptor configurations ( R≈0.8 for 141 systems). While the FFT is routinely used for molecular docking, to our knowledge this is the first time that the algorithm has been used for rigorous binding free energy calculations. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Electro-Optical Imaging Fourier-Transform Spectrometer

Science.gov (United States)

Chao, Tien-Hsin; Zhou, Hanying

2006-01-01

An electro-optical (E-O) imaging Fourier-transform spectrometer (IFTS), now under development, is a prototype of improved imaging spectrometers to be used for hyperspectral imaging, especially in the infrared spectral region. Unlike both imaging and non-imaging traditional Fourier-transform spectrometers, the E-O IFTS does not contain any moving parts. Elimination of the moving parts and the associated actuator mechanisms and supporting structures would increase reliability while enabling reductions in size and mass, relative to traditional Fourier-transform spectrometers that offer equivalent capabilities. Elimination of moving parts would also eliminate the vibrations caused by the motions of those parts. Figure 1 schematically depicts a traditional Fourier-transform spectrometer, wherein a critical time delay is varied by translating one the mirrors of a Michelson interferometer. The time-dependent optical output is a periodic representation of the input spectrum. Data characterizing the input spectrum are generated through fast-Fourier-transform (FFT) post-processing of the output in conjunction with the varying time delay.

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.

Rigid thin windows for vacuum applications

Science.gov (United States)

Meyer, Glenn Allyn; Ciarlo, Dino R.; Myers, Booth Richard; Chen, Hao-Lin; Wakalopulos, George

1999-01-01

A thin window that stands off atmospheric pressure is fabricated using photolithographic and wet chemical etching techniques and comprises at least two layers: an etch stop layer and a protective barrier layer. The window structure also comprises a series of support ribs running the width of the window. The windows are typically made of boron-doped silicon and silicon nitride and are useful in instruments such as electron beam guns and x-ray detectors. In an electron beam gun, the window does not impede the electrons and has demonstrated outstanding gun performance and survivability during the gun tube manufacturing process.

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

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

Science.gov (United States)

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

2015-10-20

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

Windows 8.1 for dummies

CERN Document Server

Rathbone, Andy

2013-01-01

The bestselling book on Windows, now updated for the new 8.1 features Microsoft has fine-tuned Windows 8 with some important new features, and veteran author Andy Rathbone explains every one in this all-new edition of a long-time bestseller. Whether you're using Windows for the first time, upgrading from an older version, or just moving from Windows 8 to 8.1, here's what you need to know. Learn about the dual interfaces, the new Start button, how to customize the interface and boot operations, and how to work with programs and files, use the web and social media, manage music and photos, and

Windows 7 the definitive guide

CERN Document Server

Stanek, William R

2010-01-01

This book provides everything you need to manage and maintain Windows 7. You'll learn all of the features and enhancements in complete detail, along with specifics for configuring the operating system to put you in full control. Bestselling author and Windows expert William Stanek doesn't just show you the steps you need to follow, he also tells you how features work, why they work, and how you can customize them to meet your needs. Learn how to squeeze every bit of power out of Windows 7 to take full advantage of its features and programs. Set up, customize, and tune Windows 7-Optimize its

Live histograms in moving windows

International Nuclear Information System (INIS)

Zhil'tsov, V.E.

1989-01-01

Application of computer graphics for specific hardware testing is discussed. The hardware is position sensitive detector (multiwire proportional chamber) which is used in high energy physics experiments, and real-out electronics for it. Testing program is described (XPERT), which utilises multi-window user interface. Data are represented as histograms in windows. The windows on the screen may be moved, reordered, their sizes may be changed. Histograms may be put to any window, and hardcopy may be made. Some program internals are discussed. The computer environment is quite simple: MS-DOS IBM PC/XT, 256 KB RAM, CGA, 5.25'' FD, Epson MX. 4 refs.; 7 figs

Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

KAUST Repository

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2017-01-01

A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy

Generating Importance Map for Geometry Splitting using Discrete Ordinates Code in Deep Shielding Problem

International Nuclear Information System (INIS)

