Structure of the Transfer Function Numerator Coefficients as One of the Factors of the Structural Precision of IIR Digital Filters

This work was carried out during the implementation of a project dedicated to the synthesis of recursive digital filters with a finite word length. The approach used in this project considers the finite word length already when calculating the zeros and poles. The calculated zeros and poles are not distorted by structural synthesis. The calculations are based on what the zeros and poles of a digital filter with finite length coefficients are algebraic numbers of the corresponding degree. Structural synthesis involves generating a topological matrix describing the structure. The purpose of the generation is to provide a given degree of algebraic numbers that are zeros and poles. The previously calculated values of zeros and poles are used to calculate the exact values of the coefficients of the generated structure. It is proposed to characterize various structures with structural precision that does not depend on the concrete values of the coefficients. This article discusses the issues of generating structures considering the structural precision of the transfer function numerator.