Design of 2-D perfect reconstruction filter banks using transformations of variables: IIR case

We have previously (1993) presented a design technique for 2-channel multidimensional filter banks. The technique is based on the transformation of variables and provides the flexibility of controlling the frequency characteristics of the resulting subband filters with ease. In this paper we extend the design technique to yield IIR filters. We emphasize the 2-D diamond subband case (with quincunx sampling) but the technique can be used for the parallelogram and diagonally quadrant subband cases as well. The IIR nature of the filters occurs from the use of IIR transformation functions instead of FIR. Two cases are considered. The first is with zero-phase IIR transformations which yield linear phase subband filters but require noncausal filtering. The second is with nonlinear phase IIR transformations which yield nonlinear phase subband filters that can be implemented in a causal manner.