Construction of Hilbert transform pairs of wavelet bases and optimal time-frequency localization
We propose a novel method of constructing exact Hilbert transform (HT) pairs of wavelet bases using fractional B-splines and state necessary and sufficient conditions for generating such wavelet pairs. In particular, we demonstrate how HT pairs of biorthogonal wavelet bases of L-2 (R) can be constructed using well-localized scaling functions with identical Riesz bounds. Finally, we illustrate this concept by constructing a family of analytic Gabor-like wavelets that exhibit near optimal time-frequency localization.
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- URL: http://bigwww.epfl.ch/publications/chaudhury0801.ps
Record created on 2010-11-30, modified on 2016-08-09