 Cybernetics and Systems Analysis /  Issue (2021, 57 (6))
Prots’ko I.,
Mishchuk M.
Block-cyclic structuring of the basis of Fourier class transforms based on cyclic substitution 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. © 2021, Springer Science+Business Media, LLC, part of Springer Nature. Keywords: block-cyclic structure, cyclic convolutions, cyclic substitution, discrete cosine transform, synthesis of algorithm, Cosine transforms, Discrete cosine transforms, Discrete Fourier transforms, Base matrix, Block-cyclic structure, Cyclic convolutions, Cyclic structures, Cyclic substitution, Fast algorithms, Primitive element, Synthesis of algorithm, Convolution
Cite:
Prots’ko I.,
Mishchuk M.
(2021). Block-cyclic structuring of the basis of Fourier class transforms based on cyclic substitution. Cybernetics and Systems Analysis, 57 (6), 183–192. doi: https://doi.org/10.1007/s10559-021-00426-x http://jnas.nbuv.gov.ua/article/UJRN-0001284200 [In Ukrainian]. |
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