Reconstruction of Exponential Sums from Fourier Data via Rational Approximation
von Markus Petz
Datum der mündl. Prüfung:2022-06-30
Erschienen:2022-07-08
Betreuer:Dr. Gerlind Plonka-Hoch
Gutachter:Dr. Gerlind Plonka-Hoch
Gutachter:Prof. Dr. Stefan Kunis
Dateien
Name:Dissertation_Petz.pdf
Size:1.79Mb
Format:PDF
Zusammenfassung
Englisch
We develop the new ESPIRA Algorithm to reconstruct exponential sums from discrete sample values, using the discrete Fourier transform of the given sample vector. We exploit the structure of the DFT values of samples from an exponential sum, which can be modelled by special rational functions. Our algorithm provides an alternative to the well-known Prony and Prony-type methods. Numerical experiments show that for noisy data our algorithm outperforms these methods.
Keywords: Exponential Sums; Fourier Analysis; Rational Approximation; Prony's Method; Exponential Analysis; ESPIRA