Number-theoretical analysis of the structures of classical IIR digital filters
Vladislav A. Lesnikov, Tatiana V. Naumovich, Alexander V. Chastikov · 2018
To implement IIR digital filters with specified requirements for frequency characteristics, a large number of structures can be used. If we do not take into account the finiteness of the word length, then all structures are equivalent in terms of the accuracy of the realization of the characteristics. However, in the practical implementation of digital Alters, the bitness is finite, and the coefficients of the filter structure, and hence the coefficients of the transfer function, are rational numbers. As a consequence, the zeros and poles of the transfer function are elements of a set of algebraic numbers. For different structures, the maximum degree of algebraic numbers that are zeros and fields themselves can be different. Therefore, the maximal degrees of zeros and poles can be used as the basis for classifying structures and dividing them into equivalence classes. The proposed method is demonstrated on classical structures.