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.

• Type: Conference
• Year: 2009
• Where: ICASSP
• Authors: Kunal Narayan Chaudhury, Michael Unser
• Keywords: B-spline Wavelets, Dual-tree Complex Wavelet Transform, Hilbert Transform, ICASSP 2009, Signal Processing