Nonuniform perfect reconstruction filter banks over lattices with application to transmultiplexers

This paper presents a multidimensional multirate theory for signals defined over lattices. We extend the notion of the z transform and present linear periodically-shift-varying (LPSV) systems. We use this theory to study transmultiplexers for signals defined over arbitrary lattices (nonuniform or unequal-band case). We give dimensionality conditions for perfect reconstruction and determine the form of the solutions. Finally, we study tree-structured transmultiplexing systems. Such systems permit us to design nonuniform filter banks from uniform filter banks. Furthermore, their multistage implementation allows lower complexity.