Q1. What are the contributions mentioned in the paper "Average running time of the fast fourier transform" ?
The authors show that the average number of operations satisfies ( l/x ) Z, ,,2n A ( n ) ( n2/9 ) ( x2/log x ).
Average running time of the fast Fourier transform
Persi Diaconis,Persi Diaconis +1 more
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Analysis is given for Good's algorithm and for two algorithms that compute the discrete Fourier transform in O(n log n) operations: the chirp-z transform and the mixed-radix algorithm that computes the transform of a series of prime length p in P log p operations.About:
This article is published in Journal of Algorithms.The article was published on 1980-06-01 and is currently open access. It has received 25 citations till now. The article focuses on the topics: Discrete Fourier transform (general) & Prime-factor FFT algorithm.read more
Citations
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Journal ArticleDOI
Computing Fourier Transforms and Convolutions on the 2-Sphere
James R. Driscoll,D. M. Healy +1 more
TL;DR: Convolution theorems generalizing well known and useful results from the abelian case are used to develop a sampling theorem on the sphere, which reduces the calculation of Fourier transforms and convolutions of band-limited functions to discrete computations.
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FFTs for the 2-Sphere-Improvements and Variations
TL;DR: A reformulation and variation of the original algorithm is presented which results in a greatly improved inverse transform, and consequent improved convolution algorithm for such functions, which indicate that variations of the algorithm are both reliable and efficient for a large range of useful problem sizes.
Generalized FFTS - A Survey of Some Recent Results
TL;DR: This paper surveys some recent work directed towards generalizing the fast Fourier transform (FFT) from the point of view of group representation theory, and discusses generalizations of the FFT to arbitrary finite groups and compact Lie groups.
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On the asymptotic distribution of large prime factors
Peter Donnelly,Geoffrey Grimmett +1 more
TL;DR: In this article, the authors established the asymptotic distribution of the vector A(n) = (loga,/logiV: i: > 1) in a transparent manner.
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Efficient computation of the Fourier transform on finite groups
TL;DR: In this paper, the Fourier transform is defined as f(p) = EsEEG f(S)P(S), where s is the EEEG signal and p is the representation of G. The authors derive fast algorithms and develop them for the symmetric group Sn, where (n!)2 is reduced to nf(nf)al2, where a is the constant for matrix multiplication.
References
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Book
The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
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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.
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An algorithm for computing the mixed radix fast Fourier transform
TL;DR: This paper presents an algorithm for computing the fast Fourier transform, based on a method proposed by Cooley and Tukey, and includes an efficient method for permuting the results in place.
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Discrete Fourier transforms when the number of data samples is prime
TL;DR: The discrete Fourier transform of a sequence of N points, where N is a prime number, is shown to be essentially a circular correlation, which permits the discrete Fouriers transform to be computed by means of a fast Fouriertransform algorithm, with the associated increase in speed, even though N is prime.
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The chirp z-transform algorithm and its application
TL;DR: Applications discussed include: enhancement of poles in spectral analysis, high resolution narrow-band frequency analysis, interpolation of band-limited waveforms, and the conversion of a base 2 fast Fourier transform program into an arbitrary radix fast Fouriers transform program.