Program of efficient implementation the discrete cosine transform of type-II using cyclic convolutions have been considered. The stages of automatic code generation the algorithms for the computation of DCT-II an arbitrary size N have been determined. The algorithm of DCT-II presents a better program performance for short sizes of transform, than known FFTW library.
The general technique of efficient computation DFT using of cyclic convolutions for sizes of integer power of two is considered. Further development of Winograd Fourier transform algorithm (WFTA) is analyzed. The hashing array for the compacting definition of the block-cyclic structure the basis matrix of DFT is proposed. The general block-cyclic structure of discrete basis matrix for the computation of DFT of sizes N=2n is determined.
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.