The Replaceability of Sampling Matrix for Multidimensional Perfect Reconstruction Filter Banks

It is shown under a divisibility condition the sampling matrix for a filter bank can be replaced without loss of perfect reconstruction. This is the generalization of the common knowledge that removing up/downsampling will not alter perfect reconstruction. The result provides a simple way to implement redundant perfect reconstruction filter banks, which constitute tight frames of l2(Z) when iterated. As an example, a quincunxsampled frame is presented, which is nearly shift-invariant as well as limited-redundancy.