Factorization of paraunitary polyphase matrices using subspace projections

Paraunitary filter banks (PUFBs) play an important role in multirate signal processing and image processing applications. In this paper a new factorization technique is presented based on the Singular Value Decomposition (SVD) that decomposes PUFBs into a product of elementary building blocks. These building blocks are parameterized by a set of angles that can be varied independently via optimization techniques to design a particular filter bank satisfying some criterion. The utility of this new matrix decomposition is that fewer free parameters are required to represent a PUFB as compared to conventional lattice factorizations, such as the Givens rotation matrix decomposition. The more economical PUFB representation presented in this paper improves the numerical behavior of nonlinear optimization programs used for designing PUFBs and allows for the design of longer channel filters without incurring additional computational complexity. A simulated design example is presented whereby a causal Finite Impulse Response (FIR) PUFB is designed to approximate an ideal, infinite order PUFB.