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Dan S Henningson - One of the best experts on this subject based on the ideXlab platform.
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Spectral Analysis of nonlinear flows
Journal of Fluid Mechanics, 2009Co-Authors: Clarence W Rowley, Igor Mezic, Shervin Bagheri, Philipp Schlatter, Dan S HenningsonAbstract:We present a technique for describing the global behaviour of complex nonlinear flows by decomposing the flow into modes determined from Spectral Analysis of the Koopman operator, an infinite-dimen ...
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Spectral Analysis of nonlinear flows
Bulletin of the American Physical Society, 2009Co-Authors: Clarence W Rowley, Igor Mezic, Shervin Bagheri, Philipp Schlatter, Dan S HenningsonAbstract:We present a technique for describing the global behaviour of complex nonlinear flows by decomposing the flow into modes determined from Spectral Analysis of the Koopman operator, an infinite-dimensional linear operator associated with the full nonlinear system. These modes, referred to as Koopman modes, are associated with a particular observable, and may be determined directly from data (either numerical or experimental) using a variant of a standard Arnoldi method. They have an associated temporal frequency and growth rate and may be viewed as a nonlinear generalization of global eigenmodes of a linearized system. They provide an alternative to proper orthogonal decomposition, and in the case of periodic data the Koopman modes reduce to a discrete temporal Fourier transform. The Arnoldi method used for computations is identical to the dynamic mode decomposition recently proposed by Schmid & Sesterhenn (Sixty-First Annual Meeting of the APS Division of Fluid Dynamics, 2008), so dynamic mode decomposition can be thought of as an algorithm for finding Koopman modes. We illustrate the method on an example of a jet in crossflow, and show that the method captures the dominant frequencies and elucidates the associated spatial structures.
C H L Peters - One of the best experts on this subject based on the ideXlab platform.
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Spectral Analysis of fetal heart rate variability for fetal surveillance review of the literature
Acta Obstetricia et Gynecologica Scandinavica, 2008Co-Authors: J O E H Van Laar, Martina Porath, C H L PetersAbstract:Background. Cardiotocography has a poor diagnostic value in detecting fetal acidosis. Spectral Analysis of fetal heart rate variability can be used to monitor the fetal autonomic nervous system. Objective. To determine the value of Spectral Analysis for fetal surveillance. Methods. A systematic search was performed in the electronic databases CENTRAL (the Cochrane Library; 2007, Issue 3), PUBMED and EMBASE up to May 2007. Articles that described Spectral Analysis of human fetal heart rate variability and compared the energy in Spectral bands with blood-gas values obtained by funipuncture or from the umbilical cord immediately postpartum were included. Results. Six studies met the inclusion criteria. The included studies were heterogeneous, various methods of Spectral Analysis and different frequency bands were used and the outcome measures varied. Five out of six studies showed a decrease in Spectral energy in the low frequency (LF) band in case of fetal distress. An extremely low LF power had a sensitivity of 97.5% and a specificity of 86.1% to detect fetal distress. Conclusions. Spectral Analysis could be a promising method for fetal surveillance. Larger prospective studies are needed to determine the exact diagnostic value of Spectral Analysis. For further research, standardisation of Spectral Analysis is recommended. Studies should focus on real time monitoring.
Petre Stoica - One of the best experts on this subject based on the ideXlab platform.
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Spectral Analysis of nonuniformly sampled data a review
Digital Signal Processing, 2010Co-Authors: Prabhu Babu, Petre StoicaAbstract:In this paper, we present a comprehensive review of methods for Spectral Analysis of nonuniformly sampled data. For a given finite set of nonuniformly sampled data, a reasonable way to choose the Nyquist frequency and the resampling time are discussed. The various existing methods for Spectral Analysis of nonuniform data are grouped and described under four broad categories: methods based on least squares; methods based on interpolation techniques; methods based on slotted resampling; methods based on continuous time models. The performance of the methods under each category is evaluated on simulated data sets. The methods are then classified according to their capabilities to handle different types of spectrum, signal models and sampling patterns. Finally the performance of the different methods is evaluated on two real life nonuniform data sets. Apart from the Spectral Analysis methods, methods for exact signal reconstruction from nonuniform data are also reviewed.
