Sampled-data design of FIR dual filter banks for dual-tree complex wavelet transforms via LMI optimization

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 z = -1. 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 H-infinity 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.