On Performance of Sparse Fast Fourier Transform Algorithms Using the Aliasing Filter

Computing the sparse fast Fourier transform (sFFT) has emerged as a critical topic for a long time because of its high efficiency and wide practicability. More than twenty different sFFT algorithms compute discrete Fourier transform (DFT) by their unique methods so far. In order to use them properly, the urgent topic of great concern is how to analyze and evaluate the performance of these algorithms in theory and practice. This paper mainly discusses the technology and performance of sFFT algorithms using the aliasing filter. In the first part, the paper introduces the three frameworks: the one-shot framework based on the compressed sensing (CS) solver, the peeling framework based on the bipartite graph and the iterative framework based on the binary tree search. Then, we obtain the conclusion of the performance of six corresponding algorithms: the sFFT-DT1.0, sFFT-DT2.0, sFFT-DT3.0, FFAST, R-FFAST, and DSFFT algorithms in theory. In the second part, we make two categories of experiments for computing the signals of different SNRs, different lengths, and different sparsities by a standard testing platform and record the run time, the percentage of the signal sampled, and the L0, L1, and L2 errors both in the exactly sparse case and the general sparse case. The results of these performance analyses are our guide to optimize these algorithms and use them selectively.

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Empirical Evaluation of Typical Sparse Fast Fourier Transform Algorithms

10.21203/rs.3.rs-132810/v1 ◽

2020 ◽

Author(s):

Bin Li ◽

Zhikang Jiang ◽

Jie Chen

Keyword(s):

Fourier Transform ◽

Theoretical Analysis ◽

Fast Fourier Transform ◽

Frequency Domain ◽

Empirical Evaluation ◽

Theoretical Research ◽

Sparse Signal ◽

Standard Testing ◽

Long Time ◽

Sparse Fast Fourier Transform

Abstract Computing the Sparse Fast Fourier Transform(sFFT) of a K-sparse signal of size N has emerged as a critical topic for a long time. The sFFT algorithms decrease the runtime and sampling complexity by taking advantage of the signal's inherent characteristics that a large number of signals are sparse in the frequency domain. More than ten sFFT lgorithms have been proposed, which can be classfied into many types according to filter, framework, method of location, method of estimation. In this paper, the technology of these algorithms is completely analyzed in theory. The performance of them is thoroughly tested and verified in practice. The theoretical analysis includes the following contents: five operations of ignal, three methods of frequency bucketization, five methods of location, four methods of estimation, two problems caused by bucketization, three methods to solve these two problems, four algorithmic frameworks. All the above technologies and methods are introduced in detail and examples are given to illustrate the above research. After theoretical research, we make experiments for computing the signals of different SNR, N, K by a standard testing platform and record the run time, percentage of the signal sampled and L0;L1;L2 error with eight different sFFT algorithms. The result of experiments satisfies the inferences obtained in theory.

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Iris-based human identity recognition with machine learning methods and discrete fast Fourier transform

Innovations in Systems and Software Engineering ◽

10.1007/s11334-021-00392-9 ◽

2021 ◽

Author(s):

Maciej Szymkowski ◽

Piotr Jasiński ◽

Khalid Saeed

Keyword(s):

Fourier Transform ◽

Fast Fourier Transform ◽

High Efficiency ◽

Principal Component ◽

Support Vector ◽

Human Identity ◽

Identity Recognition ◽

Vector Machines ◽

Principal Component Analysis Algorithm ◽

The One

AbstractOne of the most important modules of computer systems is the one that is responsible for user safety. It was proven that simple passwords and logins cannot guarantee high efficiency and are easy to obtain by the hackers. The well-known alternative is identity recognition based on biometrics. In recent years, more interest was observed in iris as a biometrics trait. It was caused due to high efficiency and accuracy guaranteed by this measurable feature. The consequences of such interest are observable in the literature. There are multiple, diversified approaches proposed by different authors. However, neither of them uses discrete fast Fourier transform (DFFT) components to describe iris sample. In this work, the authors present their own approach to iris-based human identity recognition with DFFT components selected with principal component analysis algorithm. For classification, three algorithms were used—k-nearest neighbors, support vector machines and artificial neural networks. Performed tests have shown that satisfactory results can be obtained with the proposed method.

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An Input-Adaptive Algorithm for High Performance Sparse Fast Fourier Transform

Languages and Compilers for Parallel Computing - Lecture Notes in Computer Science ◽

10.1007/978-3-319-09967-5_15 ◽

2014 ◽

pp. 252-271

Author(s):

Shuo Chen ◽

Xiaoming Li

Keyword(s):

Fourier Transform ◽

Fast Fourier Transform ◽

Adaptive Algorithm ◽

High Performance ◽

Sparse Fast Fourier Transform

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Sparse-fast-Fourier-transform-based quick synchronization for optical direct detection orthogonal frequency division multiplexing systems

Optics Letters ◽

10.1364/ol.43.002014 ◽

2018 ◽

Vol 43 (9) ◽

pp. 2014 ◽

Cited By ~ 2

Author(s):

Qiong Wu ◽

Yating Xiang ◽

Yizhao Chen ◽

Ming Tang ◽

Songnian Fu ◽

...