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Spectral Analysis of nonuniformly sampled data a new approach versus the periodogram
IEEE Transactions on Signal Processing, 2009Co-Authors: Petre StoicaAbstract:We begin by revisiting the periodogram to explain why arguably the plain least-squares periodogram (LSP) is preferable to the ldquoclassicalrdquo Fourier periodogram, from a data-fitting viewpoint, as well as to the frequently-used form of LSP due to Lomb and Scargle, from a computational standpoint. Then we go on to introduce a new enhanced method for Spectral Analysis of nonuniformly sampled data sequences. The new method can be interpreted as an iteratively weighted LSP that makes use of a data-dependent weighting matrix built from the most recent Spectral estimate. Because this method is derived for the case of real-valued data (which is typically more complicated to deal with in Spectral Analysis than the complex-valued data case), it is iterative and it makes use of an adaptive (i.e., data-dependent) weighting, we refer to it as the real-valued iterative adaptive approach (RIAA). LSP and RIAA are nonparametric methods that can be used for the Spectral Analysis of general data sequences with both continuous and discrete spectra. However, they are most suitable for data sequences with discrete spectra (i.e., sinusoidal data), which is the case we emphasize in this paper.
Antonio Artesrodriguez - One of the best experts on this subject based on the ideXlab platform.
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a robust support vector algorithm for nonparametric Spectral Analysis
IEEE Signal Processing Letters, 2003Co-Authors: J L Rojoalvarez, Manel Martinezramon, Anibal R Figueirasvidal, A Garciaarmada, Antonio ArtesrodriguezAbstract:We present a new approach to nonparametric Spectral estimation on the basis of the support vector method (SVM). A reweighted least squares error formulation avoids the computational limitations of quadratic programming. The application to a synthetic example and to a digital communication problem shows the robustness of the SVM Spectral Analysis algorithm.
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support vector robust algorithms for non parametric Spectral Analysis
Lecture Notes in Computer Science, 2002Co-Authors: J L Rojoalvarez, Manel Martinezramon, Anibal R Figueirasvidal, Arcadi Garciaalberola, Mariano Valdes, Antonio ArtesrodriguezAbstract:A new approach to the non-parametric Spectral estimation on the basis of the Support Vector (SV) framework is presented. Two algorithms are derived for both uniform and non-uniform sampling. The relationship between the SV free parameters and the underlying process statistics is discussed. The application in two real data examples, the sunspot numbers and the Heart Rate Variability, shows the higher resolution and robustness in SV Spectral Analysis algorithms.
Clarence W Rowley - One of the best experts on this subject based on the ideXlab platform.
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Spectral Analysis of nonlinear flows
Journal of Fluid Mechanics, 2009Co-Authors: Clarence W Rowley, Igor Mezic, Shervin Bagheri, Philipp Schlatter, Dan S HenningsonAbstract:We present a technique for describing the global behaviour of complex nonlinear flows by decomposing the flow into modes determined from Spectral Analysis of the Koopman operator, an infinite-dimen ...
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Spectral Analysis of nonlinear flows
Bulletin of the American Physical Society, 2009Co-Authors: Clarence W Rowley, Igor Mezic, Shervin Bagheri, Philipp Schlatter, Dan S HenningsonAbstract:We present a technique for describing the global behaviour of complex nonlinear flows by decomposing the flow into modes determined from Spectral Analysis of the Koopman operator, an infinite-dimensional linear operator associated with the full nonlinear system. These modes, referred to as Koopman modes, are associated with a particular observable, and may be determined directly from data (either numerical or experimental) using a variant of a standard Arnoldi method. They have an associated temporal frequency and growth rate and may be viewed as a nonlinear generalization of global eigenmodes of a linearized system. They provide an alternative to proper orthogonal decomposition, and in the case of periodic data the Koopman modes reduce to a discrete temporal Fourier transform. The Arnoldi method used for computations is identical to the dynamic mode decomposition recently proposed by Schmid & Sesterhenn (Sixty-First Annual Meeting of the APS Division of Fluid Dynamics, 2008), so dynamic mode decomposition can be thought of as an algorithm for finding Koopman modes. We illustrate the method on an example of a jet in crossflow, and show that the method captures the dominant frequencies and elucidates the associated spatial structures.