A Systematic Algorithm for the Design of Lattice Wave Digital Filters With Short-Coefficient Wordlength

Abstract

This paper describes an efficient algorithm for designing lattice wave digital (LWD) filters (parallel connections of two all-pass filters) with short-coefficient wordlength. The coefficient optimization is performed using the following three steps. First, an initial infinite-precision filter is designed such that it exceeds the given criteria in order to provide some tolerance for coefficient quantization. Second, a nonlinear optimization algorithm is used for determining a parameter space of the infinite-precision coefficients including the feasible space where the filter meets the given criteria. The third step involves finding the filter parameters in this space so that the resulting filter meets the given criteria with the simplest coefficient representation forms. The proposed algorithm guarantees that the optimum finite-precision solution can be found for both the fixed-point binary and multiplierless coefficient representation forms. In addition, this algorithm is applicable for producing the desired finite-precision solutions for both conventional and approximately linear-phase LWD filters. Comparisons with some other existing quantization schemes show that the proposed algorithm gives the best finite-precision solutions in all examples taken from the literature.