Mathematical properties of a semi-classical signal analysis method: Noisy signal case

Recently, a new signal analysis method based on a semi-classical approach has been proposed [1]. The main idea in this method is to interpret a signal as a potential of a Schrodinger operator and then to use the discrete spectrum of this operator to analyze the signal. In this paper, we are interested in a mathematical analysis of this method in discrete case considering noisy signals.

[1]  Olivier Gibaru,et al.  Error analysis for a class of numerical differentiator: application to state observation , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[2]  Olivier Gibaru,et al.  Error analysis of Jacobi derivative estimators for noisy signals , 2011, Numerical Algorithms.

[3]  Michel Fliess,et al.  Analyse non standard du bruit , 2006, ArXiv.

[4]  D. J. Kaup,et al.  Solitons as particles, oscillators, and in slowly changing media: a singular perturbation theory , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[5]  Y. Papelier,et al.  Arterial blood pressure analysis based on scattering transform I , 2007, 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[6]  Olivier Gibaru,et al.  Convergence Rate of the Causal Jacobi Derivative Estimator , 2010, Curves and Surfaces.

[7]  L. Trefethen.  Spectral Methods in MATLAB , 2000 .

[8]  Mouez Dimassi,et al.  Spectral asymptotics in the semi-classical limit , 1999 .

[9]  T. Laleg‐Kirati,et al.  Validation of a Semi-Classical Signal Analysis Method for Stroke Volume Variation Assessment: A Comparison with the PiCCO Technique , 2010, Annals of Biomedical Engineering.

[10]  M. Dimassi,et al.  Spectral Asymptotics in the Semi-Classical Limit: Frontmatter , 1999 .

[11]  Farid Bakir,et al.  A Semi-Classical Signal Analysis Method for the Analysis of Turbomachinery Flow Unsteadiness , 2011 .

[12]  Function Spaces Associated with Schrödinger Operators: The Pöschl-Teller Potential , 2005, math/0509642.

[13]  Dayan Liu,et al.  An error analysis in the algebraic estimation of a noisy sinusoidal signal , 2008, 2008 16th Mediterranean Conference on Control and Automation.

[14]  C. Medigue,et al.  Arterial blood pressure analysis based on scattering transform II , 2007, 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[15]  G. Stewart,et al.  Matrix Perturbation Theory , 1990 .

[16]  Taous-Meriem Laleg-Kirati,et al.  Semi-classical signal analysis , 2010, Math. Control. Signals Syst..

[17]  R. Sorrentino,et al.  Electronic Filter Simulation & Design , 2007 .