Fedorenko O. Computer-aided design of digital filters with hypercomplex coefficients

This thesis holds research in the area of digital filters computer aided design with use of hypercomplex numerical systems for transfer function coefficients representation, holds research of construction methods for such filters and possibilities for automation of construction such filters.Generalization of method for construction digital filters, transfer function coefficients of which is represented by different hypercomplex numerical systems, is done in the thesis. Hypercomplex systems of different dimensions, that are suitable for transfer function coefficients representation, were determined. For those systems, methods of transfer function construction for first order digital filters were developed. A method is offered, that is based on properties of isomorphic conversion between different hypercomplex numerical systems and allows to decrease the amount of operations, that is need for realizing of digital filter with hypercomplex coefficients.