Kim, Jong Woon; Lee, Young Ouk

2016-01-01

When we use MCNP code for a deep shielding problem, we prefer to use variance reduction technique such as geometry splitting, or weight window, or source biasing to have relative error within reliable confidence interval. To generate importance map for geometry splitting in MCNP calculation, we should know the track entering number and previous importance on each cells since a new importance is calculated based on these information. If a problem is deep shielding problem such that we have zero tracks entering on a cell, we cannot generate new importance map. In this case, discrete ordinates code can provide information to generate importance map easily. In this paper, we use AETIUS code as a discrete ordinates code. Importance map for MCNP is generated based on a zone average flux of AETIUS calculation. The discretization of space, angle, and energy is not necessary for MCNP calculation. This is the big merit of MCNP code compared to the deterministic code. However, deterministic code (i.e., AETIUS) can provide a rough estimate of the flux throughout a problem relatively quickly. This can help MCNP by providing variance reduction parameters. Recently, ADVANTG code is released. This is an automated tool for generating variance reduction parameters for fixed-source continuous-energy Monte Carlo simulations with MCNP5 v1.60

Handbook of Fourier analysis & its applications

CERN Document Server

Marks, Robert J

2009-01-01

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

Working with Windows 7 at CERN (EN)

CERN Multimedia

CERN. Geneva

2010-01-01

Overview of new concepts and user interface changes in Windows 7 as compared with older versions of Windows: XP or Vista. Availability of Windows 7 at CERN and its integration with CERN Windows infrastructure will be discussed.

Applications of Fourier transforms to generalized functions

CERN Document Server

Rahman, M

2011-01-01

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

Moving discrete breathers in a Klein-Gordon chain with an impurity

International Nuclear Information System (INIS)

Cuevas, J; Palmero, F; Archilla, J F R; Romero, F R

2002-01-01

We analyse the influence of an impurity in the evolution of moving discrete breathers in a Klein-Gordon chain with non-weak nonlinearity. Three different types of behaviour can be observed when moving breathers interact with the impurity: they pass through the impurity continuing their direction of movement; they are reflected by the impurity; they are trapped by the impurity, giving rise to chaotic breathers, as their Fourier power spectra show. Resonance with a breather centred at the impurity site is conjectured to be a necessary condition for the appearance of the trapping phenomenon. This paper establishes a difference between the resonance condition of the non-weak nonlinearity approach and the resonance condition with the linear impurity mode in the case of weak nonlinearity

Discrete maximal regularity of time-stepping schemes for fractional evolution equations.

Science.gov (United States)

Jin, Bangti; Li, Buyang; Zhou, Zhi

2018-01-01

In this work, we establish the maximal [Formula: see text]-regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order [Formula: see text], [Formula: see text], in time. These schemes include convolution quadratures generated by backward Euler method and second-order backward difference formula, the L1 scheme, explicit Euler method and a fractional variant of the Crank-Nicolson method. The main tools for the analysis include operator-valued Fourier multiplier theorem due to Weis (Math Ann 319:735-758, 2001. doi:10.1007/PL00004457) and its discrete analogue due to Blunck (Stud Math 146:157-176, 2001. doi:10.4064/sm146-2-3). These results generalize the corresponding results for parabolic problems.

DISCRETE MATHEMATICS/NUMBER THEORY

OpenAIRE

Mrs. Manju Devi*

2017-01-01

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics such as integers, graphs, and statements do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by ...

Mastering Windows Server 2012 R2

CERN Document Server

Minasi, Mark; Booth, Christian; Butler, Robert; McCabe, John; Panek, Robert; Rice, Michael; Roth, Stefan

2013-01-01

Check out the new Hyper-V, find new and easier ways to remotely connect back into the office, or learn all about Storage Spaces-these are just a few of the features in Windows Server 2012 R2 that are explained in this updated edition from Windows authority Mark Minasi and a team of Windows Server experts led by Kevin Greene. This book gets you up to speed on all of the new features and functions of Windows Server, and includes real-world scenarios to put them in perspective. If you're a system administrator upgrading to, migrating to, or managing Windows Server 2012 R2, find what you need to

Microsoft Windows Intune 20 Quickstart Administration

CERN Document Server

Overton, David

2012-01-01

This book is a concise and practical tutorial that shows you how to plan, set up and maintain Windows Intune and manage a group of PCs. If you are an administrator or partner who wants to plan, set up and maintain Windows Intune and manage a group of PCs then this book is for you . You should have a basic understanding of Windows administration, however, knowledge of Windows Intune would not be required.

Transforming the market for residential windows: design considerations for DOE's Efficient Window Collaborative

Energy Technology Data Exchange (ETDEWEB)

Eto, J.; Arasteh, D.; Selkowitz, S.

