Minimax design of two-channel nonuniform-division filterbanks using IIR allpass filters

The design of two-channel linear-phase nonuniform-division filter (NDF) banks constructed by infinite impulse response (IIR) digital allpass filters (DAFs) in the sense of L_∞ error criteria is considered. First, the theory of two-channel NDF bank structures using two IIR DAFs is developed. Then, the design problem is appropriately formulated to result in a simple optimization problem. Utilizing a variant of Karmarkar´s algorithm, we can efficiently solve the optimization problem through a frequency sampling and iterative approximation method to find the coefficients for the IIR DAFs. The resulting two-channel NDF banks can possess approximately linear-phase response without magnitude distortion. The effectiveness of the proposed technique is achieved by forming an appropriate Chebyshev approximation of a desired phase response and then to find its solution from a linear subspace in a few iterations. Several simulation examples are presented for illustration and comparison.