Publication

The Fractional Hilbert Transform And Dual-Tree Gabor-Like Wavelet Analysis

Michaël Unser, Kunal Narayan Chaudhury
2009
Conference Papers

Résumé

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.

Source officielle

https://infoscience.epfl.ch/entities/publication/06ae72be-a5c7-4240-8c61-710d695901b3

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Michaël Unser, Kunal Narayan Chaudhury
2009
Conference Papers

Résumé

Source officielle

https://infoscience.epfl.ch/entities/publication/06ae72be-a5c7-4240-8c61-710d695901b3

À propos de ce résultat

Concepts associés (15)

Wavelet transform

In mathematics, a wavelet series is a representation of a square-integrable (real- or complex-valued) function by a certain orthonormal series generated by a wavelet. This article provides a formal, mathematical definition of an orthonormal wavelet and of the integral wavelet transform. A function is called an orthonormal wavelet if it can be used to define a Hilbert basis, that is a complete orthonormal system, for the Hilbert space of square integrable functions.

Discrete wavelet transform

In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency and location information (location in time). Haar wavelet The first DWT was invented by Hungarian mathematician Alfréd Haar. For an input represented by a list of numbers, the Haar wavelet transform may be considered to pair up input values, storing the difference and passing the sum.

Ondelette

thumb|Ondelette de Daubechies d'ordre 2. Une ondelette est une fonction à la base de la décomposition en ondelettes, décomposition similaire à la transformée de Fourier à court terme, utilisée dans le traitement du signal. Elle correspond à l'idée intuitive d'une fonction correspondant à une petite oscillation, d'où son nom. Cependant, elle comporte deux différences majeures avec la transformée de Fourier à court terme : elle peut mettre en œuvre une base différente, non forcément sinusoïdale ; il existe une relation entre la largeur de l'enveloppe et la fréquence des oscillations : on effectue ainsi une homothétie de l'ondelette, et non seulement de l'oscillation.

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