Studies on N-dimensional filter transfer functions without second kind singularities

In this paper the concept of very strict Hurwitz polynomials which find applications in the design of stable two-dimensional digital filters, is extended to three and higher dimensions and the properties of such polynomials are discussed. A testing procedure to check whether a given multi-variable polynomial is a very strict Hurwitz polynomial or not is developed. Application of this concept in the design of n-dimensional digital filters without non-essential singularities of the second kind is then considered. It is shown that the concept of minimum reactive and susceptive, strict positive real functions in several variables is quite useful in the generation and testing of these filters. Such a positive real function is defined and its properties outlined. The application of transformation method to generate 3-dimensional filters from one - and two - dimensional filters is discussed.