Publications associées à A General Framework for Compressed Sensing and Parallel MRI Using Annihilating Filter Based Low-Rank Hankel Matrix

Unified Harmonic Power-Flow and Stability Analysis of Power Grids with Converter-Interfaced Distributed Energy Resources

Modern power distribution systems are experiencing a large-scale integration of Converter-Interfaced Distributed Energy Resources (CIDERs). Their presence complicates the analysis and mitigation of harmonics, whose creation and propagation may be amplified ...

EPFL2024

Nonlinear interactions of ion acoustic waves explored using fast imaging decompositions

Fast camera imaging is used to study ion acoustic waves propagating azimuthally in a magnetized plasma column. The high-speed image sequences are analyzed using proper orthogonal decomposition and 2D Fourier transform, allowing to evaluate the assets and d ...

2023

An optimal preconditioned FFT-accelerated finite element solver for homogenization

Till Junge, Ali Falsafi, Martin Ladecký

We generalize and provide a linear algebra-based perspective on a finite element (FE) ho-mogenization scheme, pioneered by Schneider et al. (2017)[1] and Leuschner and Fritzen (2018)[2]. The efficiency of the scheme is based on a preconditioned, well-scale ...

ELSEVIER SCIENCE INC2023

A Statistical Framework to Investigate the Optimality of Signal-Reconstruction Methods

Michaël Unser, Pakshal Narendra Bohra, Pol del Aguila Pla

We present a statistical framework to benchmark the performance of reconstruction algorithms for linear inverse problems, in particular, neural-network-based methods that require large quantities of training data. We generate synthetic signals as realizati ...

2023

pyFFS: A Python Library for Fast Fourier Series Computation and Interpolation with GPU Acceleration

Martin Vetterli, Paul Hurley, Eric Bezzam, Sepand Kashani, Matthieu Martin Jean-André Simeoni

Fourier transforms are an often necessary component in many computational tasks, and can be computed efficiently through the fast Fourier transform (FFT) algorithm. However, many applications involve an underlying continuous signal, and a more natural choi ...

SIAM2022

Fourier non-uniqueness sets from totally real number fields

Martin Peter Stoller

Let K be a totally real number field of degree n >= 2. The inverse different of K gives rise to a lattice in Rn. We prove that the space of Schwartz Fourier eigenfunctions on R-n which vanish on the "component-wise square root" of this lattice, is infinite ...

EUROPEAN MATHEMATICAL SOC-EMS2022

On the reconstruction of the attenuation function of a return-stroke current from the Fourier Transform of finite-duration measurements

Farhad Rachidi-Haeri, Marcos Rubinstein

A correct representation of the lightning current is crucial when the electromagnetic field radiated to a point of interest has to be computed. Based on the engineering models of Transmission Line type, such representation involves the knowledge of the ret ...

2022

An Inverse-Filter-Based Method to Locate Partial Discharge Sources in Power Transformers

Farhad Rachidi-Haeri, Marcos Rubinstein, Hamidreza Karami

Partial discharge (PD) occurrence in power transformers can lead to irreparable damage to the power network. In this paper, the inverse filter (IF) method to localize PDs in power transformers is proposed. To the best of the authors’ knowledge, this is the ...

2022

Function Integration, Reconstruction And Approximation Using Rank-1 Lattices

Fabio Nobile, Giovanni Migliorati

We consider rank-1 lattices for integration and reconstruction of functions with series expansion supported on a finite index set. We explore the connection between the periodic Fourier space and the non-periodic cosine space and Chebyshev space, via tent ...

2021

Hyperbolic Fourier series

Maryna Viazovska

In this article we explain the essence of the interrelation described in [PNAS 118, 15 (2021)] on how to write explicit interpolation formula for solutions of the Klein-Gordon equation by using the recent Fourier pair interpolation formula of Viazovska and ...

arXiv2021