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| Content Provider | IEEE Xplore Digital Library |
|---|---|
| Author | Patil, B.D. Patwardhan, P.G. Gadre, V.M. |
| Copyright Year | 1994 |
| Abstract | 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. |
| Sponsorship | IEEE Signal Processing Society |
| Starting Page | 485 |
| Ending Page | 488 |
| Page Count | 4 |
| File Size | 154072 |
| File Format | |
| ISSN | 10709908 |
| Volume Number | 15 |
| Language | English |
| Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher Date | 2008-01-01 |
| Publisher Place | U.S.A. |
| Access Restriction | One Nation One Subscription (ONOS) |
| Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subject Keyword | Finite impulse response filter Filter bank Polynomials Lagrangian functions Frequency response Design methodology Filtering theory Spline Digital signal processing regularity polynomial factorization |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Signal Processing Electrical and Electronic Engineering |
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