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On the design of FIR wavelet filter banks using factorization of a halfband polynomial

DSpace at IIT Bombay

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Title On the design of FIR wavelet filter banks using factorization of a halfband polynomial
 
Creator PATIL, BD
PATWARDHAN, PG
GADRE, VM
 
Subject filter bank
polynomial factorization
regularity
 
Description A classic method of designing two-channel biorthogonal wavelet FIR filter banks is by the factorization of a halfband polynomial. Most of the popular biorthogonal filter banks are designed by the factorization of the Lagrange halfband polynomial, which has the maximum number of zeros at z = -1. However, the Lagrange halfband polynomial does not have any "free parameter," and thus, there is no direct control over the frequency response of the filters obtained by factorization. In this letter, our aim is have some control over the frequency response of the filters designed by factorization. To achieve this, we start with a general halfband filter (not the Lagrange halfband filter) whose coefficients are parameters to be designed. We then impose the regularity constraint by imposing zeros at z = -1. The number of zeros we impose is less than the maximum possible. Imposing the zeros gives a set of constraints on the coefficients of the halfband polynomial. We then factorize the halfband polynomial by expressing it in terms of the independent (free) parameters after imposing the regularity constraints. We use the free parameters to control the frequency response of the filters. We present design examples to illustrate this method.
 
Publisher IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
 
Date 2011-08-01T10:40:39Z
2011-12-26T12:53:21Z
2011-12-27T05:34:45Z
2011-08-01T10:40:39Z
2011-12-26T12:53:21Z
2011-12-27T05:34:45Z
2008
 
Type Article
 
Identifier IEEE SIGNAL PROCESSING LETTERS, 15(), 485-488
1070-9908
http://dx.doi.org/10.1109/LSP.2008.922295
http://dspace.library.iitb.ac.in/xmlui/handle/10054/8409
http://hdl.handle.net/10054/8409
 
Language en