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-output systems, and multirate systems. The main result of this paper is to prove that when N - P ges M, then H(z) is generically invertible; whereas when N - P Lt M, then H(z) is generically noninvertible. As a result, we can have an alternative approach in design of the multidimensional systems.