1998-08-01

Market adoption of recent, commercially available technological advances that improve the energy performance of windows will lead to immediate economic and energy savings benefits to the nation. This paper is a scoping study intended to inform the design of a major DOE initiative to accelerate market adoption of these windows in the residential sector. We describe the structure of the US residential window market and the interests of the various market players. We then briefly review five recent market transformation initiatives. Finally, we summarize our findings in a list of considerations we believe will be important for the DOE's initiative to transform the US residential window market.

Resonance and web structure in discrete soliton systems: the two-dimensional Toda lattice and its fully discrete and ultra-discrete analogues

International Nuclear Information System (INIS)

Maruno, Ken-ichi; Biondini, Gino

2004-01-01

We present a class of solutions of the two-dimensional Toda lattice equation, its fully discrete analogue and its ultra-discrete limit. These solutions demonstrate the existence of soliton resonance and web-like structure in discrete integrable systems such as differential-difference equations, difference equations and cellular automata (ultra-discrete equations)

Fourier Series

Indian Academy of Sciences (India)

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

Travailler avec Windows 7 au CERN

CERN Multimedia

CERN. Geneva

2011-01-01

Vue d'ensemble des nouveaux concepts et des changements dans l'interface utilisateur survenus dans Windows 7 depuis les versions antérieures de Windows (XP ou Vista). Le plan de migration à Windows 7 sera aussi débattu.

Travailler avec Windows 7 au CERN

CERN Multimedia

CERN. Geneva

2012-01-01

Vue d'ensemble des nouveaux concepts et des changements dans l'interface utilisateur survenus dans Windows 7 depuis les versions antérieures de Windows (XP ou Vista). Le plan de migration à Windows 7 sera aussi débattu.

Alternating multivariate trigonometric functions and corresponding Fourier transforms

International Nuclear Information System (INIS)

Klimyk, A U; Patera, J

2008-01-01

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

Windows VPN Set Up | High-Performance Computing | NREL

Science.gov (United States)

Windows VPN Set Up Windows VPN Set Up To set up Windows for HPC VPN, here are the steps: Download your version of Windows. Note: We only support the the Endian Connect software when connecting to the a VPN connection to the HPC systems. Windows Version Connect App Windows 10

Fourier transform n.m.r. spectroscopy

International Nuclear Information System (INIS)

Shaw, D.

1976-01-01

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

Fourier transform n. m. r. spectroscopy

Energy Technology Data Exchange (ETDEWEB)

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

1976-01-01

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

Properties of the distributional finite Fourier transform

OpenAIRE

Carmichael, Richard D.

2016-01-01

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

Generalized Fourier transforms classes

DEFF Research Database (Denmark)

Berntsen, Svend; Møller, Steen

2002-01-01

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

The Nicest way to migrate your Windows computer ( The Windows 2000 Migration Task Force)

CERN Document Server

2001-01-01

With Windows 2000, CERN users will discover a more stable and reliable working environment and will have access to all the latest applications. The Windows 2000 Migration Task Force - a representative from each division.

Peliohjelmointi Windows Phone 8:lle

OpenAIRE

Bäckström, Toni

2014-01-01

Tässä insinöörityössä tutustutaan Windows Phone 8 -mobiilikäyttöjärjestelmään peliohjelmoijan näkökulmasta. Työn tavoitteena oli erityisesti esitellä Microsoftin itse kehittämiä XNA- ja DirectX-peliohjelmointikirjastoja teoriassa ja käytännössä. Työn aluksi käydään läpi hieman Windows Phonen historiaa ja yleisesti kehittämistä Windows Phone 8:lle. Tämän jälkeen luodaan katsaus Windows Phone 8:aan pelialustana. Työn suurin osuus on XNA:n ja DirectX:n esittely teoriassa; kummastakin men...

Solar Heat Gain Coefficient (SHGC) | Efficient Windows Collaborative

Science.gov (United States)

Foundry Foundry New Construction Windows Window Selection Tool Selection Process Design Guidance Installation Replacement Windows Window Selection Tool Assessing Options Selection Process Design Guidance Installation Understanding Windows Benefits Design Considerations Measuring Performance Performance Standards

Mapped Fourier Methods for stiff problems in toroidal geometry

OpenAIRE

Guillard , Herve

2014-01-01

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

Thin Film & Deposition Systems (Windows)

Data.gov (United States)

Federal Laboratory Consortium — Coating Lab: Contains chambers for growing thin film window coatings. Plasma Applications Coating Lab: Contains chambers for growing thin film window coatings. Solar...

