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Titlebook: Statistical Signal Processing; Modelling and Estima Thierry Chonavel Textbook 2002 Springer-Verlag London 2002 Estimation.Filtering.Fourier

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Introduction,ry processes, and their filtering. Some digressions from this theme are aimed at pointing out the existence of techniques that generalise the methods only involving second order statistics, that is, those that only rely on the mean and autocovariance functions of processes. Indeed, it is often neces
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Non-linear Transforms of Processes,tained in the context of filtering. In fact, studying these relations must generally be done case by case. Here, we present some simple examples of memoryless non-linear transforms that we encounter commonly in the fields of electronics and telecommunications.
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Particular Filtering Techniques,ted to that of .., or to that of .. = . {..,.....}, we may opt to evaluate .. by X./.., or .... The resolution of these problems is known as . and . respectively. We next indicate how Kaiman’s recursive filtering can be generalised to computing recursively the distribution of .. conditional to {Y.,.
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Non-parametric Spectral Estimation,ce coefficients are not known exactly but are only estimated. Here, we address the problem of non-parametric estimation of these coefficients, hence that of non-parametric spectral estimation by means of the periodogram estimator.
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Parametric Spectral Estimation,y a small number of autocovariance coefficients of the process being studied are available from the observation. In such situations, parametric spectral estimation techniques are often preferred, and in particular techniques involving rational spectra models.
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Bayesian Methods and Simulation Techniques,or this, we use a Bayesian approach, which allows possible . information about the desired parameters to be incorporated. In order to be able to perform the numerical computation of the estimators, we use Monte Carlo techniques to solve integration and maximisation problems that appear in Bayesian e
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