Factorizations of two families of two-dimensional IIR paraunitary matrices

Paraunitary matrices play an important role in the design of perfect reconstruction filter banks. There are building blocks that generate the whole family of both FIR and IIR one-dimensional paraunitary matrices over the complex field. Because of applications in digital signal and image processing, there has been an attempt to generalize the factorization methods to the two-dimensional case. However, no general building block that covers all two-dimensional IIR paraunitary matrices has been found yet. In this paper, we present a factorization for two families of such matrices.