Design of causal stable perfect reconstruction two-channel IIR filter banks

An efficient optimization algorithm is proposed for designing causal stable perfect-reconstruction two-channel infinite impulse response filter banks originally introduced by Basu, Chiang, and Choi. The problem is stated as a constrained optimization problem where the maximum of the stopband energies of the analysis filters is minimized subject to the given constraints. First, the maximum allowable passband ripple of both filters is fixed and the maximum value in the transition bands is the maximum allowable passband value. Second, the poles of these filters are forced to lie inside the unit circle. It is shown that the second constraint can be included in the proposed algorithm by using Rouche's theorem. Several examples are included illustrating the efficiency of the proposed design scheme as well as the superiority of the resulting banks compared to those obtainable by using other existing design techniques.