Design of 2-D recursive digital filters with constant group delay characteristics using separable denominator transfer function and a new stability test

In this paper, based on a new stability test, two 1-D polynomials in z1and z2having all their zeros inside the unit circles in z1and z2planes are generated and assigned to the denominator of a separable denominator 2-D transfer function while the numerator is left to a 2-D nonseparable polynomial in z1and z2. Now any suitable nonlinear optimization technique can be used to calculate the parameters of the 2-D filter in such a way so as to minimize the general mean square error between the ideal and the designed magnitude and group delay responses of the 2-D filter subject to the coefficient constraints given by the new stability test. To illustrate the method, an example is given.