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ICASSP
2009
IEEE

The fractional Hilbert transform and dual-tree Gabor-like wavelet analysis

10 years 4 months ago
The fractional Hilbert transform and dual-tree Gabor-like wavelet analysis
We provide an amplitude-phase representation of the dual-tree complex wavelet transform by extending the fixed quadrature relationship of the dual-tree wavelets to arbitrary phase-shifts using the fractional Hilbert transform (fHT). The fHT is a generalization of the Hilbert transform that extends the quadrature phase-shift action of the latter to arbitrary phase-shifts—a real shift parameter controls this phase-shift action. Next, based on the proposed representation and the observation that the fHT operator maps well-localized B-spline wavelets (that resemble Gaussian-windowed sinusoids) into B-spline wavelets of the same order but different shift, we relate the corresponding dual-tree scheme to the paradigm of multiresolution windowed Fourier analysis.
Kunal Narayan Chaudhury, Michael Unser
Added 21 May 2010
Updated 21 May 2010
Type Conference
Year 2009
Where ICASSP
Authors Kunal Narayan Chaudhury, Michael Unser
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