Discrete Multiwavelet Critical-Sampling Transform-Based OFDM System over Rayleigh Fading Channels

Directory of Open Access Journals (Sweden)

Sameer A. Dawood

2015-01-01

Full Text Available Discrete multiwavelet critical-sampling transform (DMWCST has been proposed instead of fast Fourier transform (FFT in the realization of the orthogonal frequency division multiplexing (OFDM system. The proposed structure further reduces the level of interference and improves the bandwidth efficiency through the elimination of the cyclic prefix due to the good orthogonality and time-frequency localization properties of the multiwavelet transform. The proposed system was simulated using MATLAB to allow various parameters of the system to be varied and tested. The performance of DMWCST-based OFDM (DMWCST-OFDM was compared with that of the discrete wavelet transform-based OFDM (DWT-OFDM and the traditional FFT-based OFDM (FFT-OFDM over flat fading and frequency-selective fading channels. Results obtained indicate that the performance of the proposed DMWCST-OFDM system achieves significant improvement compared to those of DWT-OFDM and FFT-OFDM systems. DMWCST improves the performance of the OFDM system by a factor of 1.5–2.5 dB and 13–15.5 dB compared with the DWT and FFT, respectively. Therefore the proposed system offers higher data rate in wireless mobile communications.

Accurate measurements and temperature dependence of the water vapor self-continuum absorption in the 2.1 μm atmospheric window

International Nuclear Information System (INIS)

Ventrillard, I.; Romanini, D.; Mondelain, D.; Campargue, A.

2015-01-01

In spite of its importance for the evaluation of the Earth radiative budget, thus for climate change, very few measurements of the water vapor continuum are available in the near infrared atmospheric windows especially at temperature conditions relevant for our atmosphere. In addition, as a result of the difficulty to measure weak broadband absorption signals, the few available measurements show large disagreements. We report here accurate measurements of the water vapor self-continuum absorption in the 2.1 μm window by Optical Feedback Cavity Enhanced Absorption Spectroscopy (OF-CEAS) for two spectral points located at the low energy edge and at the center of the 2.1 μm transparency window, at 4302 and 4723 cm −1 , respectively. Self-continuum cross sections, C S , were retrieved with a few % relative uncertainty, from the quadratic dependence of the spectrum base line level measured as a function of water vapor pressure, between 0 and 16 Torr. At 296 K, the C S value at 4302 cm −1 is found 40% higher than predicted by the MT-CKD V2.5 model, while at 4723 cm −1 , our value is 5 times larger than the MT-CKD value. On the other hand, these OF-CEAS C S values are significantly smaller than recent measurements by Fourier transform spectroscopy at room temperature. The temperature dependence of the self-continuum cross sections was also investigated for temperatures between 296 K and 323 K (23-50 °C). The derived temperature variation is found to be similar to that derived from previous Fourier transform spectrometer (FTS) measurements performed at higher temperatures, between 350 K and 472 K. The whole set of measurements spanning the 296-472 K temperature range follows a simple exponential law in 1/T with a slope close to the dissociation energy of the water dimer, D 0 ≈ 1100 cm −1

Imaging windows for long-term intravital imaging

Science.gov (United States)

Alieva, Maria; Ritsma, Laila; Giedt, Randy J; Weissleder, Ralph; van Rheenen, Jacco

2014-01-01

Intravital microscopy is increasingly used to visualize and quantitate dynamic biological processes at the (sub)cellular level in live animals. By visualizing tissues through imaging windows, individual cells (e.g., cancer, host, or stem cells) can be tracked and studied over a time-span of days to months. Several imaging windows have been developed to access tissues including the brain, superficial fascia, mammary glands, liver, kidney, pancreas, and small intestine among others. Here, we review the development of imaging windows and compare the most commonly used long-term imaging windows for cancer biology: the cranial imaging window, the dorsal skin fold chamber, the mammary imaging window, and the abdominal imaging window. Moreover, we provide technical details, considerations, and trouble-shooting tips on the surgical procedures and microscopy setups for each imaging window and explain different strategies to assure imaging of the same area over multiple imaging sessions. This review aims to be a useful resource for establishing the long-term intravital imaging procedure. PMID:28243510

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)

Content adaptive illumination for Fourier ptychography.

