Exact reconstruction of sparse non-harmonic signals from their Fourier coefficients

DOI10.1007/s43670-021-00007-1zbMath1496.94019arXiv2011.13346OpenAlexW3162601490MaRDI QIDQ2059803

Nadiia Derevianko, Markus Petz, Gerlind Plonka-Hoch

Publication date: 14 December 2021

Published in: Sampling Theory, Signal Processing, and Data Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.13346

zbMATH Keywords

Fourier coefficientsrational approximationbarycentric representationAAA algorithmnon-harmonic Fourier sumsreconstruction of sparse non-periodic signalssparse exponential sums

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Approximation by rational functions (41A20) General harmonic expansions, frames (42C15) Algorithms for approximation of functions (65D15) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)

Related Items (5)

Exact reconstruction of extended exponential sums using rational approximation of their Fourier coefficients ⋮ Super-resolution of generalized spikes and spectra of confluent Vandermonde matrices ⋮ ESPRIT versus ESPIRA for reconstruction of short cosine sums and its application ⋮ Exact reconstruction of sparse non-harmonic signals from their Fourier coefficients ⋮ Data-Driven Algorithms for Signal Processing with Trigonometric Rational Functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Data-driven atomic decomposition via frequency extraction of intrinsic mode functions
• Parameter estimation for nonincreasing exponential sums by Prony-like methods
• On the problem of parameter estimation in exponential sums
• Synchrosqueezed wavelet transforms: an empirical mode decomposition-like tool
• Parameter estimation for exponential sums by approximate prony method
• Numerical Fourier analysis
• Optimal approximation with exponential sums by a maximum likelihood modification of Prony's method
• Computation of adaptive Fourier series by sparse approximation of exponential sums
• Exact reconstruction of sparse non-harmonic signals from their Fourier coefficients
• How to get high resolution results from sparse and coarsely sampled data
• Adaptive Fourier series---a variation of greedy algorithm
• Barycentric rational interpolation with no poles and high rates of approximation
• On approximation of functions by exponential sums
• Data-Driven Parametrized Model Reduction in the Loewner Framework
• Nonlinear Approximation by Sums of Exponentials and Translates
• Some New Aspects of Rational Interpolation
• The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
• Sampling Piecewise Sinusoidal Signals With Finite Rate of Innovation Methods
• Rational Minimax Approximation via Adaptive Barycentric Representations
• FRESH—FRI-Based Single-Image Super-Resolution Algorithm
• Convergence of Linear Barycentric Rational Interpolation for Analytic Functions
• Prony methods for recovery of structured functions
• Sampling signals with finite rate of innovation
• Reconstruction of stationary and non-stationary signals by the generalized Prony method
• The AAA Algorithm for Rational Approximation

This page was built for publication: Exact reconstruction of sparse non-harmonic signals from their Fourier coefficients