A simple method to build oversampled filter banks and tight frames.

Abstract

This paper presents conditions under which the sampling lattice for a filter bank can be replaced without loss of perfect reconstruction. This is the generalization of common knowledge that removing up/downsampling will not lose perfect reconstruction. The results provide a simple way of building oversampled filter banks. If the original filter banks are orthogonal, these oversampled banks construct tight frames of l2 (Z(n)) when iterated. As an example, a quincunx lattice is used to replace the rectangular one of the standard wavelet transform. This replacement leads to a tight frame that has a higher sampling in both time and frequency. The frame transform is nearly shift invariant and has intermediate scales. An application of the transform to image fusion is also presented.