Sampled-Data Design of FIR Dual Filter Banks for Dual-Tree Complex Wavelet Transforms via LMI Optimization

Authors:
R. Yu;A. Baradarani
Affiliations:
Dept. of Electr. & Electron. Eng., Eastern Mediterranean Univ., Mersin;-
Venue:
IEEE Transactions on Signal Processing - Part II
Year:
2008

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Abstract

Starting from a given finite-impulse-response (FIR) primal filter bank, we design a dual filter bank such that the complex wavelets associated with the dual-tree filter bank are (almost) analytic. The dual filter bank is required to be FIR and have a prescribed number of zeros at . We formulate a sampled-data optimization problem based on the half-sample delay condition on scaling filters. A discrete-time filter is introduced in the formulation to specify the number of the zeros. The optimization problem is converted into an equivalent discrete-time control problem; the latter is further reduced to an LMI optimization problem. We then present a procedure for design of FIR dual filter banks. Illustrative examples are provided; the results compare favorably to early designs.