Titlebook: Algorithms for Discrete Fourier Transform and Convolution; R. Tolimieri,Myoung An,Chao Lu,C. S. Burrus (Profe Book 19891st edition Springe

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Cooley-Tukey FFT Algorithms,structure of the indexing set . to define mappings of the input and output data vectors into 2-dimensional arrays. Algorithms are then designed, transforming 2-dimensional arrays which, when combined with these mappings, compute the .-point FFT. The stride permutations of chapter 2 play a major role

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Good-Thomas PFA,his multiplicative structure can be applied, in the case of transform size . = ., where . and . are relatively prime, to design a FT algorithm, similar in structure to these additive algorithms, but no longer requiring the twiddle factor multiplication. The idea is due to Good [2] in 1958 and Thomas

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Agarwal-Cooley Convolution Algorithm,hods are required. First as discussed in chapter 6, these algorithms keep the number of required multiplications small, but can require many additions. Also, each size requires a different algorithm. There is no uniform structure that can be repeatedly called upon. In this chapter, a technique simil

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,: The Prime Case,n fact, for a prime ., . is a field and the unit group .(.) is cyclic. Reordering input and output data corresponding to a generator of .(.), the .-point FFT becomes essentially a (.−1) × .−1) . matrix. We require 2(.−1) additions to make this change. Rader computes this skew-circulant action by the

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,: Transform Size , = ,,,f relatively primes. These algorithms start with the multiplicative ring-structure of the indexing set, in the spirit of the Good-Thomas PFA and compute the resulting factorization by combining Rader and Winograd small FFT algorithms. The basic factorization is . where . is a block diagonal matrix w