# Multidimensional ESPRIT for Damped and Undamped Signals: Algorithm, Computations and Perturbation Analysis

1 GIPSA-CICS - CICS
GIPSA-DIS - Département Images et Signal
Abstract : In this paper we present and analyze the performance of multidimensional ESPRIT ($N$-D ESPRIT) method for estimating parameters of $N$-D superimposed damped and/or undamped exponentials. $N$-D ESPRIT algorithm is based on low-rank decomposition of multilevel Hankel matrices formed by the $N$-D data. In order to reduce the computational complexity for large signals, we propose a fast $N$-D ESPRIT using truncated singular value decomposition (SVD). Then, through a first-order perturbation analysis, we derive simple expressions of the variance of the estimates in $N$-D multiple-tones case. These expressions do not involve the factors of the SVD. We also derive closed-form expressions of the variances of the complex modes, frequencies and damping factors estimates in the $N$-D single-tone case. Computer results are presented to sho
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Type de document :
Pré-publication, Document de travail
Accepted version. 2017

https://hal.archives-ouvertes.fr/hal-01360438
Contributeur : Konstantin Usevich <>
Soumis le : mercredi 7 juin 2017 - 11:52:19
Dernière modification le : jeudi 22 juin 2017 - 14:38:22

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TSPperturbations.pdf
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### Identifiants

• HAL Id : hal-01360438, version 3

### Citation

Souleymen Sahnoun, Konstantin Usevich, Pierre Comon. Multidimensional ESPRIT for Damped and Undamped Signals: Algorithm, Computations and Perturbation Analysis. Accepted version. 2017. <hal-01360438v3>

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