Multiwavelet analysis and signal processing

In this paper we present some results and applications concerning the recent theory of multiscaling functions and multiwavelets. In particular, we present the theory in compact notation with the use of some types of recursive block matrices. This allows a flexible schematization of the construction of semi-orthogonal multiwavelets. As in the scalar case, an efficient algorithm for the computation of the coefficients of a multiwavelet transform can be obtained, in which r input sequences are involved. This is a crucial point: the choice of a good prefilter which can provide a good approximation of the true initial coefficient sequences, when applied to the input data, is critical in the context of multiwavelet analysis. We explore this problem with concrete examples, showing the strong dependence of the prefilter on the chosen multiwavelet basis. Finally, an application of the multiwavelet-based algorithm to signal compression is shown. The goal is both to compare the results obtained with different multiwavelet bases, and to test the effectiveness of multiwavelets in this kind of problem with respect to scalar wavelets.