AUTHOR=Potts Daniel , Tasche Manfred , Volkmer Toni TITLE=Efficient Spectral Estimation by MUSIC and ESPRIT with Application to Sparse FFT JOURNAL=Frontiers in Applied Mathematics and Statistics VOLUME=2 YEAR=2016 URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2016.00001 DOI=10.3389/fams.2016.00001 ISSN=2297-4687 ABSTRACT=

In spectral estimation, one has to determine all parameters of an exponential sum for finitely many (noisy) sampled data of this exponential sum. Frequently used methods for spectral estimation are MUSIC (MUltiple SIgnal Classification) and ESPRIT (Estimation of Signal Parameters via Rotational Invariance Technique). For a trigonometric polynomial of large sparsity, we present a new sparse fast Fourier transform by shifted sampling and using MUSIC resp. ESPRIT, where the ESPRIT based method has lower computational cost. Later this technique is extended to a new reconstruction of a multivariate trigonometric polynomial of large sparsity for given (noisy) values sampled on a reconstructing rank-1 lattice. Numerical experiments illustrate the high performance of these procedures.