Biorthonormal filter banks and the theory of transfer matrix inversion

Biorthonormal filter banks are essentially maximally decimated perfect reconstruction filter banks. The role of causal transfer matrices with anticausal inverses in biorthonormal filter bank theory has recently been recognized. These matrices help to characterize all biorthonormal filter banks in the FIR case; in the IIR case they are useful in finding stable anticausal inverses of analysis banks (when stable causal inverses do not exist), thereby enabling stable reconstruction of signals from subbands. This paper is dedicated to a discussion of the properties of transfer matrices with anticausal inverses