A Sequential Constrained Least-Squares Approach To Constrained Chebyshev Design Of IIR Digital Filter

This paper considers the design of IIR (infinite impulse response) digital filter, mainly concentrates on the constrained Chebyshev design. Firstly, a constrained least-squares (CLS) problem is considered, then a sequence of CLS method is used to approach the constrained Chebyshev design, which named sequential constrained least-squares technique (SCLS). Design examples are given to illustrate the effectiveness of the proposed SCLS technique. The paper is arranged in four sections.The first section is introduction. Firstly, it presents some definitions of IIR digital filter, and then it introduces the research actuality in resent years, mainly includes some algorithms of Chebyshev design and least-squares design. The emphasis of this section is the origin of SCLS technique of Chebyshev design, and the application of this technique for IIR filter design.The second section describes the model of IIR digital filter firstly. Then it introduces the stability of IIR digital filter, and emphasizes the stability that IIR digital filter design must guarantee. Some different stable constraints are analyzed in the followed. Lastly, three kinds of criteria for IIR digital filter are given, the character of the criterions are analyzed.The third section presents two techniques. One is the method of constrained least-squares design with filter's magnitude ripple bounds is considered; the other is the extend of least-squares design: an algorithm based on least P-Power Error Criterion. The CLS of IIR digital filter design is a non-convex programming with nonlinear constrained. Usually, we transfer it into a succession of standard quadratic programming (QP) problem, which is easy to solve. By changing the value of magnitude constraint in the emluator,we can obtain its influences on magnitude error.The fourth section applies the relation between magnitude constrained least-squares design and constrained Chebyshev design. The relation is the stand of SCLS technique: By producing a sequence of ripple bounds tighter and tighter, we obtain a sequence of CLS problem whose solutions are shown to converge to one of constrained Chebyshev filter. The SCLS technique is feasible and always converge independent on the choice of initial point. Finally, design examples are given to analyze the primary reasons bringing about algorithm error, and methods are put forward to resolve it.