Implementation of the Poles of IIR Digital Filters with a Declared Structural Precision

Abstract

This study is an integral part of a project focusing on the synthesis of IIR digital filters with finite word length. The implementation of the project involves considering the finite word length already at the stage of computation zeros and poles. The results of this stage are final and are not distorted at the stage of structural synthesis. The computation uses the fact that the zeros and poles of a practically implemented digital filter are elements of the set of algebraic numbers of the corresponding degree. At the stage of structural synthesis, a digital filter block diagram is generated. This block diagram provides specified degrees of algebraic numbers, which are zeros and poles. The exact values of the coefficients of the generated digital filter structure are calculated taking into account previously calculated zeros and poles. Different structures are characterized by structural precision, independent of specific coefficient values. This paper is devoted to the study of the generation of structures that provide a given structural precision of the denominator of the transfer function and a given degree of algebraic numbers that are poles.