Structures for time-reversed inversion in filter banks

Abstract

Anticausal inversion of IIR transfer functions has gained importance in recent years, in the efficient implementation of IIR digital filter banks. In this paper we first introduce the idea of a causal dual, as an intermediate step in the implementation of anticausal IIR inverses. With time reversal operators at the input and output of the casual dual, we get the anticausal inverse of the original structure. The causal dual eliminates the need for similarity transformations, during a key step called blockwise state transfer, in implementing anticausal inverses. In the paper we identify efficient structures for causal duals of standard structures like the direct-form, cascade-form, coupled form, and IIR lattice structures, including the tapped lattice.