Abstract
The widely popular famous fast Cooley–Tukey algorithms for the discrete Fourier transform of mixed radix are presented in two forms: classical and with a constant structure. A matrix representation of these algorithms is proposed in terms of two types of tensor product of matrices: the Kronecker product and the b-product. This matrix representation shows that the structure of these algorithms is identical to two fast Good algorithms for a Kronecker power of a matrix. A technique for constructing matrix-form fast algorithms for the discrete Fourier and Chrestenson transforms with mixed radix and for the discrete Vilenkin transform is demonstrated. It is shown that the constant-structured algorithm is preferable in the case of more sophisticated constructions.
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Translated by I. Ruzanova
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Bespalov, M.S. Generalization of the Fast Fourier Transform with a Constant Structure. Comput. Math. and Math. Phys. 63, 1371–1380 (2023). https://doi.org/10.1134/S0965542523080031
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DOI: https://doi.org/10.1134/S0965542523080031