Multiwavelet analysis and signal processing

In this paper we present some results and applications
concerning the recent theory of multiscaling funetions
and multiwavelets. In particular, we present the theory
in compact notation with the use of some types of recursive
block matrices. This allows a ftexible 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
Il good prefilter which can provide a good approximation of
the true initial coefficient sequences, when applied to the input
data, is criticai 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.