SOFTWARE ANALYSIS OF STRUCTURE BLOCK-CYCLIC BASIC MATRIX OF DCT

Abstract

Context. The matrix notation is used to formalize the subject area within the framework of the algebraic approach. Effective computation of the discrete cosine transforms uses the reduction of a harmoniс basis to a block-cyclic matrix structure with the subsequent calculation of the transform using fast cyclic convolutions. An analysis of the structure of the basic block matrix of transforms provides a synthesis of algorithms of effective discrete cosine transforms of arbitrary sizes. The software implementation of the analysis of block-cyclic structures generates a description of the structure, which allows to reduce the computational complexity of the algorithm of effective discrete cosine transform and to perform parallelization of computation the cyclic convolutions.Objective. The work is to determine the algorithmic features of the analysis of the structure of a block-cyclic matrix containing integer arguments of basic harmonic functions, which will reduce the computational complexity of the synthesized discrete cosine transform algorithm based on cyclic convolutions.Method. Search and analysis by enumerating elements of the matrix with a variable step, taking into account the blockiness and cyclicity of the formed basis matrix of the discrete cosine transform, allows you to quickly analyze the structure of the block matrix of transform in comparison with full scanning.Results. Algorithmic and software for analyzing the structure of a block-cyclic basis matrix have been developed, with the help of which an array of data parameters for a formal description of the basis matrix structure of a discrete cosine transform is determined. The analysis of the structure of the base matrix allows us to determine the presence of identical cyclic submatrices placed horizontally or vertically relative to each other and, thereby, reduce the number of cycles of convolutions.Conclusions. An effective analysis of the block-cyclic structure of the basis matrix based on the developed software is an important part of the fast algorithm synthesis process, which provides a reduction in computational complexity and the ability to parallelize the implementation of the discrete cosine transform. The developed algorithmic and software for performing the analysis of the structure of a block-cyclic matrix can also be used to analyze the structure and search for the corresponding submatrices in any matrices with integer, real, and zero elements.