Efficient Spectral Estimation by MUSIC and ESPRIT with Application to Sparse FFT

Frontiers in Applied Mathematics and Statistics

Potts, Daniel¹  Volkmer, Toni²  Tasche, Manfred³ 

[1] Faculty of Mathematics, Technische UniversitäInstitute of Mathematics, University of Rostock, Rostock, Germany;t Chemnitz, Chemnitz, Germany

关键词: spectral estimation;    ESPRIT;    Music;    exponential sum;    sparsity;    frequency analysis;    Parameter identification;    Rectangular Hankel matrix;    sparse fast Fourier transform;    sparse trigonometric polynomial.;   

DOI  :  10.3389/fams.2016.00001

学科分类：数学（综合）

来源: Frontiers

【 摘 要 】

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.

【 授权许可】

CC BY