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Rank \(M\) wavelets with \(N\) vanishing moments. (English) Zbl 0828.15022

The author generalizes the rank 2 (scale factor of 2) orthogonal wavelet sequences of I. Daubechies to the case of a rank \(M\) wavelet matrix. He gives several equivalent definitions of \(N\)th order vanishing moments for rank \(M\) wavelets. He develops explicit formulas for rank \(M\) scaling sequences with \(N\) vanishing wavelet moments, completes the construction of a full rank \(M\) wavelet matrix (one scaling sequence and \(M- 1\) wavelet sequences) and gives a scaling sequence and a Haar wavelet matrix. He concludes by giving several examples of his construction.
Reviewer: K.Trimeche (Tunis)

MSC:

15B57 Hermitian, skew-Hermitian, and related matrices
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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