Balanced multiwavelets

Abstract

This paper deals with multiwavelets which are a generalization of wavelets in the context of multirate filter banks and their applications to signal processing and especially compression. By their inherent structure, multiwavelets are fit for processing multi-channel signals. First, we recall some general results on multiwavelets and the convergence of the iterated matrix product. Then, we define under what conditions we can apply systems based on multiwavelets to one-dimensional signals in a simple way. That means we give some natural and simple conditions that should help in the design of new multiwavelets for signal processing. Finally, we provide some tools in order to construct multiwavelets with the required properties, the so-called 'balanced multiwavelets'.