Design of Real and Complex Linear-Phase IIR Modified QMF Banks

A design of linear-phase IIR (infinite impulse response) modified QMF banks including both real and complex valued coefficients is proposed. This design is based on parallel structure of two complex allpass filters. We first introduce a complex analog allpass filter, designed using elliptic functions and the PR (perfect reconstruction) conditions. We use bilinear transformation to obtain the digital counterpart of this analog allpass filter. Depending on the parity of the order N of the complex allpass filter, the resulting IIR filters in the filter bank can be either real or complex. If N is even, the IIR filters are real, otherwise they are complex. Using complex IIR analysis filters, the corresponding magnitude responses have an extra zero around omega = 3pi/2. The method is illustrated by means of examples