Design of Halfband Filters for Orthogonal Wavelets via Sum of Squares Decomposition

Author

Yu, Runyi ; Baradarani, Aryaz

Author_Institution

Dept. of Electr. & Electron. Eng., Eastern Mediterranean Univ., Gazimagusa

Volume

15

fYear

2008

fDate

6/30/1905 12:00:00 AM

Firstpage

437

Lastpage

440

Abstract

This letter is concerned with design of halfband product filters for orthogonal wavelets. We first remark that the recent zero-pinning technique for orthogonal wavelet design cannot always guarantee the nonnegativity of the filter. We then propose to use sum of squares (SOS) decomposition to ensure its nonnegativity. The use of SOS decomposition also allows us to solve two optimization problems on the halfband filter via semidefinite programming. For a given length with pre-specified number of zeros at , we obtain halfband filters with maximal passband width. Design examples are provided.

Keywords

discrete time filters; mathematical programming; polynomial approximation; wavelet transforms; Bernstein polynomial approximation; discrete-time filter; filter nonnegativity; halfband product filter design; maximal passband width; optimization problem; orthogonal wavelet design; semidefinite programming; sum of squares decomposition; zero-pinning technique; Constraint optimization; Discrete wavelet transforms; Equations; Frequency response; Lead; Nonlinear filters; Passband; Polynomials; Product design; Voice mail; Bernstein polynomial; halfband filter; orthogonal wavelets; sum of squares decomposition;

fLanguage

English

Journal_Title

Signal Processing Letters, IEEE

Publisher

ieee

ISSN

1070-9908

Type

jour

DOI

10.1109/LSP.2008.923791

Filename

4512094