Journal ArticleDOI
The Fast Fourier Transform and Its Applications
TLDR
A description of the alogorithm and its programming is given here and followed by a theorem relating its operands, the finite sample sequences, to the continuous functions they often are intended to approximate.Abstract:
The advent of the fast Fourier transform method has greatly extended our ability to implement Fourier methods on digital computers A description of the alogorithm and its programming is given here and followed by a theorem relating its operands, the finite sample sequences, to the continuous functions they often are intended to approximate An analysis of the error due to discrete sampling over finite ranges is given in terms of aliasing Procedures for computing Fourier integrals, convolutions and lagged products are outlinedread more
Citations
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Book
Remote sensing, models, and methods for image processing
TL;DR: The Nature of Remote Sensing: Introduction, Sensor Characteristics and Spectral Stastistics, and Spatial Transforms: Introduction.
Journal ArticleDOI
Single tone parameter estimation from discrete-time observations
D. Rife,R. Boorstyn +1 more
TL;DR: Estimation of the parameters of a single-frequency complex tone from a finite number of noisy discrete-time observations is discussed and appropriate Cramer-Rao bounds and maximum-likelihood estimation algorithms are derived.
Journal ArticleDOI
Fast Fourier transforms for nonequispaced data
A. Dutt,Vladimir Rokhlin +1 more
TL;DR: In this paper, a group of algorithms is presented generalizing the fast Fourier transform to the case of noninteger frequencies and nonequispaced nodes on the interval $[ - \pi,\pi ].
Journal ArticleDOI
A precorrected-FFT method for electrostatic analysis of complicated 3-D structures
J.R. Phillips,Jacob K. White +1 more
TL;DR: A new algorithm for accelerating the potential calculation which occurs in the inner loop of iterative algorithms for solving electromagnetic boundary integral equations, which can be superior to the fast multipole based schemes by more than an order of magnitude.
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.
Journal ArticleDOI
What is the fast Fourier transform
W.T. Cochran,J.W. Cooley,D.L. Favin,H. Helms,R. A. Kaenel,W.W. Lang,G. Maling,D.E. Nelson,C. Rader,Peter D. Welch +9 more
TL;DR: The discrete Fourier transform of a time series is defined, some of its properties are discussed, the associated fast method for computing this transform is derived, and some of the computational aspects of the method are presented.