A new method for the design of 2-dimensional stable recursive digital filters satisfying prescribed magnitude and group delay response

This paper presents a technique for the design of 2-Dimensional (2-D) stable recursive digital filters satisfying prescribed magnitude and constant group delay response. This technique uses the properties of positive definite matrices and their application in generating 2-variable Very Strictly Hurwitz Polynomials (VSHP) which will be assigned to the denominator of a 2-D analog reference filter. Bi-linear transformations is then applied to the transfer function of the 2-D analog reference filter to obtain the discrete version of the 2-D filter. Parameters of the discrete 2-D filter can be used as the variables of optimization to minimize the least mean square error of the desired and designed magnitude and group delay response of the filter. This technique is illustrated by examples.