Journal ArticleDOI
Application of the fast Fourier transform to computation of Fourier integrals, Fourier series, and convolution integrals
TLDR
In this article, the properties of the fast Fourier transform are related to commonly used integral transforms including the Fourier Transform and convolution integrals, and the relationship between the Fast Fourier Transformer and Fourier series is discussed.Abstract:
The fast Fourier transform is a computational procedure for calculating the finite Fourier transform of a time series. In this paper, the properties of the finite Fourier transform are related to commonly used integral transforms including the Fourier transform and convolution integrals. The relationship between the finite Fourier transform and Fourier series is also discussed.read more
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Journal ArticleDOI
The Shannon sampling theorem—Its various extensions and applications: A tutorial review
TL;DR: In this paper, the authors present the various contributions made for the sampling theorems with the necessary mathematical details to make it self-contained, including sampling for functions of more than one variable, random processes, nonuniform sampling, nonband-limited functions, implicit sampling, sampling with the function and its derivatives as suggested by Shannon in his original paper, and sampling for general integral transforms.
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A Class of Algorithms for Fast Digital Image Registration
TL;DR: A class of algorithms, which may be used to determine similarity in a far more efficient manner than methods currently in use, is introduced in this paper and may be a saving of computation time of two orders of magnitude or more by adopting this new approach.
Journal ArticleDOI
Effects of local geology on ground motion near San Francisco Bay
TL;DR: In this article, the authors compared the ground motion generated by nuclear explosions in Nevada with the strong-motion recordings of the San Francisco earthquake of March 22, 1957, and found that areas of high amplification determined from small ground motions may also be areas with high intensity in future earthquakes.
Journal ArticleDOI
Numerical Inversion of Laplace Transforms: An Efficient Improvement to Dubner and Abate's Method
TL;DR: An accurate method is presented for the numerical inversion of Laplace transform, which is a natural continuation to Dubner and Abate's method, and the error bound on the inverse f{t) becomes independent of t, instead of being exponential in t.
Journal ArticleDOI
The Fast Fourier Transform and Its Applications
TL;DR: 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.