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Concept

Convergence of Fourier series

Related publications (15)

Local Nondeterminism and Local Times of the Stochastic Wave Equation Driven by Fractional-Colored Noise

Cheuk Yin Lee

We investigate the existence and regularity of the local times of the solution to a linear system of stochastic wave equations driven by a Gaussian noise that is fractional in time and colored in space. Using Fourier analytic methods, we establish strong l ...

SPRINGER BIRKHAUSER2022

CPGD: Cadzow Plug-and-Play Gradient Descent for Generalised FRI

Martin Vetterli, Paul Hurley, Matthieu Martin Jean-André Simeoni, Adrien Georges Jean Besson

Finite rate of innovation (FRI) is a powerful reconstruction framework enabling the recovery of sparse Dirac streams from uniform low-pass filtered samples. An extension of this framework, called generalised FRI (genFRI), has been recently proposed for han ...

2020

Fourier movement primitives: an approach for learning rhythmic robot skills from demonstrations

Sylvain Calinon, Thibaut Antoine Kulak

Whether in factory or household scenarios, rhythmic movements play a crucial role in many daily-life tasks. In this paper we propose a Fourier movement primitive (FMP) representation to learn such type of skills from human demonstrations. Our approach take ...

2020

Non-linear transfer function identification of pressure probes using Siren Disks

Jürg Alexander Schiffmann, Karim Magdi Zakaria Abdelrahman Shalash

This article presents a Siren Disk proof of concept for the dynamic excitation of pressure probes, and a method to reconstruct distorted signals due to pneumatic channels. Constraints in sensor installation require placing a pressure transducer distant fro ...

2018

Large Sieve Inequalities for Algebraic Trace Functions

Philippe Michel, Ping Xi

The large sieve inequalities for algebraic trace functions are considered in this article. A fundamental iterative relation is established by classical Fourier analysis, and l-adic Fourier analysis and multiplicative convolutions of sheaves are also requir ...

Oxford Univ Press2017

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

Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: application to random elliptic PDEs

Fabio Nobile, Lorenzo Tamellini

In this work we provide a convergence analysis for the quasi-optimal version of the sparse-grids stochastic collocation method we presented in a previous work: “On the optimal polynomial approximation of stochastic PDEs by Galerkin and collocation methods” ...

Springer2016

Closed fringe demodulation using phase decomposition by Fourier basis functions

Pramod Rastogi, Rishikesh Dilip Kulkarni

We report a new technique for the demodulation of a closed fringe pattern by representing the phase as a weighted linear combination of a certain number of linearly independent Fourier basis functions in a given row/column at a time. A state space model is ...

2016

Use of Convex Model Approximations for Real-Time Optimization via Modifier Adaptation

Dominique Bonvin, Grégory François

Real-Time Optimization (RTO) via modifier adaptation is a class of methods for which measurements are used to iteratively adapt the model via input-affine additive terms. The modifier terms correspond to the deviations between the measured and predicted co ...

American Chemical Society2013

On-line frequency adaptation and movement imitation for rhythmic robotic tasks

Auke Ijspeert, Tadej Petric

In this paper we present a novel method to obtain the basic frequency of an unknown periodic signal with an arbitrary waveform, which can work online with no additional signal processing or logical operations. The method originates from non-linear dynamica ...

SAGE Publications2011

Fast O(1) Bilateral Filtering Using Trigonometric Range Kernels

Michaël Unser, Daniel Sage, Kunal Narayan Chaudhury

It is well known that spatial averaging can be realized (in space or frequency domain) using algorithms whose complexity does not scale with the size or shape of the filter. These fast algorithms are generally referred to as constant-time or O(1) algorithm ...

IEEE2011

Turbulence in basic toroidal plasmas

Stefan Müller

This thesis work contributes to the improvement of the experimental assessment of turbulence in fusion-relevant toroidal plasmas via the construction and dedicated exploitation of the TORPEX basic toroidal plasma experiment. Several contributions to the co ...

EPFL2007

Data-Driven Estimation of the Infinity Norm of a Dynamical System

Dominique Bonvin, Alireza Karimi

The estimation of a system’s infinity norm using one set of measured input and output data is investigated. It is known that, if the data set is noise free, this problem can be solved using convex optimization. In the presence of noise, convergence of this ...

2007

An Efficient Discretization of the Navier–Stokes Equations in an Axisymmetric Domain. Part 1: The Discrete Problem and its Numerical Analysis

Simone Deparis

Any solution of the Navier–Stokes equations in a three-dimensional axisymmetric domain admits a Fourier expansion with respect to the angular variable, and it can be noted that each Fourier coefficient satisfies a variational problem on the meridian domain ...

2006

A truncated Fourier/finite element discretization of the Stokes equations in an axisymmetric domain

Simone Deparis

We consider the Stokes problem in a three-dimensional axisymmetric domain and, by writing the Fourier expansion of its solution with respect to the angular variable, we observe that each Fourier coefficient satisfies a system of equations on the meridian d ...

2006