Iterative least squares algorithms for digital filter design.

Abstract

In this thesis, we propose new algorithms to simplify and improve the design of IIR digital filters and M-band cosine modulated filter banks. These algorithms are based on the Iterative Least Squares (ILS) approach. We first review the various Iterative Reweighted Least Squares (IRLS) methods used to design Chebyshev and $L\sb{p}$ linear phase FIR filters. Then we focus on the ILS design of IIR filters and filter banks. For the design of Chebyshev IIR filters in the log magnitude sense, we propose a Remez-type IRLS algorithm. This novel approach accelerates significantly Kobayashi's and Lim's IRLS methods and simplifies the traditional rational Remez algorithm. For the design of M-band cosine modulated filter banks, we propose three new ILS algorithms. These algorithms are specific to the design of Pseudo Quadrature Mirror Filter (QMF) banks, Near Perfect Reconstruction (NPR) Pseudo QMF banks and Perfect Reconstruction (PR) QMF banks. They are fast convergent, simple to implement and flexible compared to traditional nonlinear optimization methods. Short MATLAB programs implementing the proposed algorithms are included.