Publication
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% f