Daniel Potts, Manfred Tasche, Toni Volkmer: Efficient spectral estimation by MUSIC and ESPRIT with application to sparse FFT

Author(s):

Daniel Potts
Manfred Tasche
Toni Volkmer

Title:

Daniel Potts, Manfred Tasche, Toni Volkmer: Efficient spectral estimation by MUSIC and ESPRIT with application to sparse FFT

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 14, 2015

Mathematics Subject Classification:

    65T50 []
    42A16 []
    94A12 []

Abstract:

In the spectral estimation, one has to determine all parameters of an exponential sum, if only finitely many (noisy) sampled data of this exponential sum are given. 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 methods will be faster. Later this technique is extended to the reconstruction of multivariate trigonometric polynomials of large sparsity, if (noisy) sampled values on a reconstructing rank-1 lattice are given. Numerical experiments illustrate the high performance of this procedure.

Keywords:

Spectral estimation, ESPRIT, MUSIC, exponential sum, sparsity, frequency analysis, parameter identification, rectangular Hankel matrix, sparse fast Fourier transform, sparse trigonometric polynomial

Language:

English

Publication time:

08/2015