The Research Of Iterative Reweightd Least Squares Techniques For FIR Digital Filters

This paper considers the design of FIR filters, mainly concentrates on the iterative reweighted least squares techniques (IRLS) applied to linear FIR filter design. Through studying the algorithm at present, this paper applies the IRLS techniques to the design of 1-D FIR filters with time-domain constraints and 2-D FIR filters with frequency-domain constraints. It develops a new algorithm—iterative reweighted constrained least squares techniques (IRCLS). The paper is arranged in five sections.The first section is introduction, mainly presents some definitions of filters and filters design. It introduces some algorithms of Chebyshev design and least squares design. The emphasis of this section is the introduction of IRLS techniques, including the meaning of the research and the applications. At last, the contribution of this paper is proposed.The second section describes the model of FIR filter firstly, including 1-D and 2-D.Then three kinds of criteria for FIR filter design and the algorithms based on these criteria are given. The character of the algorithms is also presented in this section.The third section presents the IRLS techniques. The theoretical basis is given firstly, then the Lawson's algorithm is introduced. At the same time, the paper presents the drawbacks of the Lawson's algorithm and several modifications. Lang's algorithm is introduced in this section, which is the illumination of this paper.The forth section presents how to solve time-domain Chebyshev design problem with IRLS techniques and proposes a new algorithms-IRCLS. This section gives model of the design problem firstly, then gives the constrained least squares problem equivalently. In this section, the weight update is performed using the envelope of the magnitude of the error function. In the iterative reweighted constrained least squares procedure of this section, the weighted constrained least squares problem in eachiteration is converted into a QP formulation with linear constraints. In the end. Chebyshev design of FIR filters with step response constraints and design of Nyquist filter are described as the model that can use the IRCLS's algorithm directly.Similar to the forth section, the fifth section applies IRCLS's algorithm to the design of 2-D FIR filter with frequency-domain. The model is given firstly, and then the design model is converted to the model that can use IRCLS's algorithm directly.In the forth and fifth sections, some design examples are presented .