A weighted least squares algorithm for quasi-equiripple FIR and IIR digital filter design

Author

Lim, Yong Ching ; Lee, Ju-Hong ; Chen, C.K. ; Yang, Rong-Huan

Author_Institution

Dept. of Electr. Eng., Nat. Univ. of Singapore, Singapore

Volume

40

Issue

3

fYear

1992

fDate

3/1/1992 12:00:00 AM

Firstpage

551

Lastpage

558

Abstract

It has been demonstrated by several authors that if a suitable frequency response weighting function is used in the design of a finite impulse response (FIR) filter, the weighted least squares solution is equiripple. The crux of the problem lies in the determination of the necessary least squares frequency response weighting function. A novel iterative algorithm for deriving the least squares frequency response weighting function which will produce a quasi-equiripple design is presented. The algorithm converges very rapidly. It typically produces a design which is only about 1 dB away from the minimax optimum solution in two iterations and converges to within 0.1 dB in six iterations. Convergence speed is independent of the order of the filter. It can be used to design filters with arbitrarily prescribed phase and amplitude response

Keywords

digital filters; frequency response; least squares approximations; FIR filter; IIR digital filter; amplitude response; convergence speed; filter design; finite impulse response; frequency response; iterative algorithm; phase response; quasiequiripple filters; weighted least squares algorithm; weighting function; Algorithm design and analysis; Digital filters; Finite impulse response filter; Fourier series; Frequency response; Helium; Iterative algorithms; Least squares approximation; Least squares methods; Minimax techniques;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.120798

Filename

120798