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Generic Invertibility of Multidimensional FIR Filter Banks and MIMO Systems

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3 Author(s)
Ka L. Law ; Dept. of Math., Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA ; Robert M. Fossum ; Minh N. Do

In this paper, we study the invertibility of M-variate Laurent polynomial N times P matrices. Such matrices represent multidimensional systems in various settings such as filter banks, multiple-input multiple-output systems, and multirate systems. Given an N times P Laurent polynomial matrix H(z1, ..., zM) of degree at most k, we want to find a P times N Laurent polynomial left inverse matrix G(z) of H(z) such that G(z)H(z) = J. We provide computable conditions to test the invertibility and propose algorithms to find a particular inverse. The main result of this paper is to prove that H(z) is generically invertible when N - P ges M; whereas when N - P < M, then H(z) is generically noninvertible. As a result, we propose an algorithm to find a particular inverse of a Laurent polynomial matrix that is faster than current algorithms known to us.

Published in:

IEEE Transactions on Signal Processing  (Volume:57 ,  Issue: 11 )