Sukalo A. Methods of modeling of digital signals processing by means of hypercomplex calculations

The thesis is devoted to increase of efficiency of mathematical modeling the problems of digital signals processing by methods and means of hypercomplex calculations. The present state of mathematical modeling of digital signal processing tasks is analyzed. As a result of the analysis of the methods of constructing the HNS, the principle of doubling for the generation of fourth-dimensional systems, which are most suitable in the mathematical modeling of the digital signal processing tasks, is singled out. The classes of hypercomplex number systems of the fourth dimensionality have been constructed using the Grassmann-Clifford doubling procedure. It is proposed to use the method of an associated system of linear differential equations for constructing representations of exponential, trigonometric and hyperbolic functions in new classes of the HNS. А software complex of hypercomplex computations was developed, this package of procedures allows you to effectively build mathematical models of different levels of complexity using hypercomplex data representation. It is proposed to reduce the computational complexity of the mathematical modeling of the digital signal processing tasks using an approach based on the properties of the isomorphic transition between different HNS. Software modules for the synthesis of digital signal processing tasks are developed with the help of procedures of the software complex of hypercomplex computations.