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

摘要

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 $H_{infty}$ 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.