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Concept

Filtre adaptatif

Un filtre adaptatif est un système avec un filtre linéaire dont la fonction de transfert est contrôlée par des paramètres variables et un moyen d'ajuster ces paramètres selon un algorithme d'optimisation. En raison de la complexité des algorithmes d'optimisation, presque tous les filtres adaptatifs sont des filtres numériques. Les filtres adaptatifs sont nécessaires pour certaines applications parce que certains paramètres du traitement souhaité (par exemple, l'emplacement des surfaces réfléchissantes dans un espace réverbérant) ne sont pas connus à l'avance ou changent. Le filtre adaptatif en boucle fermée utilise une rétroaction sous la forme d'un signal d'erreur pour affiner sa fonction de transfert. De manière générale, le processus adaptatif en boucle fermée implique l'utilisation d'une fonction objectif, qui est un critère de performance optimale du filtre, pour alimenter un algorithme, qui détermine comment modifier la fonction de transfert du filtre pour minimiser le coût à l

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Adaptive frequency tracking and application to biomedical signals

Yann Prudat

The main information of a signal resides in its frequency, its amplitude (or its power) and in their temporal evolution. Thus, a great number of methods for instantaneous frequency estimation have been proposed in the literature. Most of these algorithms use an adaptive filter-based (notch or bandpass filter) structure. In many applications, the information of interest is present in more than one signal. However, to our knowledge no algorithm able to track the frequency on several signals has been presented in the literature. Usually, frequency components are estimated and extracted on each signal independently. Artifacts or noise relative to a specific signal can thus disturb the frequency estimation process. Moreover, low amplitude components present in every signal (but non dominant) will not be estimated. The objective in the first part of this thesis is to develop different methods able to extend existing frequency tracking algorithm in order to improve the quality of the estimate, in terms of estimation variance and robustness with respect to noise. The proposed methods can be applied to algorithms using adaptive filters for the frequency estimation. For the multi-signal frequency tracking extension, these methods use the redundancy of information present in the signals under study. A first approach uses a unique filter for every signal. A set of weights is computed, depending on a measure of the estimate quality, and makes it possible to balance the influence of each signal on the tracking filter update. The second approach consists in using a different adaptive filter for each signal. A set of constraints links the central frequencies of each filter so that they are as similar as possible. Both methods yield frequency estimates more robust with respect to noise and more stable, without any decrease in estimation accuracy. For the harmonic frequency tracking, we propose a method using the information present in the harmonic component to improve the estimate of the fundamental frequency. The proposed methods also permit to extract the signal components corresponding to the estimated frequencies. These components are very useful for subsequent study. In the second part of this thesis, the algorithms developed in the first part are applied to biomedical signals. Two different applications are studied in this work : electrocardiograms and electroencephalograms. Firstly, a frequency tracking algorithm as well as its multi-signal extension are used to predict the success of electrical cardioversion attempts in patients suffering from atrial fibrillation. The instantaneous frequency is estimated using the algorithms and the corresponding signal component is extracted from electrocardiograms recorded prior to the attempt. With a few parameters computed on the estimated frequency and the corresponding signal component, we were able to predict the result of the cardioversion attempt on our database comprising 18 patients with a success rate of 94% for both algorithms. We think that this result can be very useful for helping the clinician to choose the appropriate therapy for atrial fibrillation management. The developed algorithms are also used to track the oscillatory components present in electroencephalograms. The performance of the basic algorithm is illustrated using single-trial electroencephalogram signals from a visual evoked potential experiment. The algorithm is used to track the gamma component (30-50 Hz). It is able to successfully track the spectral component in spite of the fact that large amplitude variations are present in the signal. A complex version of the multi-signal extension is also used to have an algorithm able to track multiple frequency components on multiple signals. The performance of this algorithm is also illustrated with single-trial electroencephalogram signals. It was shown to be able to correctly track up to four frequency components simultaneously. The quality of the estimation is improved using multiple lead signals.

