Efficient design of cosine-modulated filter banks via convex optimization

Authors:
Ha Hoang Kha;Hoang Duong Tuan;Truong Q. Nguyen
Affiliations:
School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, NSW, Australia;School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, NSW, Australia;Department of Electrical and Computer Engineering, University of California in San Diego, La Jolla, CA
Venue:
IEEE Transactions on Signal Processing
Year:
2009

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Abstract

This paper presents efficient approaches for designing cosine-modulated filter banks with linear phase prototype filter. First, we show that the design problem of the prototype filter being a spectral factor of 2 Mth-band filter is a nonconvex optimization problem with low degree of nonconvexity. As a result, the nonconvex optimization problem can be cast into a semi-definite programming (SDP) problem by a convex relaxation technique. Then the reconstruction error is further minimized by an efficient iterative algorithm in which the closed-form expression is given in each iteration. Several examples are given to illustrate the effectiveness of the proposed method over the existing ones.