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Construction of Hilbert Transform Pairs of Wavelet Bases and Optimal Time-Frequency Localization

K.N. Chaudhury, M. Unser

Proceedings of the Thirty-Third IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'08), Las Vegas NV, USA, March 30-April 4, 2008, pp. 3277-3280.



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 L2(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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