Designing two-channel causal stable IIR PR filter banks and wavelet bases by model order reduction and constrained optimization

In this paper, two methods for designing two-channel causal stable IIR PR filter banks are introduced. The first method makes use of model reduction and constrained optimization to obtain a causal stable IIR filter bank from the structural PR FIR filter bank proposed by Phoong et al (1995). It yields better frequency characteristics than the original FIR filter bank and avoids the dump at π/2 when allpass filters are used. Using a 1-D to 2-D transformation, a two dimensional PR IIR filter bank can readily be obtained from these prototypes. The second method is based on a constrained optimization technique using the general PR condition. Using this technique, filter banks with low system delay and flexible frequency characteristics can be designed. The technique can also be modified to design causal stable IIR dyadic wavelet bases with added regularity conditions. A number of design examples are used to demonstrate the usefulness of the proposed design methods