Keyword(s):

Fourier Transform ◽

Fast Fourier Transform ◽

Orthogonal Frequency Division Multiplexing ◽

Direct Detection ◽

Frequency Division Multiplexing ◽

Frequency Division ◽

Sparse Fast Fourier Transform ◽

Multiplexing Systems

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A Fast Method for Solving Contact Plasticity in a Half Space

ASME/STLE 2011 Joint Tribology Conference ◽

10.1115/ijtc2011-61147 ◽

2011 ◽

Author(s):

Zhanjiang Wang ◽

Xiaoqing Jin ◽

Shuangbiao Liu ◽

Leon M. Keer ◽

Jian Cao ◽

...

Keyword(s):

Fourier Transform ◽

Residual Stresses ◽

Fast Fourier Transform ◽

Half Space ◽

Three Dimensional ◽

New Method ◽

Fast Method ◽

Discrete Convolution ◽

Influence Coefficients ◽

The One

This paper presents a new method of contact plasticity analysis based on Galerkin vectors to solve the eigenstresses due to eigenstrain. The influence coefficients relating eigenstrains to eigenstresses thus can be divided into four terms the one due to the eigenstrains in the full space, others due to the mirrored eigenstrains in the mirror half space. Each term can be solved fast and efficient by using the three-dimensional discrete convolution and fast Fourier transform (DC-FFT) or the three-dimensional discrete correlation and fast Fourier transform (DCR-FFT). The new method is used to analyze the contact plastic residual stresses in half space.

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Waiting for Spring to Come Again: Feminist Theatre, 1978 and 1989

New Theatre Quarterly ◽

10.1017/s0266464x00003961 ◽

1990 ◽

Vol 6 (21) ◽

pp. 43-56 ◽

Cited By ~ 1

Author(s):

Gillian Hanna

Keyword(s):

Theory And Practice ◽

New Yorker ◽

Royal Court ◽

Feminist Theatre ◽

Dario Fo ◽

Theatre Company ◽

To Come ◽

And Performance ◽

The One ◽

And Shifts

Most of the heavily-quoted interviews available on feminist theatre are in serious need of updating. A current account is needed of ‘feminism and theatre’ as experienced by feminist theatre practitioners, and as perceived by feminist theatre students, critics, players and their audiences. To meet this need, NTQ plans a series of interviews with women involved in the British feminist theatre movement today, whose career paths trace developments and shifts in the feminist theory and practice of the past fifteen years. The first interview is with Gillian Hanna, who worked with the 7:84 Theatre Company and with Belt and Braces from 1971 to 1975, before co-founding the Monstrous Regiment feminist theatre group in 1975. Hanna worked exclusively within the Regiment from 1975 until 1981–82. and is one of the three original members who still actively participate in Regimental management, production, and performance, though she now works extensively outside the group as well, having acted in repertory at the Liverpool Everyman and in Newcastle, Sheffield and Derby. Recently, Hanna spent the best part of a year playing in The House of Bernardo Alba. which opened at the Lyric. Hammersmith, and ran in the West End, and in the Spring of 1989 she played in Caryl Churchill's Ice Cream at the Royal Court. Her acting credits include work in TV and film, and her interests extend to translation of playtexts from French and Italian: she translated Dario Fo's Elizabeth, and is currently on a commission to translate (and re-translate) the complete oeuvre of the one-woman plays of Franca Rame and Dario Fo. Three of the Rame/Fo plays – under the joint title A Common Woman – were recently produced at the Sheffield Crucible and at the Half Moon in London, for which performance Hanna won the 1989 Time Out ‘01 for London’ Award. Projects currently under way within the Regiment include an adaptation of a Marivaux play (The Colony), and possible plans to tour both A Common Woman and Beatrice. She is interviewed by Lizbeth Goodman, originally a New Yorker, and currently a junior member and scholar of St. John's College and a graduate researcher in the English Faculty of Cambridge University, where she is working on a doctoral thesis on feminist theatre since 1968, and a book on the politics of theatre funding.

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An Efficient Galerkin Averaging-Incremental Harmonic Balance Method Based on the Fast Fourier Transform and Tensor Contraction

Volume 1: Acoustics, Vibration, and Phononics ◽

10.1115/imece2020-24009 ◽

2020 ◽

Author(s):

R. Ju ◽

W. Fan ◽

W. D. Zhu

Keyword(s):

Fourier Transform ◽

Fast Fourier Transform ◽

Harmonic Balance ◽

High Efficiency ◽

Jacobian Matrix ◽

Sampling Rate ◽

Harmonic Balance Method ◽

Incremental Harmonic Balance ◽

Tensor Contraction ◽

Ihb Method

Abstract An efficient Galerkin averaging-incremental harmonic balance (EGA-IHB) method is developed based on the fast Fourier transform (FFT) and tensor contraction to increase efficiency and robustness of the IHB method when calculating periodic responses of complex nonlinear systems with non-polynomial nonlinearities. As a semi-analytical method, derivation of formulae and programming are significantly simplified in the EGA-IHB method. The residual vector and Jacobian matrix corresponding to nonlinear terms in the EGA-IHB method are expressed using truncated Fourier series. After calculating Fourier coefficient vectors using the FFT, tensor contraction is used to calculate the Jacobian matrix, which can significantly improve numerical efficiency. Since inaccurate results may be obtained from discrete Fourier transform-based methods when aliasing occurs, the minimal non-aliasing sampling rate is determined for the EGA-IHB method. Performances of the EGA-IHB method are analyzed using several benchmark examples; its accuracy, efficiency, convergence, and robustness are analyzed and compared with several widely used semi-analytical methods. The EGA-IHB method has high efficiency and good robustness for both polynomial and nonpolynomial nonlinearities, and it has considerable advantages over the other methods.

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