Developing efficient computation of FFT using cyclic convolutions for size the integer power of two is considered. The structures of basis matrices of DFT are presented via the hashing arrays. The interconnection of the structures or hashing arrays of DFT for the sizes the integer powers of two is determined. Proposed left-circulant components of structure are suitable for applying in monolithic single-chip MEMS+ASIC.

Processing module of FFT in monolithic single-chip MEMS

Розглянуто підходи ефективного обчислення дискретних перетворень класу Фур’є 
на основі циклічних згорток. Описано сутність переформулювання базисних матриць перетворення ДПФ на блочно-циклічні структури для кожного підходу. Аналізуються переваги і недоліки алгоритмів для кожного підходу. The enumeration approaches of efficient computation discrete transform of Fourier class using cyclic convolutions is considered. The formulation of the basis matrix of transforms into the block cyclic structures is described of each approach. The analysis of the advantages and imperfections of the algorithms are discussed.

/pdf/ogliad-algoritmiv-efektivnogo-obchislennia-dpf-na-osnovi-2ebsv3x6ve.pdf

Огляд алгоритмів ефективного обчислення дпф на основі циклічних згорток

http://ena.lp.edu.ua:8080/bitstream/ntb/31329/1/42-306-312.pdf

Розпаралелення на рівні підзадач алгоритму ШГП на основі циклічних згорток

The new DFT algorithm of S. Winograd is developed and presented in detail. This is an algorithm which uses about 1/5 of the number of multiplications used by the Cooley-Tukey algorithm and is applicable to any order which is a product of relatively prime factors from the following list: 2,3,4,5,7,8,9,16. The algorithm is presented in terms of a series of tableaus which are convenient, compact, graphical representations of the sequence of arithmetic operations in the corresponding parts of the algorithm. Using these in conjunction with included Tables makes it relatively easy to apply the algorithm and evaluate its performance.

S. Zohar

Papers

Faster fourier transformation: The algorithm of S. Winograd