Reconstruction of Exponential Sums from Fourier Data via Rational Approximation

by Markus Petz
Doctoral thesis
Date of Examination:2022-06-30
Date of issue:2022-07-08
Advisor:Dr. Gerlind Plonka-Hoch
Referee:Dr. Gerlind Plonka-Hoch
Referee:Prof. Dr. Stefan Kunis
Persistent Address: http://dx.doi.org/10.53846/goediss-9339

 

 

Files in this item

Name:Dissertation_Petz.pdf
Size:1.79Mb
Format:PDF

The following license files are associated with this item:

Abstract

English

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
 
Statistik