How to capture all FIR perfect reconstruction QMF banks with unimodular matrices?

Author

Vaidyanathan, P.P.

Author_Institution

Dept. of Electr. Eng., California Inst. of Technol., Pasadena, CA, USA

fYear

1990

fDate

1-3 May 1990

Firstpage

2030

Abstract

The problem of perfect reconstruction in maximally decimated FIR (finite impulse response) QMF (quadrature mirror filter) banks is revisited. A necessary and sufficient condition for perfect reconstruction in this system is that the polyphase matrix of the analysis bank must have a determinant equal to a delay. The author explores various avenues to completely parameterize such matrices. It is shown that the problem can always be decomposed into two problems: one of parameterizing lossless matrices, and one of parameterizing unimodular matrices. Several possibilities for unimodular parameterization are explored

Keywords

digital filters; matrix algebra; signal processing; finite impulse response filter; lossless matrices parameterisation; maximally decimated FIR QMF banks; perfect reconstruction; polyphase matrix; quadrature mirror filter banks; unimodular matrices; unimodular parameterization; Artificial intelligence; Constraint optimization; Delay; Filter bank; Finite impulse response filter; Hafnium; Matrix decomposition; Polynomials; State-space methods; Sufficient conditions;

fLanguage

English

Publisher

ieee

Conference_Titel

Circuits and Systems, 1990., IEEE International Symposium on

Conference_Location

New Orleans, LA

Type

conf

DOI

10.1109/ISCAS.1990.112152

Filename

112152