From ESPRIT to ESPIRA: estimation of signal parameters by iterative rational approximation

Abstract We introduce a new method for Estimation of Signal Parameters based on Iterative Rational Approximation (ESPIRA) sparse exponential sums. Our algorithm uses the AAA rational approximation discrete Fourier transform given equidistant signal values. show that ESPIRA can be interpreted as matrix pencil (MPM) applied to Loewner matrices. These matrices are closely connected with Hankel usually employed recovery. Due construction via an adaptive selection index sets, MPM is stabilized. achieves similar recovery results exact data ESPRIT and MPM, but less computational effort. Moreover, strongly outperforms noisy by short