Design of two-channel causal stable IIR PR filter banks and wavelet bases using constrained model reduction

This paper proposes a new method for designing two-channel causal stable IIR perfect reconstruction (PR) filter banks (FBs) with prescribed peak error and K-regularity constraints. It is based on the model reduction of the FIR functions in the structural PR filter banks of Phoong et al by a new model reduction technique, which was a modification of the technique previously proposed by Brandenstein et al. The proposed model reduction method retains the denominator of the conventional techniques and formulates the optimal design of the numerator as a semi-definite programming problem. Therefore, linear and convex quadratic inequalities such as peak error and K-regularity constraints for the IIR filters can be imposed and solved optimally. Design examples show that the proposed method gives better performance, more flexibility in incorporating a wide variety of constraints, and lower design complexity than conventional method.