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Least-squares approach to IIR digital filters and an application to equiripple solutions

โœ Scribed by Masahiro Okuda; Masaaki Ikehara; Shin-ichi Takahashi

Book ID
101293780
Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
245 KB
Volume
81
Category
Article
ISSN
1042-0967

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โœฆ Synopsis

This paper formulates the modified least-squares method presented by Mullis in a general form so that weighting can be applied. Then, an algorithm is proposed with which a least-squares approximation can be derived for an IIR digital filter, by solving iteratively a system of equations. The method is extended to a complex Chebyshev approximation that minimizes the maximum magnitude of the complex error, by multiplying the weight, which is newly derived in this paper, with the modified least-squares error. The method is compared with a conventional complex Chebyshev approximation by means of a computer simulation and the effectiveness of the proposed method is demonstrated.

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## Abstract The method of โ€˜least squaresโ€™, which falls under the category of weighted residual processes, is applied as a timeโ€stepping algorithm to oneโ€dimensional transient problems including the heat conduction equation, diffusionโ€convection equation, and a nonโ€linear unsaturated flow equation.