MFTA: Product of Two Distinct Primes
Part of the Signal Processing and Digital Filtering book series (SIGNAL PROCESS)
The results of chapter 9 will now be extended to the case of transform size N, N a product of two distinct primes. As mentioned in the general introduction to multiplicative FT algorithms, several approaches exist for combining small size FT algorithms into medium or large size FT algorithms by the Good-Thomas FT algorithms. Our approach emphasizes and is motivated by the results of chapter 9. By employing tensor product rules to a generalization of Rader’s multiplicative FT algorithms, we derive the fundamental factorization
where C is a block-diagonal matrix having skew-circulant blocks (rotated Winograd cores) and tensor products of these skew-circulant blocks and A is a matrix of pre-additions, all of whose entries are 0, 1 or −1. Variants will then be derived.
KeywordsTensor Product Discrete Fourier Transform Unit Group Fundamental Factorization Zero Divisor
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