New exchange rules for IIR filter design

Author

Selesnick, Ivan W.

Author_Institution

Dept. of Electr. & Comput. Eng., Rice Univ., Houston, TX, USA

Volume

3

fYear

1997

fDate

21-24 Apr 1997

Firstpage

2209

Abstract

This paper introduces a new set of exchange rules for a Remez-like algorithm for the Chebyshev design of IIR digital filters. It is explained that the essential difficulty, in applying the Remez algorithm to rational functions, is that on some iterations, there may be no solution to the interpolation problem for which the denominator is strictly non-zero in the interval of approximation. Then the usual procedure for updating the interpolation points cannot be applied. The new rules for updating the interpolation points address precisely this problem for the two-pole case. It is shown with examples that, when the Remez-like algorithm of Hofstetter et al. (1971) is applied to rational functions, there is a way to update the interpolation points so that the algorithm converges rapidly, even when poles arise in the interval of approximation

Keywords

Chebyshev filters; IIR filters; approximation theory; convergence of numerical methods; interpolation; iterative methods; network synthesis; poles and zeros; Chebyshev design; IIR filter design; Remez-like algorithm; algorithm convergence; approximation; denominator; digital filters; exchange rules; interpolation points update; iterations; rational functions; two-pole case; Algorithm design and analysis; Approximation algorithms; Chebyshev approximation; Convergence; Digital filters; Finite impulse response filter; IIR filters; Interpolation; Iterative algorithms; Polynomials;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech, and Signal Processing, 1997. ICASSP-97., 1997 IEEE International Conference on

Conference_Location

Munich

ISSN

1520-6149

Print_ISBN

0-8186-7919-0

Type

conf

DOI

10.1109/ICASSP.1997.599489

Filename

599489