Concept
Generalized Fourier series
Related publications (9)
Spectral analysis for transmission eigenvalue problems with and without the complementing conditions
The interior transmission eigenvalue problem is a system of partial differential equations equipped with Cauchy data on the boundary: the transmission conditions. This problem appears in the inverse scattering theory for inhomogeneous media when, for some ...
EPFL2022The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equations
Hoài-Minh Nguyên, Jean Louis-Alexandre Fornerod
Cakoni and Nguyen recently proposed very general conditions on the coefficients of Maxwell equations for which they established the discreten ess of the set of eigenvalues of the transmission problem and studied their locations. In this paper, we establish ...
2021Continuous-Domain Signal Reconstruction Using L-p-Norm Regularization
Michaël Unser, Pakshal Narendra Bohra
We focus on the generalized-interpolation problem. There, one reconstructs continuous-domain signals that honor discrete data constraints. This problem is infinite-dimensional and ill-posed. We make it well-posed by imposing that the solution balances data ...
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020Measurement of Displacement and Its Derivatives from a Phase Fringe Pattern
Pramod Rastogi, Rishikesh Dilip Kulkarni
Noting the fact that the phase and phase derivatives carry the information on the mechanical deformation in optical interferometric measurements techniques, we propose a noise robust fringe analysis technique for the simultaneous estimation of unwrapped ph ...
SPRINGER INTERNATIONAL PUBLISHING AG2019Sub-Nyquist artifacts and sampling moiré effects, Part 2: Spectral-domain analysis
Sampling moiré effects occur due to aliasing (foldover) when a continuous periodic signal g(x) is sampled using a sampling frequency that does not respect the Nyquist condition. However, visible beating artifacts may also occur when g(x) is sampled using s ...
2015Fourier Analysis of Functional Time Series, with Applications to DNA Dynamics
This work is about time series of functional data (functional time series), and consists of three main parts. In the first part (Chapter 2), we develop a doubly spectral decomposition for functional time series that generalizes the Karhunen–Loève expansion ...
EPFL2014A generalization of the Wiener rational basis functions on infinite intervals, Part II - Numerical investigation
In Part I we introduced the generalized Wiener rational basis functions, and here in Part II we continue our investigation with numerical experiments. Wiener's generalized basis can utilize the fast Fourier transform for integer values of the decay paramet ...
ELSEVIER SCIENCE BV2013Signal Processing in Space and Time
Francisco Pereira Correia Pinto
Sound waves propagate through space and time by transference of energy between the particles in the medium, which vibrate according to the oscillation patterns of the waves. These vibrations can be captured by a microphone and translated into a digital sig ...
EPFL2010Turbulence in basic toroidal plasmas
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