On necessary and sufficient conditions for perfect reconstruction multidimensional delay chain systems

We present some necessary and sufficient conditions for a perfect reconstruction (PR) modified multidimensional (MD) delay chain system. With these results, one is able to systematically check if a D-dimensional delay chain system with a D×D sampling matrix M and a D×D delay matrix L has a PR property in a simpler way than before, where the matrix module operations are avoided. Moreover, given a D×D sampling matrix M, in many cases one can determine all possible D×D delay matrices L so that the delay chain systems with the sampling matrix M have a PR property. Several examples are provided. We also present a method to generate D×D sampling and delay matrices M and L such that their corresponding traditional MD delay chain systems are PR