On non-separable multidimensional perfect reconstruction filter

In a previous paper the authors (see Basu and Chiang, 1992) have stated without proof a result describing how the previously open problem of completely parametrizing all 2D paraunitary filter banks can be resolved. This paper provides a complete proof of the result. The proof is essentially an adaptation of the network theoretic method of synthesis of 2D bounded transfer functions to the case of discrete FIR systems. An example is given, to show how the parametrization can be used to generate a broader class of transfer functions than the separable examples constructed by earlier workers in the field