Hilbert pairs of M-band orthonormal wavelet bases

Abstract : Recently, there has been a growing interest for wavelet frames corresponding to the union of an orthonormal wavelet basis and its dual Hilbert transformed wavelet basis. However, most of the existing works specifically address the dyadic case. In this paper, we consider orthonormal M-band wavelet decompositions, since we are motivated by their advantages in terms of frequency selectivity and symmetry of the analysis functions, for M > 2. More precisely, we establish phase conditions for a pair of critically subsampled M-band filter banks. The conditions we obtain generalize a previous result given in the two-band case. We also show that, when the primal filter bank and its wavelets have symmetry, it is inherited by their duals. Furthermore, we give a design example where the number of vanishing moments of the approximate dual wavelets is imposed numerically to be the same as for the primal ones.
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Caroline Chaux, Laurent Duval, Jean-Christophe Pesquet. Hilbert pairs of M-band orthonormal wavelet bases. Proc. European Signal Processing Conference Conference (EUSIPCO'04), Sep 2004, Vienna, Austria, France. pp.1187-1190. ⟨hal-00621901⟩

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