Classification of structures of IIR digital filters

In this paper, number-theoretic and algebraic aspects of a choice of the block diagram of the IIR digital filter are considered. It is supposed that generation of structures of digital filters is carried out. The structure of the filter is described by a topological matrix of transfer coefficients between block diagram nodes. It is considered that zeros and poles of the filter with coefficients with a finite word length are elements of a set of algebraic numbers. Structures are classified by degree of algebraic numbers. The interrelation between degree of algebraic numbers and thin structure of a topological matrix is shown.