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

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2 Author(s)
Runyi Yu ; Dept. of Electr. & Electron. Eng., Eastern Mediterranean Univ., Mersin ; Baradarani, A.

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.

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Signal Processing, IEEE Transactions on  (Volume:56 ,  Issue: 7 )