Design of Symmetric 2-D IIR Digital Filters with Finite Word Length Coefficients

Abstract

A serious limitation arising in the implementation of two-dimensional (2-D) IIR digital filters is the finite word lenght representation of their coefficients. These coefficients are usually determined by the design procedure with infinite accuracy (large word length) and subsequently implemented with the word length allowed by the registers chosen. In this paper a method is proposed for the design of 2-D IIR digital filters with finite word length coefficients. This method is based on the successive rounding of some filter coefficients and the subsequent optimization of the remaining coefficients. Each set of coefficients to be rounded is chosen using a criterion based on the sensitivity of the objective function to the variation of each coefficient. The method is applied to the design of 2-D IIR digital filters possessing octagonal symmetry. Some design examples are presented, and the efficiency of the method is judged by comparing the resulting filters with those possessing coefficients of infinite precision.