New method for generating two-variable VSHPs and its application in the design of two-dimensional recursive digital filters with prescribed magnitude and constant group delay responses

Abstract

In the paper a method is presented for the design of 2-D stable recursive digital filters satisfying prescribed magnitude and constant group delay responses. This technique uses the properties of positive definite matrices and their application in generating 2-variable Very Strictly Hurwitz Polynomials (VSHPs), which will be assigned to the denominator of a 2-D analogue reference filter. Bilinear transformations are then applied to the transfer function of the derived 2-D analogue 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 optimisation to minimise the leastmean-square error between the desired and designed magnitude and group delay responses of the filter. To show the usefulness of the technique, an example is given.