四海为家的人 发表于 2025-3-25 06:41:50
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 roleFAZE 发表于 2025-3-25 09:00:27
http://reply.papertrans.cn/16/1533/153219/153219_22.png预示 发表于 2025-3-25 11:40:56
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 in 1958 and ThomasExpostulate 发表于 2025-3-25 17:48:41
http://reply.papertrans.cn/16/1533/153219/153219_24.pngPALSY 发表于 2025-3-25 23:37:36
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舞蹈编排 发表于 2025-3-26 03:08:02
http://reply.papertrans.cn/16/1533/153219/153219_26.png明确 发表于 2025-3-26 04:46:24
,: 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过多 发表于 2025-3-26 12:01:15
http://reply.papertrans.cn/16/1533/153219/153219_28.pnghumectant 发表于 2025-3-26 15:31:53
http://reply.papertrans.cn/16/1533/153219/153219_29.png混乱生活 发表于 2025-3-26 17:29:42
,: 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