Construction of Hilbert transform pairs of wavelet bases and optimal time-frequency localization

Construction of Hilbert transform pairs of wavelet bases and optimal time-frequency localization
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DOI：
10.1109/icassp.2008.4518350
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发表时间：
2008-03
期刊：
2008 IEEE International Conference on Acoustics, Speech and Signal Processing
影响因子：
--
通讯作者：
K. Chaudhury;M. Unser
K. Chaudhury;M. Unser
中科院分区：
其他
文献类型：
--
作者：
K. Chaudhury;M. Unser

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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.