Title :
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
fDate :
6/30/1905 12:00:00 AM
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;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2008.923791