Showing papers on "Prime-factor FFT algorithm published in 1973"
TL;DR: A diagrammatic representation of mixed radix and highest radix FFT algorithms is derived, and two broad classes of FFT hard-ware are explored, from the point of view of speed, parallelism, radix number, and type of memory.
Abstract: The fast Fourier transform algorithm is derived by means of successive fracturing of one-dimensional data strings into two-dimensional arrays. Using this formulation, a diagrammatic representation of mixed radix and highest radix FFT algorithms is derived. Using this representation, two broad classes of FFT hard-ware are explored, from the point of view of speed, parallelism, radix number, and type of memory.
106 citations
IBM1
TL;DR: Results are summarized of a computer study of the algorithm that performs the deconvolution iteratively, using the fast Fourier transform (FFT) algorithm at each stage.
Abstract: A solution is given to the problem of deconvolving two time sequences using discrete Fourier transform (DFT) techniques when one of the sequences is of infinite duration. Both input- and impulse-response deconvolution problems are considered. Results are summarized of a computer study of the algorithm that performs the deconvolution iteratively, using the fast Fourier transform (FFT) algorithm at each stage.
35 citations
01 Jan 1973
TL;DR: The algorithm for Lie transforms proposed in this article reduces the number of Poisson brackets to be evaluated in a part of the implementation of the Analytical Lunar Theory by a factor of three.
Abstract: The algorithm for Lie transforms proposed here reduce the amount of computation to be carried out in particular but typical problems of Perturbation Theory. In conjunction with the formulas for inverting and composing Lie transforms it is shown to reduce by a factor of three the number of Poisson brackets to be evaluated in a part of the implementation of the Analytical Lunar Theory.
32 citations
01 Mar 1973
TL;DR: In this article, it was shown that the classes of modular rings of integers in which the FFT may be computed is completely characterized by the prime decomposition of the modulus.
Abstract: : The paper presents several results relating modular arithmetic schemes and the Fast Fourier transform. In particular, the classes of modular rings of integers in which the FFT may be computed is completely characterized by the prime decomposition of the modulus. Also, an extension of this result for computation structures similar to modular rings of integers yields a sufficiency hypothesis for the computation of FFT.
7 citations
TL;DR: This FFT method, in conjunction with the optimization technique, is found to be an efficient, general procedure to facilitate convolutions of phase time distributions using the FFT.
Abstract: This paper provides a numerical technique for the solution of the fraction of labelled mitoses curve. The essence of the method is to facilitate convolutions of phase time distributions using the FFT. This FFT method, in conjunction with the optimization technique, is found to be an efficient, general procedure.
6 citations
TL;DR: Concepts of group theory are used to explain the difference between two major fast Fourier transform algorithms and the relation between FFT and fast Walsh transforms.
Abstract: Concepts of group theory are used to explain the difference between two major fast Fourier transform (FFT) algorithms and the relation between FFT and fast Walsh transforms.
5 citations