Angular Parameterization of Real Paraunitary Matrices

The design problem of paraunitary filter banks has been addressed in many publications. The authors propose factorized structures that are obtained using transformations of the polyphase matrix of an analysis bank. In this letter, we focus, using a different approach, on the factorization of real-valued square paraunitary matrices. Using fundamental properties of real algebraic sets, we theoretically prove that, for the set of all paraunitary matrices of given size and order, one can get a full characterization of a complete and minimal set of mutually disjoint parameterized subsets. Thus, our analysis opens new horizons for the implementation and design of paraunitary filter banks.