Digital filter design with short word-length coefficients

Abstract

This paper describes an algorithm for the design of digital filters with short word-length coefficients. Starting with a set of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> optimized <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</tex> -plane poles and zeros that meet specifications with some margin, the algorithm sequentially applies a limited search (up to 16 grid points) for the locally optimum grid point in the neighborhood of a particular <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</tex> -plane singularity, followed by a global continuous reoptimization of the remaining <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N-1</tex> singularities. As the number of available singularities decreases to zero, the algorithm terminates with a limited search in the neighborhood of the last singularity for the best grid point. The success depends crucially on the sequence in which the singularities are fixed at the locally optimum grid points in the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</tex> plane. The sequence itself is an integral part of the algorithm. The algorithm has been applied successfully to the design of high-order filters with stringent specifications, and the solutions obtained show 0- , 1- , or 2-bit improvement in the coefficient word length over the previously published results.