A mixed norm performance measure for the design of multirate filterbanks

Author

Banavar, Ravi N. ; Kalele, Amit A.

Author_Institution

Syst. & Control Eng., Indian Inst. of Technol., Mumbai, India

Volume

49

Issue

2

fYear

2001

fDate

2/1/2001 12:00:00 AM

Firstpage

354

Lastpage

359

Abstract

A mixed norm performance measure is presented to design the synthesis filters of a multirate filterbank. The mixed norm performance measure is based on the energy as well as the peak value of the error signal. Mathematically, the performance measure minimizes the l₂-norm of the error signal subject to the l_∞-norm of the error being bounded by some positive value v (this imposes a bound on the peak value of the error signal). The design problem is shown to be that of a mixed ℋ₂/ℋ_∞ optimization problem. The theory of linear matrix inequalities (LMIs) offers a tractable solution to such multiobjective synthesis problems. The synthesis filters designed with the new performance measure are compared with those obtained by similar induced norm minimization techniques in terms of degree of reconstruction, order of the synthesis filters, SNR, and aliasing distortion

Keywords

H^∞ optimisation; channel bank filters; circuit optimisation; digital filters; matrix algebra; network synthesis; signal reconstruction; signal synthesis; SNR; aliasing distortion; error signal energy; error signal peak value; induced norm minimization; linear matrix inequalities; mixed norm performance measure; multiobjective synthesis problems; multirate filterbanks design; optimization problem; reconstruction; synthesis filter order; synthesis filters design; Control system synthesis; Filters; Image reconstruction; Linear matrix inequalities; Mirrors; Phase distortion; Signal analysis; Signal design; Signal synthesis; Transfer functions;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.902117

Filename

902117