Generic invertibility of multidimensional FIR multirate systems and filter banks

We study the invertibility of M-variate polynomial (respectively : Laurent polynomial) matrices of size N by P. Such matrices represent multidimensional systems in various settings including filter banks, multiple-input multiple-outputsystems, and multirate systems. The main result of this paper is to prove that when N − P ≥ M, then H(z) is generically invertible; whereas when N − P < M, then H(z) is generically noninvertible. As a result, we can have an alternative approach in design of the multidimensional systems.

• Type: Conference
• Year: 2009
• Where: ICASSP
• Authors: K. L. Law, Robert M. Fossum, Minh N. Do
• Keywords: ICASSP 2009, Laurent Polynomial, Multidimensional Systems, Signal Processing, Such Matrices