EPFL2009

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Adaptive tracking of EEG oscillations

Cédric Duchene, Yann Prudat, Laurent Renaud Uldry, Jérôme Sébastien Van Zaen, Jean-Marc Vesin

Neuronal oscillations are an important aspect of EEG recordings. These oscillations are supposed to be involved in several cognitive mechanisms. For instance, oscillatory activity is considered a key component for the top-down control of perception. However, measuring this activity and its influence requires precise extraction of frequency components. This processing is not straightforward. Particularly, difficulties with extracting oscillations arise due to their time-varying characteristics. Moreover, when phase information is needed, it is of the utmost importance to extract narrow-band signals. This paper presents a novel method using adaptive filters for tracking and extracting these time-varying oscillations. This scheme is designed to maximize the oscillatory behavior at the output of the adaptive filter. It is then capable of tracking an oscillation and describing its temporal evolution even during low amplitude time segments. Moreover, this method can be extended in order to track several oscillations simultaneously and to use multiple signals. These two extensions are particularly relevant in the framework of EEG data processing, where oscillations are active at the same time in different frequency bands and signals are recorded with multiple sensors. The presented tracking scheme is first tested with synthetic signals in order to highlight its capabilities. Then it is applied to data recorded during a visual shape discrimination experiment for assessing its usefulness during EEG processing and in detecting functionally relevant changes. This method is an interesting additional processing step for providing alternative information compared to classical time-frequency analyses and for improving the detection and analysis of cross-frequency couplings.

2010

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Adaptive Filtering Methods for Identifying Cross-Frequency Couplings in Human EEG

Jérôme Sébastien Van Zaen, Jean-Marc Vesin

Oscillations have been increasingly recognized as a core property of neural responses that contribute to spontaneous, induced, and evoked activities within and between individual neurons and neural ensembles. They are considered as a prominent mechanism for information processing within and communication between brain areas. More recently, it has been proposed that interactions between periodic components at different frequencies, known as cross-frequency couplings, may support the integration of neuronal oscillations at different temporal and spatial scales. The present study details methods based on an adaptive frequency tracking approach that improve the quantification and statistical analysis of oscillatory components and cross-frequency couplings. This approach allows for time-varying instantaneous frequency, which is particularly important when measuring phase interactions between components. We compared this adaptive approach to traditional band-pass filters in their measurement of phase-amplitude and phase-phase cross-frequency couplings. Evaluations were performed with synthetic signals and EEG data recorded from healthy humans performing an illusory contour discrimination task. First, the synthetic signals in conjunction with Monte Carlo simulations highlighted two desirable features of the proposed algorithm vs. classical filter-bank approaches: resilience to broad-band noise and oscillatory interference. Second, the analyses with real EEG signals revealed statistically more robust effects (i.e. improved sensitivity) when using an adaptive frequency tracking framework, particularly when identifying phase-amplitude couplings. This was further confirmed after generating surrogate signals from the real EEG data. Adaptive frequency tracking appears to improve the measurements of cross-frequency couplings through precise extraction of neuronal oscillations.

Public Library of Science2013

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Linear prediction

Linear prediction is a mathematical operation where future values of a discrete-time signal are estimated as a linear function of previous samples. In digital signal processing, linear prediction is

Minimum mean square error

In statistics and signal processing, a minimum mean square error (MMSE) estimator is an estimation method which minimizes the mean square error (MSE), which is a common measure of estimator quality,

Kernel adaptive filter

In signal processing, a kernel adaptive filter is a type of nonlinear adaptive filter. An adaptive filter is a filter that adapts its transfer function to changes in signal properties over time by mi

EE-512: Applied biomedical signal processing

The goal of this course is twofold: (1) to introduce physiological basis, signal acquisition solutions (sensors) and state-of-the-art signal processing techniques, and (2) to propose concrete examples of applications for vital sign monitoring and diagnosis purposes.

COM-500: Statistical signal and data processing through applications

Building up on the basic concepts of sampling, filtering and Fourier transforms, we address stochastic modeling, spectral analysis, estimation and prediction, classification, and adaptive filtering, with an application oriented approach and hands-on numerical exercises.

MICRO-311(b): Signals and systems II (for SV)

Ce cours aborde la théorie des systèmes linéaires discrets invariants par décalage (LID). Leurs propriétés et caractéristiques fondamentales y sont discutées, ainsi que les outils fondamentaux permettant de les étudier (transformée de Fourier et transformée en Z).