Efficient spectral estimation by MUSIC and ESPRIT with application to sparse FFT

Abstract

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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 viaRotational Invariance Technique).For a trigonometric polynomial of large sparsity, we present a new sparse fast Fourier transform byshifted 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 thehigh performance of these procedures.

Keywords

• Music
• frequency analysis
• sparsity
• spectral estimation
• Parameter identification
• exponential sum