Balanced MultiWavelets - Theory and Design

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