Causal FIR matrices with anticausal FIR inverses, and application in characterization of biorthonormal filter banks

The new analysis and synthesis filters are z-1MH(z) Abstract and zIMFk(z), which means that the frequency charCausal FIR matrices with anticausal FIR inverses have acteristics are unchanged. By choosing I large enough a key role in the theory of FIR perfect reconstruction we can make E&) causal and its inverse R&) antifilter banks. We explore the theory of such matricausal. So the class of all FIR PR filter banks can be ces. Some general results on nature of inverses of first characterized by considering the cafacafi class. Unlike order causal FIR matrices are then presented. This arbitrary FIR systems with FIR inverses, cafacafi syso rd e c a u al I R m t ri c s a e t h n p r s e n e d . h i s t e rm s h a v e s p e c ial s y te m -t h e o r e t ic p r o p e rte:2 , 3 . leads, in particular, to a complete parameterization tes1aen speal stemtoret prertest 2, [3] of the Biorthonormai Lapped Tranisform (BOLT) reand generally spealing, are more interesting. In [3] earlie r B ihn Lapit is shown that the most general degree one cafacafi ported earlier in Ill. system has the form GoVn(z) where