On the Derivation of Winograd-Type DFT Algorithms for Input Sequences Whose Length Is a Power of Two

Abstract

Winograd’s algorithms are an effective tool for calculating the discrete Fourier transform (DFT). These algorithms described in well-known articles are traditionally represented either with the help of sets of recurrent relations or with the help of products of sparse matrices obtained on the basis of various methods of the DFT matrix factorization. Unfortunately, in the mentioned papers, it is not shown how the described relations were obtained or how the presented factorizations were found. In this paper, we use a simple, understandable and fairly unified approach to the derivation of the Winograd-type DFT algorithms for the cases N = 8, N = 16 and N = 32. It is easy to verify that algorithms for other lengths of sequences that are powers of two can be synthesized in a similar way.