Multiwavelet Analysis and Signal Processing

In this work we present some results and applications concerning the recent theory of multi-scaling 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 exible schematization of the construction of semi-orthogonal multiwavelets. As in the scalar case, an eecient algorithm for the computation of the coeecients of a multiwavelet transform can be obtained, in which r input sequences are involved. This is a crucial point: the choice of a good preelter which can provide a good approximation of the true initial coeecient 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 preelter 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 diierent multiwavelet bases, and to test the eeectiveness of multiwavelets in this kind of problem with respect to scalar wavelets.