Publication

Wavelet and footprint sampling of signals with a finite rate of innovation

Martin Vetterli, Pier Luigi Dragotti
2004
Conference Papers

Abstract

In this paper, we consider classes of not bandlimited signals, namely, streams of Diracs and piecewise polynomial signals, and show that these signals can be sampled and perfectly reconstructed using wavelets as sampling kernel. Due to the multiresolution structure of the wavelet transform, these new sampling theorems naturally lead to the development of a new resolution enhancement algo- rithm based on wavelet footprints [2]. Preliminary results show the potentiality of this algorithm.

Official source

https://infoscience.epfl.ch/entities/publication/4fdff76a-0c4c-4c6f-9312-8f4fdec6af5b

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Martin Vetterli, Pier Luigi Dragotti
2004
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/4fdff76a-0c4c-4c6f-9312-8f4fdec6af5b

About this result

Related concepts (24)

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.

Wavelet

A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing. For example, a wavelet could be created to have a frequency of Middle C and a short duration of roughly one tenth of a second.

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.

Related publications (13)

Wavelet and footprint sampling of signals with a finite rate of innovation

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