Generation of 2-D stable transfer functions having variable magnitude characteristics starting from the sum of two 1-D Schur polynomials

Sufficient conditions have been obtained when a sum of two second-order 1-D Schur polynomials, one in each variable, results in a 2-D Schur polynomial. This has been extended to the case when a delay unit in each variable and multipliers have been added to obtain such 2-D Schur polynomials. Different filters can be designed using these polynomials as the denominator of a 2-D discrete polydomain transfer function. A numerical example has been provided to illustrate the method