The features of the computational model of discrete transforms of Fourier class based on cyclic convolutions to determine the algorithmic calculation error are analyzed. Based on the approach of efficient computation of discrete transforms of Fourier class of arbitrary size N, using of a hashing array to transform a discrete basis matrix into a set of block-cyclic submatrices, the components of computational costs are considered. These components of computational costs depend on the type of transform, the size and the block-cycle structure of the transformation core.
The main modifications and standards of OFDM technology that provide high quality communication in multipath transmission of the transmitted signal are highlighted. It is analyzed in the structure of the transmitter of the communication system based on OFDM technology of execution of fast transforms of Fourier class. The orthogonal frequency division multiplexing / demultiplexing function is assigned to the fast computer of transform, and the precoder is used to reduce the high peak factor inherent in OFDM technology.
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 method of efficient computation discrete harmonic transforms for size the integer power of two on base of circular convolutions is considered. Hash array discrete basis matrixes of harmonic transforms are analysed. Interconnection hash arrays and structures of basis matrix between harmonic transforms are determined.
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.
The general method of efficient computation four types discrete sine transform using of circular convolutions is considered. The parameters of hash array the basis square matrix for algorithm synthesis are used.