Topic
Prime-factor FFT algorithm
About: Prime-factor FFT algorithm is a research topic. Over the lifetime, 2346 publications have been published within this topic receiving 65147 citations. The topic is also known as: Prime Factor Algorithm.
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TL;DR: This paper presents an efficient Fortran program that computes the Duhamel-Hollmann split-radix FFT, which seems to require the least total arithmetic of any power-of-two DFT algorithm.
Abstract: This paper presents an efficient Fortran program that computes the Duhamel-Hollmann split-radix FFT. An indexing scheme is used that gives a three-loop structure for the split-radix FFT that is very similar to the conventional Cooley-Tukey FFT. Both a decimation-in-frequency and a decimation-in-time program are presented. An arithmetic analysis is made to compare the operation count of the Cooley-Tukey FFT fo several different radixes to that of the split-radix FFT. The split-radix FFT seems to require the least total arithmetic of any power-of-two DFT algorithm.
222 citations
TL;DR: In this paper, the Karhunen-Loeve transform for a class of signals is proven to be a set of periodic sine functions and this k-means expansion can be obtained via an FFT algorithm.
Abstract: The Karhunen-Loeve transform for a class of signals is proven to be a set of periodic sine functions and this Karhunen-Loeve series expansion can be obtained via an FFT algorithm. This fast algorithm obtained could be useful in data compression and other mean-square signal processing applications.
215 citations
TL;DR: A fast high accuracy Polar FFT based on the pseudo-Polar domain, an FFT where the evaluation frequencies lie in an oversampled set of nonangularly equispaced points, including fast forward and inverse transforms.
197 citations
TL;DR: In this paper, a new atomic-parameters least-squares refinement method is presented, which makes use of the fast Fourier transform algorithm at all stages of the computation.
Abstract: A new atomic-parameters least-squares refinement method is presented which makes use of the fast Fourier transform algorithm at all stages of the computation. For large structures, the amount of computation is almost proportional to the size of the structure making it very attractive for large biological structures such as proteins. In addition the method has a radius of convergence of approximately 0.75 A making it applicable at a very early stage of the structure-determination process. The method has been tested on hypothetical as well as real structures. The method has been used to refine the structure of insulin at 1.5 A resolution, barium beauvuricin complex at 1.2 A resolution, and myoglobin at 2 A resolution. Details of the method and brief summaries of its applications are presented in the paper.
185 citations
TL;DR: A Fortran program that calculates the discrete Fourier transform using a prime factor algorithm is presented that is faster than both the Cooley-Tukey algorithm and the Winograd nested algorithm.
Abstract: This paper presents a Fortran program that calculates the discrete Fourier transform using a prime factor algorithm. A very simple indexing scheme is employed that results in a flexible, modular algorithm that efficiently calculates the DFT in-place. A modification of this algorithm gives the output both in-place and in-order at a slight cost in flexibility. A comparison shows it to be faster than both the Cooley-Tukey algorithm and the Winograd nested algorithm.
183 citations