cyclic convolution

Розглянуто підхід до ефективного обчислення основних чотирьох типів дискретного перетворення Хартлі (ДПХ) на основі циклічних згорток. Параметри твірного масиву базисної квадратної матриці використано для синтезу алгоритму.

The general method of efficient computation four types discrete Hartley transform using of circular convolutions is considered. The parameters of hash array of basis square matrix for algorithm synthesis are used.

Розглянуто підхід ефективного обчислення основних чотирьох видів дискретного косинусного перетворення (ДКП) на базі циклічних згорток. Параметри твірного масиву базисної квадратної матриці використано для синтезу алгоритму.

The general method of efficient computation four types discrete cosine transform using of circular convolutions is considered. The parameters of hash array of basis square matrix for algorithm synthesis are used.

Розглянуто узагальнену блок-схему синтезу ефективного обчислення дискретних гармонічних перетворень, що здійснюється на основі циклічних згорток. Параметри твірного масиву базисної квадратної матриці використано в алгоритмі синтезу.

The general block diagram of synthesis the efficient computation discrete harmonic transforms is considered. The computation of discrete harmonic transforms is performed on base of cyclic convolutions. The parameters of hash array a basis square matrix for algorithm synthesis are used.

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 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.