On the factorization of two-dimensional paraunitary filter banks

The factorization of 2D FIR paraunitary filter banks is addressed in this paper. Our work is a generalization of the factorization algorithm for 1D paraunitary matrices. We present a complete factorization for multichannel, 2D, FIR paraunitary filter banks. The main idea is considering a bivariate FIR matrix as a univariate polynomial whose coefficients are matrices with univariate polynomial entries. With this representation, a generalized version of the factorization algorithm for the 1D case, developed in this paper, can be used. In this direction, a new definition for paraunitary matrices is proposed and a new degree-one building block is presented. The final result is a building block that generates all 2D FIR paraunitary matrices.