Multiwavelet moments and projection prefilters

An efficient projection procedure is derived for use of orthogonal multiwavelets in the analysis of discrete data sequences. A family of simple prefilters corresponding to numerical quadrature evaluation of the projection integrals provides exact results for locally-polynomial data. The full approximation order of the multiwavelet basis can thus always be enabled. For nonpolynomial signals, the prefilters provide approximations to the coefficients of the multiwavelet series whose convergence accelerates quickly with increase in sampling rate. Comparison is also made with previous time-invariant multiwavelet prefilters. * This work was supported by the Robert A. Welch Foundation and by Grant CHE9528248 from the National Science Foundation. * The author is with the Department of Chemistry and the Rice Quantum Institute, MS #600, Rice University, Houston, TX 77251-1892. Telephone: 713-348-5103; Fax: 713348-5401; email: [email protected]. EDICS Classification: SP 2.4.4, 2-MWAV