DEVELOPMENT OF WFTA BASED ON THE HASHING ARRAY
DOI:
https://doi.org/10.15588/1607-3274-2018-2-15Keywords:
fast Fourier transform, Winograd Fourier transform algorithm, hashing array, block-cyclic structure, cyclic convolutionAbstract
Context. A method of efficient computation of DFT using cyclic convolutions for sizes of integer power of two has been considered.The further development of Winograd Fourier transform algorithm based on a hashing array has been proposed. The research object is the
process of the reformulation the basis matrix of DFT into the block-cyclic structures. The research subject lays in the technique of the
reformulation the basis matrix of DFT for sizes of integer power of two into the block-cyclic structures.
Objective. The purpose of the work is the analysis of the structure specifics the left-circulant submatrices of the basis square matrix
WN for sizes of transform N = 2i using the hashing arrays.
Method. The article considers a technique for the efficient computation of DFT using cyclic convolutions for sizes of integer power
of two, which is based on the cyclic decomposition of substitution. A hashing array has been proposed for the compressed description of the
block-cyclic structure of discrete basis matrix and for the efficient computation of DFT for sizes of integer power of two.
Results. A generalized block-cyclic structure of discrete basis matrix for the efficient computation of DF using cyclic convolutions for
sizes of an integer power of two based on the hashing arrays has been determined. The proposed technique is relevant for concurrent
programming of DFT and for its implementation in parallel systems.
Conclusions. A general block-cyclic structure of basis matrix of DFT is regularly formed with an increase in the value of the exponent
of two and is recommended for use in practice when developing the efficient means of DFT. The prospects for further research will include
the formation of block-cyclic structure of basis matrix of DFT for arbitrary sizes.
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