Alias reduction: Generalised pseudocirculant conditions

Abstract

Complete alias cancellation, in an arbitrary nonuniform and/or nonmaximally decimated filter bank structure, is not guaranteed. Also it is well known that the inversion of a linear periodically time varying (LPTV) system is not always guaranteed. In this paper we exploit the ability of uniform filter bank (UFB) framework to provide alternative models for these structures. We propose a simplification by generalising the well known pseudocirculant conditions [1] (Vaidyanathan and Mitra, 1988). UFB can be characterised by the two switching representations of the LPTV systems. The set of linear time invariant (LTI) systems in each representation is uniquely related to the rows and columns of the matrix associated with the UFB. Under the pseudocirculant conditions the UFB reduces to an LTI system. Here we obtain a set of generalised pseudocirculant conditions which reduce the UFB to an LPTV of lower order.