Perturbation Analysis of Subspace-Based Methods in Estimating a Damped Complex Exponential

Djermoune, El‐Hadi; Tomczak, Marc

doi:10.1109/tsp.2009.2024030

Cited by 13 publications

(17 citation statements)

References 19 publications

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“…[32]. We are mostly interested in the methods that can be applied to any time series of finite rank given in the form (9).…”

Section: Brief Review Of Other Subspace-based Methodsmentioning

confidence: 99%

“…As for damped complex exponentials, the result is that the optimal window length lies between N/3 and N/2 and approaches N/2 as the damping factor increases. It is shown in [9] that for s n = exp((α + iβ)n), i = √ −1, the first-order variances of the ESPRIT estimates of α and β are equal. Therefore, the optimal window lengths are the same for estimators of the damping factor α and of the frequency β .…”

Section: Dependence On the Window Lengthmentioning

confidence: 99%

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On the choice of parameters in singular spectrum analysis and related subspace-based methods

Golyandina

2010

Statistics and Its Interface

138

101

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In the present paper we investigate methods related to both the Singular Spectrum Analysis (SSA) and subspace-based methods in signal processing. We describe common and specific features of these methods and consider different kinds of problems solved by them such as signal reconstruction, forecasting and parameter estimation. General recommendations on the choice of parameters to obtain minimal errors are provided. We demonstrate that the optimal choice depends on the particular problem. For the basic model 'signal + residual' we show that the error behavior depends on the type of residuals, deterministic or stochastic, and whether the noise is white or red. The structure of errors and the convergence rate are also discussed. The analysis is based on known theoretical results and extensive computer simulations.

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“…[32]. We are mostly interested in the methods that can be applied to any time series of finite rank given in the form (9).…”

Section: Brief Review Of Other Subspace-based Methodsmentioning

confidence: 99%

Section: Dependence On the Window Lengthmentioning

confidence: 99%

On the choice of parameters in singular spectrum analysis and related subspace-based methods

Golyandina

2010

Statistics and Its Interface

138

101

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“…The reader is referred to [39,58] for more details on this topic. Also, a theoretical study of the estimation accuracy of eigenstructure-based model estimators has shown that an optimal prediction order is existing for damped complex exponential signals [59]. All estimation free-parameters are included in vector p in the algorithms presented in Tables 1, 2.…”

Section: The Free Parametersmentioning

confidence: 99%

NMR Data Analysis: A Time-Domain Parametric Approach Using Adaptive Subband Decomposition

Djermoune

Tomczak

Brie

2013

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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and available online here Cet article fait partie du dossier thématique ci-dessous publié dans la revue OGST, Vol. 69, n°2, et téléchargeable ici Résumé -Analyse de données RMN : une approche paramétrique basée sur une décomposi-tion en sous-bandes adaptative -Dans ce papier, nous proposons une méthode rapide d'analyse de signaux de spectroscopie de Résonance Magnétique Nucléaire (RMN), dans le cas Lorentzien, fondée sur une décomposition adaptative en sous-bandes. Cette dernière est obtenue par une succession d'étages de filtrage/décimation aboutissant à un arbre de décomposition. À chaque noeud de l'arbre, les paramètres du signal correspondant à la sous-bande sont estimés par une méthode haute-résolution. Puis l'erreur d'estimation est utilisée dans un test d'arrêt qui permet de décider si la décomposition doit être poursuivie ou non dans cette branche. Ainsi, cette approche permet la sélection automatique du niveau de décimation ce qui conduit la décomposition à s'adapter au contenu fréquentiel du signal. De plus, la méthode entraîne une réduction du temps de calcul et facilite le choix des paramètres libres comparativement à une analyse globale du signal. Son efficacité est illustrée au travers d'exemples de signaux RMN 13 C 1-D et 2-D.

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“…Introduce the H-matrix G B,T with the elements g ij as follows: The computation complexity of the calculation of the Hmatrix is determined by the complexity of the SVDs for series F i,i+B and the complexity of calculation of all heterogeneity indices g ij as defined by the equation (8).…”

Section: Detection Of Structural Changesmentioning

confidence: 99%

“…This almost prevents the use of the optimum window lengths even for time series of moderate length (say, few thousand). The problem is much more severe for 2D-SSA [15] or subspace-based methods [2,8,13], where a window size is typically large.…”

Section: Introductionmentioning

confidence: 99%

Computation- and space-efficient implementation of SSA

Korobeynikov

2010

Statistics and Its Interface

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The computational complexity of different steps of the Basic SSA is discussed. It is shown that the use of the general-purpose "blackbox" routines which can be found in packages like LAPACK leads to a huge waste of time since the Hankel structure of the trajectory matrix is not taken into account.We outline several state-of-the-art algorithms including the Lanczos-based truncated Singular Value Decomposition (SVD) which can be modified to exploit the structure of the trajectory matrix. The key components here are Hankel matrix-vector multiplication and the hankelization operator. We show that both operations can be computed efficiently by means of the Fast Fourier Transform.The use of these methods yields the reduction of the worst-case computational complexity from O(N 3 ) to O(kN log N ), where N is the series length and k is the number of desired eigentriples.

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Perturbation Analysis of Subspace-Based Methods in Estimating a Damped Complex Exponential

Cited by 13 publications

References 19 publications

On the choice of parameters in singular spectrum analysis and related subspace-based methods

On the choice of parameters in singular spectrum analysis and related subspace-based methods

NMR Data Analysis: A Time-Domain Parametric Approach Using Adaptive Subband Decomposition

Computation- and space-efficient implementation of SSA

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