A Truncated Polynomial Interpolation and Its Application to Polynomially WLS Design of IIR Filters

Hiroshi HASEGAWA  Masashi NAKAGAWA  Isao YAMADA  Kohichi SAKANIWA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E86-A   No.7   pp.1742-1748
Publication Date: 2003/07/01
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
Keyword: 
Walsh's theorem,  weighted least-squares approximation,  rational approximation,  design of IIR filters,  

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Summary: 
In this paper, we propose a simple method to find the optimal rational function, with a fixed denominator, which minimizes an integral of polynomially weighted squared error to given analytic function. Firstly, we present a generalization of the Walsh's theorem. By using the knowledge on the zeros of the fixed denominator, this theorem characterizes the optimal rational function with a system of linear equations on the coefficients of its numerator polynomial. Moreover when the analytic function is specially given as a polynomial, we show that the optimal numerator can be derived without using any numerical integration or any root finding technique. Numerical examples demonstrate the practical applicability of the proposed method.