Design of 2-D Digital Filters with Almost Quadrantal Symmetric Magnitude Response without 1-D Separable Denominator Factor Constraint

Abstract

A design approach is presented for 2-D digital filters possessing approximate quadrantal magnitude symmetry without the constraint of the denominator having only 1-D separable factors. To ensure the BIBO stability of the filter, the planar least square inverse stabilization approach is employed. It is illustrated through design examples that the proposed approach results in filters with sharper transition band and lower error relative to the given filter specifications. Also, for certain cases, it is shown that a lower order non-separable denominator design can achieve the same result as a higher order separable denominator design, thus providing savings in the number of multipliers. Finally, 2-D VLSI realizations without global broadcast are presented for the optimized transfer function with non-separable denominator factors and approximate quadrantal symmetry.