3 papers
math.NA2021
From ESPRIT to ESPIRA: Estimation of Signal Parameters by Iterative Rational Approximation
Nadiia Derevianko, Gerlind Plonka, Markus Petz
We introduce a new method for Estimation of Signal Parameters based on Iterative Rational Approximation (ESPIRA) for sparse exponential sums. Our algorithm uses the AAA algorithm f…
math.NA2020
Exact Reconstruction of Sparse Non-Harmonic Signals from Fourier Coefficients
Markus Petz, Gerlind Plonka, Nadiia Derevianko
In this paper, we derive a new reconstruction method for real non-harmonic Fourier sums, i.e., real signals which can be represented as sparse exponential sums of the form $f(t) =…
math.NA2020
Optimal Rank-1 Hankel Approximation of Matrices: Frobenius Norm, Spectral Norm, and Cadzow's Algorithm
Hanna Knirsch, Markus Petz, Gerlind Plonka
We characterize optimal rank-1 matrix approximations with Hankel or Toeplitz structure with regard to two different norms, the Frobenius norm and the spectral norm, in a new way. M…