Questioning the signal to noise ratioin digital communications

Fliesś, Michel

doi:10.46298/arima.1908

Cited by 9 publications

(1 citation statement)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These approaches are based on module theory, differential algebra, and operational calculus. They permit the annihilation of structured perturbations and exhibit good robustness properties with respect to corrupting disturbances, without the need to know their statistical properties, as discussed in Fliess (2006Fliess ( , 2008.…”

Section: Bibliographical and Historical Commentsmentioning

confidence: 99%

Contributions to numerical differentiation using orthogonal polynomials and its application to fault detection and parameter identification

Othmane

2023

At - Automatisierungstechnik

View full text Add to dashboard Cite

show abstract

Section: Bibliographical and Historical Commentsmentioning

confidence: 99%

Contributions to numerical differentiation using orthogonal polynomials and its application to fault detection and parameter identification

Othmane

2023

At - Automatisierungstechnik

View full text Add to dashboard Cite

show abstract

Convergence Rate of the Causal Jacobi Derivative Estimator

Liu

Gibaru

Perruquetti

2012

Curves and Surfaces

View full text Add to dashboard Cite

Abstract. Numerical causal derivative estimators from noisy data are essential for real time applications especially for control applications or fluid simulation so as to address the new paradigms in solid modeling and video compression. By using an analytical point of view due to Lanczos [9] to this causal case, we revisit n th order derivative estimators originally introduced within an algebraic framework by Mboup, Fliess and Join in [14,15]. Thanks to a given noise level δ and a well-suitable integration length window, we show that the derivative estimator error can be O(δ q+1 n+1+q ) where q is the order of truncation of the Jacobi polynomial series expansion used. This so obtained bound helps us to choose the values of our parameter estimators. We show the efficiency of our method on some examples.

show abstract

Error analysis of Jacobi derivative estimators for noisy signals

2011

View full text Add to dashboard Cite

International audienceRecent algebraic parametric estimation techniques (see \cite{garnier,mfhsr}) led to point-wise derivative estimates by using only the iterated integral of a noisy observation signal (see \cite{num0,num}). In this paper, we extend such differentiation methods by providing a larger choice of parameters in these integrals: they can be reals. For this, %as in \cite{num0,num}, the extension is done via a truncated Jacobi orthogonal series expansion. Then, the noise error contribution of these derivative estimations is investigated: after proving the existence of such integral with a stochastic process noise, their statistical properties (mean value, variance and covariance) are analyzed. In particular, the following important results are obtained: \begin{description} \item[$a)$] the bias error term, due to the truncation, can be reduced by tuning the parameters, \item[$b)$] such estimators can cope with a large class of noises for which the mean and covariance are polynomials in time (with degree smaller than the order of derivative to be estimated), \item[$c)$] the variance of the noise error is shown to be smaller in the case of negative real parameters than it was in \cite{num0,num} for integer values. \end{description} Consequently, these derivative estimations can be improved by tuning the parameters according to the here obtained knowledge of the parameters' influence on the error bounds

show abstract

Questioning the signal to noise ratioin digital communications

Cited by 9 publications

References 24 publications

Contributions to numerical differentiation using orthogonal polynomials and its application to fault detection and parameter identification

Contributions to numerical differentiation using orthogonal polynomials and its application to fault detection and parameter identification

Convergence Rate of the Causal Jacobi Derivative Estimator

Error analysis of Jacobi derivative estimators for noisy signals

Contact Info

Product

Resources

About