Design of two-dimensional recursive digital filters using mirror-image polynomials

In this paper, a computationally efficient technique is developed for the design of two-dimensional (2-D) recursive digital filters that meet simultaneously magnitude and group delay specifications. The denominator in the filter is chosen structurally stable so that the filter stability is always guaranteed. Alternatively, the numerator is expressed in terms of a 2-D mirror-image polynomial. This makes it possible to design the denominator and the numerator separately. As a result, the amount of calculations can be reduced to some extent and the convergence can also be improved. Finally, two examples are given to illustrate the utility of the proposed technique.