Topic

# Fast Fourier transform

About: Fast Fourier transform is a(n) research topic. Over the lifetime, 25390 publication(s) have been published within this topic receiving 405838 citation(s). The topic is also known as: Fast Fourier Transform, FFT & FFT.

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Kyoto University

^{1}TL;DR: A simplified scoring system is proposed that performs well for reducing CPU time and increasing the accuracy of alignments even for sequences having large insertions or extensions as well as distantly related sequences of similar length.

Abstract: A multiple sequence alignment program, MAFFT, has been developed. The CPU time is drastically reduced as compared with existing methods. MAFFT includes two novel techniques. (i) Homologous regions are rapidly identified by the fast Fourier transform (FFT), in which an amino acid sequence is converted to a sequence composed of volume and polarity values of each amino acid residue. (ii) We propose a simplified scoring system that performs well for reducing CPU time and increasing the accuracy of alignments even for sequences having large insertions or extensions as well as distantly related sequences of similar length. Two different heuristics, the progressive method (FFT-NS-2) and the iterative refinement method (FFT-NS-i), are implemented in MAFFT. The performances of FFT-NS-2 and FFT-NS-i were compared with other methods by computer simulations and benchmark tests; the CPU time of FFT-NS-2 is drastically reduced as compared with CLUSTALW with comparable accuracy. FFT-NS-i is over 100 times faster than T-COFFEE, when the number of input sequences exceeds 60, without sacrificing the accuracy.

9,539 citations

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24 Jan 2005

TL;DR: It is shown that such an approach can yield an implementation of the discrete Fourier transform that is competitive with hand-optimized libraries, and the software structure that makes the current FFTW3 version flexible and adaptive is described.

Abstract: FFTW is an implementation of the discrete Fourier transform (DFT) that adapts to the hardware in order to maximize performance. This paper shows that such an approach can yield an implementation that is competitive with hand-optimized libraries, and describes the software structure that makes our current FFTW3 version flexible and adaptive. We further discuss a new algorithm for real-data DFTs of prime size, a new way of implementing DFTs by means of machine-specific single-instruction, multiple-data (SIMD) instructions, and how a special-purpose compiler can derive optimized implementations of the discrete cosine and sine transforms automatically from a DFT algorithm.

4,792 citations

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TL;DR: Iterative algorithms for phase retrieval from intensity data are compared to gradient search methods and it is shown that both the error-reduction algorithm for the problem of a single intensity measurement and the Gerchberg-Saxton algorithm forThe problem of two intensity measurements converge.

Abstract: Iterative algorithms for phase retrieval from intensity data are compared to gradient search methods. Both the problem of phase retrieval from two intensity measurements (in electron microscopy or wave front sensing) and the problem of phase retrieval from a single intensity measurement plus a non-negativity constraint (in astronomy) are considered, with emphasis on the latter. It is shown that both the error-reduction algorithm for the problem of a single intensity measurement and the Gerchberg-Saxton algorithm for the problem of two intensity measurements converge. The error-reduction algorithm is also shown to be closely related to the steepest-descent method. Other algorithms, including the input-output algorithm and the conjugate-gradient method, are shown to converge in practice much faster than the error-reduction algorithm. Examples are shown.

4,654 citations

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01 Jan 1992TL;DR: This paper presents a meta-analysis of the Z-Transform and its application to the Analysis of LTI Systems, and its properties and applications, as well as some of the algorithms used in this analysis.

Abstract: 1. Introduction. 2. Discrete-Time Signals and Systems. 3. The Z-Transform and Its Application to the Analysis of LTI Systems. 4. Frequency Analysis of Signals and Systems. 5. The Discrete Fourier Transform: Its Properties and Applications. 6. Efficient Computation of the DFT: Fast Fourier Transform Algorithms. 7. Implementation of Discrete-Time Systems. 8. Design of Digital Filters. 9. Sampling and Reconstruction of Signals. 10. Multirate Digital Signal Processing. 11. Linear Prediction and Optimum Linear Filters. 12. Power Spectrum Estimation. Appendix A. Random Signals, Correlation Functions, and Power Spectra. Appendix B. Random Numbers Generators. Appendix C. Tables of Transition Coefficients for the Design of Linear-Phase FIR Filters. Appendix D. List of MATLAB Functions. References and Bibliography. Index.

3,837 citations

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01 Jan 2000TL;DR: This paper presents a meta-analyses of Chebyshev differentiation matrices using the DFT and FFT as a guide to solving fourth-order grid problems.

Abstract: Preface 1 Differentiation matrices 2 Unbounded grids: the semidiscrete Fourier transform 3 Periodic grids: the DFT and FFT 4 Smoothness and spectral accuracy 5 Polynomial interpolation and clustered grids 6 Chebyshev differentiation matrices 7 Boundary value problems 8 Chebyshev series and the FFT 9 Eigenvalues and pseudospectra 10 Time-stepping and stability regions 11 Polar coordinates 12 Integrals and quadrature formulas 13 More about boundary conditions 14 Fourth-order problems Afterword Bibliography Index

3,329 citations