Construction of Hilbert transform pairs of wavelet bases and optimal time-frequency localization
Kunal N. Chaudhury, Michael A. Unser · IEEE International Conference on Acoustics Speech and Signal Processing · 2008
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(K) 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.