A frequency–domain design of two–dimensional recursive digital filters

Abstract

AbstractThis paper presents a technique for the design of two‐dimensional recursive digital filters in the frequency domain. The filter consists of the denominator being structurally stable and the numerator being a mirror‐image polynomial. To find the denominator, a stable two‐dimensional all‐pole filter is designed first so as to approximate the constant group delay specified in each direction. This is done by using the Davidon‐Fletcher and Powell algorithm. The numerator is then designed so that the whole rational transfer function approximates the desired magnitude response under the assumption that the denominator is fixed. This is done by solving a linear equation. The present technique has the advantage of always ensuring the stability of the resultant filter. Two examples are given to illustrate the utility of the proposed technique.