By Topic

On the Design of FIR Wavelet Filter Banks Using Factorization of a Halfband Polynomial

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Patil, B.D. ; Dept. of Electr. Eng., Indian Inst. of Technol., Mumbai ; Patwardhan, P.G. ; Gadre, V.M.

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.

Published in:

Signal Processing Letters, IEEE  (Volume:15 )