EPFL | Biomedical Imaging Group

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, in press.

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We propose a novel method for constructing exact Hilbert transform (HT) pairs of wavelet bases using fractional B-splines and state the 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. We illustrate the concept by constructing an analytic Gabor-like wavelet that exhibits near optimal time-frequency localization.

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