Journal ArticleDOI
The fast Fourier transform
E. O. Brigham,R. E. Morrow +1 more
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TLDR
The Fast Fourier Transform (FFT) as discussed by the authors is a computer algorithm that computes the discrete Fourier transform much faster than other algorithms, and it can be used to compute an N = 210-point transform 100 times faster than using a direct approach.Abstract:
The fast Fourier transform (FFT), a computer algorithm that computes the discrete Fourier transform much faster than other algorithms, is explained. Examples and detailed procedures are provided to assist the reader in learning how to use the algorithm. The savings in computer time can be huge; for example, an N = 210-point transform can be computed with the FFT 100 times faster than with the use of a direct approach.read more
Citations
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Journal ArticleDOI
Spectrum analysis—A modern perspective
Steven Kay,S.L. Marple +1 more
TL;DR: In this paper, a summary of many of the new techniques developed in the last two decades for spectrum analysis of discrete time series is presented, including classical periodogram, classical Blackman-Tukey, autoregressive (maximum entropy), moving average, autotegressive-moving average, maximum likelihood, Prony, and Pisarenko methods.
Book
Characterization of Frequency Stability
J.A. Barnes,Andrew R. Chi,Leonard S. Cutler,Daniel J. Healey,D. B. Leeson,Thomas E. McGunigal,James A. Mullen,Warren L. Smith,Richard L. Sydnor,R. F. C. Vessot,Gernot M. R. Winkler +10 more
TL;DR: In this article, the spectral density S y (f) of the function y(t) where the spectrum is considered to be one-sided on a per hertz basis is defined.
Journal ArticleDOI
A guided tour of the fast Fourier transform
TL;DR: This article is intended as a primer on the fast Fourier transform, which has revolutionized the digital processing of waveforms and is needed for a whole new range of applications for this classic mathematical device.
Journal ArticleDOI
Hadamard transform image coding
TL;DR: A high-speed computational algorithm, similar to the fast Fourier transform algorithm, which performs the Hadamard transformation has been developed, which provides a potential toleration to channel errors and the possibility of reduced bandwidth transmission.
Journal ArticleDOI
A linear filtering approach to the computation of discrete Fourier transform
TL;DR: It is shown that the discrete equivalent of a chirp filter is needed to implement the computation of the discrete Fourier transform (DFT) as a linear filtering process, and that use of the conventional FFT permits the computations in a time proportional to N \log_{2} N for any N.
References
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Journal ArticleDOI
An algorithm for the machine calculation of complex Fourier series
J.W. Cooley,John W. Tukey +1 more
TL;DR: Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.
Proceedings ArticleDOI
Fast Fourier Transforms: for fun and profit
W. M. Gentleman,G. Sande +1 more
TL;DR: The "Fast Fourier Transform" has had a major effect on several areas of computing, the most striking example being techniques of numerical convolution, which have been completely revolutionized.
Proceedings ArticleDOI
High-speed convolution and correlation
TL;DR: A procedure for synthesizing and analyzing Fourier series for discrete periodic complex functions and computation times are proportional to log 2sub 2 as expressed in Eq.