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

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 ord...

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Vydané v:	IEEE transactions on signal processing Ročník 65; číslo 22; s. 5897 - 5910
Hlavní autori:	Sahnoun, Souleymen, Usevich, Konstantin, Comon, Pierre
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	IEEE 15.11.2017 Institute of Electrical and Electronics Engineers
Predmet:	2-D ESPRIT Algorithm design and analysis Computational complexity Computer Science Frequency estimation harmonic retrieval Manganese Matrix decomposition multilevel Hankel matrix perturbation analysis Perturbation methods Signal and Image Processing Signal processing algorithms Tensile stress truncated SVD multilevel Hankel matrix harmonic retrieval truncated SVD Frequency estimation perturbation analysis 2-D ESPRIT
ISSN:	1053-587X, 1941-0476
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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 show effectiveness of the fast version of N-D ESPRIT and verify theoretical expressions.
AbstractList	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 show effectiveness of the fast version of N-D ESPRIT and verify theoretical expressions.
Author	Comon, Pierre Sahnoun, Souleymen Usevich, Konstantin
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SubjectTerms	2-D ESPRIT Algorithm design and analysis Computational complexity Computer Science Frequency estimation harmonic retrieval Manganese Matrix decomposition multilevel Hankel matrix perturbation analysis Perturbation methods Signal and Image Processing Signal processing algorithms Tensile stress truncated SVD
Title	Multidimensional ESPRIT for Damped and Undamped Signals: Algorithm, Computations, and Perturbation Analysis
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