Realization of multidimensional digital transfer functions with separable numerator or denominator polynomials (Q1289156)

An \(M\) dimensional digital filter is characterized in the \(z\)-domain description by its transfer function which is the ratio of two polynomials in \(M\) complex variables. Of interest is the case when the numerator and/or the denominator are separable, i.e. they are expressible as the product of \(M\) polynomials each in a single complex variable. The paper provides a systematic approach to the realization of a transfer function for the case when the numerator or the denominator are separable (the two corresponding cases are treated separately). The advantages of the proposed method are: It requires a minimum number of multiplications and it gives a procedure for minimizing the number of delay elements. The proposed approach rests on some previous results of the authors. A design example illustrates the way to apply the method.