Codes and Expansions (CodEx) Seminar

Nadiia Derevianko (Universität Göttingen)
Estimation of Signal Parameters by Iterative Rational Approximation

We study a new algorithm for the recovery of complex exponential sums that are determined by a finite number of parameters. Our recovery algorithm is based on the observation that Fourier coefficients of exponential sums have a special rational structure. We use the AAA algorithm recently proposed by Nakatsukasa et al. (2018) to reconstruct this structure in a stable way. We require at least 2M+1 Fourier coefficients for the recovery of an exponential sum of order M. The Fourier coefficients can be also replaced by DFT coefficients which makes the algorithm more suitable for applications. Our method can be considered as a good alternative to the known Prony-type algorithms for the recovery of exponential sums. The connection to the known Matrix Pencil Method and ESPRIT method will be also presented during the talk.

The talk will be based on joint research with Markus Petz and Gerlind Plonka.