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Concept

Peigne de Dirac

Publications associées (15)

Versatile shaping of optical frequency combs and applications

Jianqi Hu

Optical frequency combs are a series of phase-locked and equidistant laser lines in the spectral domain. In the time domain, they correspond to periodic pulse trains by the Fourier relation. The ability to shape optical combs and pulse trains is pivotal to ...

EPFL2021

Resonant Supercontinuum Generation in Normal and Anomalous Dispersion

Tobias Kippenberg, Junqiu Liu, Wenle Weng, Tobias Herr, Miles Henry Anderson

We demonstrate broadband resonant supercontinuum generation based on stable bright soliton formation in Si3N4 microresonators with either anomalous or normal dispersion. The frequency combs have an electronically detectable repetition rate of 28 GHz, and s ...

IEEE2020

Functional Inverse Problems on Spheres: Theory, Algorithms and Applications

Matthieu Martin Jean-André Simeoni

Many scientific inquiries in natural sciences involve approximating a spherical field -namely a scalar quantity defined over a continuum of directions- from generalised samples of the latter (e.g. directional samples, local averages, etc). Such an approxim ...

EPFL2020

Method for estimating synchrophasors during static and dynamic conditions

Mario Paolone, Asja Derviskadic, Paolo Romano

A method for performing synchrophasor estimation of an input signal, whereby the input signal is a sinusoidal power system voltage or current signal, comprising: a. Periodic sampling of a continuous time-domain waveform, consisting of a power system voltag ...

2018

Self-referenced photonic chip soliton Kerr frequency comb

Tobias Kippenberg, Erwan Guillaume Albert Lucas, Victor Brasch, John David Jost, Michael Wolfgang Geiselmann

Self-referencing turns pulsed laser systems into self-referenced frequency combs. Such frequency combs allow counting of optical frequencies and have a wide range of applications. The required optical bandwidth to implement self-referencing is typically ob ...

2017

A Spectral Method for Generating Surrogate Graph Signals

Dimitri Nestor Alice Van De Ville, Elvira Pirondini, Martina Coscia

The increasing availability of network data is leading to a growing interest in processing of signals on graphs. One notable tool for extending conventional signal-processing operations to networks is the graph Fourier transform that can be obtained as the ...

IEEE Institute of Electrical and Electronics Engineers2016

Moments And Growth Indices For The Nonlinear Stochastic Heat Equation With Rough Initial Conditions

Robert Dalang, Le Chen

We study the nonlinear stochastic heat equation in the spatial domain R, driven by space-time white noise. A central special case is the parabolic Anderson model. The initial condition is taken to be a measure on R, such as the Dirac delta function, but th ...

Inst Mathematical Statistics2015

Moments, Intermittency, and Growth Indices for Nonlinear Stochastic PDE's with Rough Initial Conditions

Le Chen

In this thesis, we study several stochastic partial differential equations (SPDE’s) in the spatial domain R, driven by multiplicative space-time white noise. We are interested in how rough and unbounded initial data affect the random field solution and the ...

EPFL2013

Chebyshev Polynomial Approximation for Distributed Signal Processing

Pascal Frossard, Pierre Vandergheynst, David Shuman

Unions of graph Fourier multipliers are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators to the high-dimensional signals collected by sen ...

2011

Random Sampling ADC for Sparse Spectrum Sensing

Andreas Peter Burg

Scanning large bandwidths (spectrum sensing) pushes today’s analog hardware to its limits since periodic sampling at Nyquist rate with sufficient resolution is often prohibitively complex. In this paper, we consider a scenario where the signal to be acquir ...

2011

Analytical Footprints: Compact Representation of Elementary Singularities in Wavelet Bases

Michaël Unser, Dimitri Nestor Alice Van De Ville, Thierry Blu

We introduce a family of elementary singularities that are point-Holder alpha-regular. These singularities are self-similar and are the Green functions of fractional derivative operators; i.e., by suitable fractional differentiation, one retrieves a Dirac ...

Institute of Electrical and Electronics Engineers2010

CMOS Compressed Imaging by Random Convolution

Yusuf Leblebici, Pierre Vandergheynst, Alexandre Schmid, Laurent Jacques, Vahid Majidzadeh Bafar

We present a CMOS imager with built-in capability to perform Compressed Sensing. The adopted sensing strategy is the random Convolution due to J. Romberg. It is achieved by a shift register set in a pseudo-random configuration. It acts as a convolutive fil ...

2009

A Method for Generalized Sampling and Reconstruction of Finite-Rate-of-Innovation Signals

Michaël Unser, Chandra Sekhar Seelamantula

We address the problem of generalized sampling and reconstruction of finite-rate-of-innovation signals. Specifically, we consider the problem of sampling streams of Dirac impulses and propose a two-channel method that enables fast, local reconstruction und ...

LATP2009

Sound Field Analysis Along a Circle and its Application to HRTF Interpolation

Martin Vetterli, Christof Faller, Luciano Sbaiz, Thibaut Ajdler

The sampling and interpolation of a sound field in two and three dimensions along a circle is discussed. The Fourier domain representation of the sound field is used, and an angular sampling theorem is developed for the sampling of the sound field along a ...

2008

A Generalized Sampling Method for Finite-Rate-of-Innovation-Signal Reconstruction

Michaël Unser, Chandra Sekhar Seelamantula

The problem of sampling signals that are not admisible within the classical Shannon framework has received much attention in the recent past. Typically, these signals have a parametric representation with a finite number of degrees of freedom per time unit ...

IEEE Institute of Electrical and Electronics Engineers2008