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Block-Cyclic Structuring of the Basis of Fourier Transforms Based on Cyclic Substitution

  • NEW MEANS OF CYBERNETICS, INFORMATICS, COMPUTER ENGINEERING, AND SYSTEMS ANALYSIS
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Abstract

The use of substitution as a primitive element in forming a cyclic basis matrix of the Fourier transform is considered. A cyclic substitution is used for block-cyclic structuring of the harmonic basis, which allows synthesizing the algorithms for fast discrete Fourier transforms of arbitrary size based on cyclic convolutions. The rearrangement of the cycles order and their first elements in cyclic substitutions is shown to reduce the amount of computation of cyclic convolutions in fast algorithms for the discrete Fourier transforms.

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Authors and Affiliations

  1. Lviv Polytechnic National University, Lviv, Ukraine

    I. Prots’ko & M. Mishchuk

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  1. I. Prots’ko
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  2. M. Mishchuk
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Correspondence to I. Prots’ko.

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Translated from Kibernetyka ta Systemnyi Analiz, No. 6, November–December, 2021, pp. 183–192.

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Prots’ko, I., Mishchuk, M. Block-Cyclic Structuring of the Basis of Fourier Transforms Based on Cyclic Substitution. Cybern Syst Anal 57, 1008–1016 (2021). https://doi.org/10.1007/s10559-021-00426-x

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  • DOI: https://doi.org/10.1007/s10559-021-00426-x

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