Context. A method of efficient computation of DFT using cyclic convolutions for sizes of integer power of two has been considered.<br />The further development of Winograd Fourier transform algorithm based on a hashing array has been proposed. The research object is the<br />process of the reformulation the basis matrix of DFT into the block-cyclic structures. The research subject lays in the technique of the<br />reformulation the basis matrix of DFT for sizes of integer power of two into the block-cyclic structures.<br />Objective. The purpose of the work is the analysis of the structure specifics the left-circulant submatrices of the basis square matrix<br />WN for sizes of transform N = 2i using the hashing arrays.<br />Method. The article considers a technique for the efficient computation of DFT using cyclic convolutions for sizes of integer power<br />of two, which is based on the cyclic decomposition of substitution. A hashing array has been proposed for the compressed description of the<br />block-cyclic structure of discrete basis matrix and for the efficient computation of DFT for sizes of integer power of two.<br />Results. A generalized block-cyclic structure of discrete basis matrix for the efficient computation of DF using cyclic convolutions for<br />sizes of an integer power of two based on the hashing arrays has been determined. The proposed technique is relevant for concurrent<br />programming of DFT and for its implementation in parallel systems.<br />Conclusions. A general block-cyclic structure of basis matrix of DFT is regularly formed with an increase in the value of the exponent<br />of two and is recommended for use in practice when developing the efficient means of DFT. The prospects for further research will include<br />the formation of block-cyclic structure of basis matrix of DFT for arbitrary sizes.
Науковий журнал «Радіоелектроніка, інформатика, управління»
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Prots’ko, I. O.; Lviv National Polytechnic University, Lviv, Ukraine Teslyuk, V. M.; Lviv National Polytechnic University, Lviv, Ukraine |
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Context. A method of efficient computation of DFT using cyclic convolutions for sizes of integer power of two has been considered.<br />The further development of Winograd Fourier transform algorithm based on a hashing array has been proposed. The research object is the<br />process of the reformulation the basis matrix of DFT into the block-cyclic structures. The research subject lays in the technique of the<br />reformulation the basis matrix of DFT for sizes of integer power of two into the block-cyclic structures.<br />Objective. The purpose of the work is the analysis of the structure specifics the left-circulant submatrices of the basis square matrix<br />WN for sizes of transform N = 2i using the hashing arrays.<br />Method. The article considers a technique for the efficient computation of DFT using cyclic convolutions for sizes of integer power<br />of two, which is based on the cyclic decomposition of substitution. A hashing array has been proposed for the compressed description of the<br />block-cyclic structure of discrete basis matrix and for the efficient computation of DFT for sizes of integer power of two.<br />Results. A generalized block-cyclic structure of discrete basis matrix for the efficient computation of DF using cyclic convolutions for<br />sizes of an integer power of two based on the hashing arrays has been determined. The proposed technique is relevant for concurrent<br />programming of DFT and for its implementation in parallel systems.<br />Conclusions. A general block-cyclic structure of basis matrix of DFT is regularly formed with an increase in the value of the exponent<br />of two and is recommended for use in practice when developing the efficient means of DFT. The prospects for further research will include<br />the formation of block-cyclic structure of basis matrix of DFT for arbitrary sizes. |
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Zaporizhzhya National Technical University 2018-10-04 12:10:39 |
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application/pdf http://ric.zntu.edu.ua/article/view/143544 |
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Radio Electronics, Computer Science, Control; No 2 (2018): Radio Electronics, Computer Science, Control |
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Copyright (c) 2018 I. O. Prots’ko, V. M. Teslyuk |
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