In this paper we present some results and applications concerningnthe recent theory of multiscaling functions and multiwavelets. Innparticular, we present the theory in compact notation with the use ofnsome types of recursive block matrices. This allows a flexiblenschematization of the construction of semi-orthogonal multiwavelets. Asnin the scalar case, an efficient algorithm for the computation of thencoefficients of a multiwavelet transform can be obtained, in which rninput sequences are involved. This is a crucial point: the choice of angood prefilter which can provide a good approximation of the trueninitial coefficient sequences, when applied to the input data, isncritical in the context of multiwavelet analysis. We explore thisnproblem with concrete examples, showing the strong dependence of thenprefilter on the chosen multiwavelet basis. Finally, an application ofnthe multiwavelet-based algorithm to signal compression is shown. Thengoal is both to compare the results obtained with different multiwaveletnbases, and to test the effectiveness of multiwavelets in this kind ofnproblem with respect to scalar wavelets
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