Science.gov (United States)

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

2014-12-01

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

Vacuum window glazings for energy-efficient buildings

Energy Technology Data Exchange (ETDEWEB)

Benson, D.K.; Smith, L.K.; Tracy, C.E.; Potter, T.; Christensen, C. (Solar Energy Research Inst., Golden, CO (USA)); Soule, D.E. (Western Illinois Univ., Macomb, IL (USA))

1990-05-01

The technical feasibility of a patented, laser-welded, evacuated insulating window was studied. The window has two edge-sealed sheets of glass separated by 0.5-mm glass spheres spaced 30 mm apart in a regular array. A highly insulating frame is required and several designs were analyzed. The vacuum window's combination of high solar transmittance and low thermal conductance makes it superior to many other windows in cold climates. In the US Pacific Northwest, the vacuum window could save about 6 MJ of heating energy annually per square meter of window in comparison to conventional, double-glazed windows. A large, vacuum laser-welding facility was designed and installed to conduct glass welding experiments and to fabricate full-sized vacuum windows. Experiments confirmed the feasibility of laser-sealing glass in vacuum but identified two difficulties. Under some circumstances, bubbles of dissolved gases form during welding and weaken the seal. Glass also vaporizes and contaminates the laser beam steering mirror. A novel moving metal foil mirror was developed to circumvent the contamination problem, but it has not yet been used to complete welding experiments and fabricate full-sized vacuum windows. 63 refs., 53 figs., 19 tabs.

(Anti)symmetric multivariate exponential functions and corresponding Fourier transforms

International Nuclear Information System (INIS)

Klimyk, A U; Patera, J

2007-01-01

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

Windows 7 A quick, hands-on introduction

CERN Document Server

Lee, Wei-Meng

2009-01-01

This compact book offers the quickest path for Windows users to get started with Microsoft's Windows 7 operating system. You get the essential information you need to upgrade or install the system and configure it to fit your activities, along with a tour of Windows 7's features and built-in applications. Microsoft has learned from the mistakes of Windows Vista, and Windows 7 shows it-this new OS is much faster and more stable. With Windows 7: Up and Running, you'll learn what's new and what's changed from XP and Vista, and get advice on ways to use this system for work, entertainment, inst

Windows 8.1 for seniors for dummies

CERN Document Server

Weverka, Peter

2013-01-01

Seniors, here's what you need to get up and running on Windows 8.1 Microsoft, now a little older and wiser, is back with Windows 8.1, the revamped version that brings fresh changes and welcome improvements to the Windows 8 operating system. And now you savvy seniors can get the very most out of this easier-to-use Windows 8.1 with our friendly new guide. Using large print that makes the book easier to read plus magnified screen shots to help make Windows less intimidating, this book walks you through common tasks and show you how to get things done in fine style. Helps you get to know Windows

Windows Server 2012 R2 administrator cookbook

CERN Document Server

Krause, Jordan

2015-01-01

This book is intended for system administrators and IT professionals with experience in Windows Server 2008 or Windows Server 2012 environments who are looking to acquire the skills and knowledge necessary to manage and maintain the core infrastructure required for a Windows Server 2012 and Windows Server 2012 R2 environment.

Dual-window dual-bandwidth spectroscopic optical coherence tomography metric for qualitative scatterer size differentiation in tissues.

Science.gov (United States)

Tay, Benjamin Chia-Meng; Chow, Tzu-Hao; Ng, Beng-Koon; Loh, Thomas Kwok-Seng

2012-09-01

This study investigates the autocorrelation bandwidths of dual-window (DW) optical coherence tomography (OCT) k-space scattering profile of different-sized microspheres and their correlation to scatterer size. A dual-bandwidth spectroscopic metric defined as the ratio of the 10% to 90% autocorrelation bandwidths is found to change monotonically with microsphere size and gives the best contrast enhancement for scatterer size differentiation in the resulting spectroscopic image. A simulation model supports the experimental results and revealed a tradeoff between the smallest detectable scatterer size and the maximum scatterer size in the linear range of the dual-window dual-bandwidth (DWDB) metric, which depends on the choice of the light source optical bandwidth. Spectroscopic OCT (SOCT) images of microspheres and tonsil tissue samples based on the proposed DWDB metric showed clear differentiation between different-sized scatterers as compared to those derived from conventional short-time Fourier transform metrics. The DWDB metric significantly improves the contrast in SOCT imaging and can aid the visualization and identification of dissimilar scatterer size in a sample. Potential applications include the early detection of cell nuclear changes in tissue carcinogenesis, the monitoring of healing tendons, and cell proliferation in tissue scaffolds.