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.


Published in:
2008 Ieee International Conference On Acoustics, Speech And Signal Processing, Vols 1-12, 3277-3280
Presented at:
33rd IEEE International Conference on Acoustics, Speech and Signal Processing, Las Vegas, NV, Mar 30-Apr 04, 2008
Year:
2008
Publisher:
Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa
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 Record created 2010-11-30, last modified 2018-03-17

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