Jérôme Sébastien Van Zaen
Amplitude and frequency are the two primary features of one-dimensional signals, and thus both are widely utilized to analysis data in numerous fields. While amplitude can be examined directly, frequency requires more elaborate approaches, except in the simplest cases. Consequently, a large number of techniques have been proposed over the years to retrieve information about frequency. The most famous method is probably power spectral density estimation. However, this approach is limited to stationary signals since the temporal information is lost. Time-frequency approaches were developed to tackle the problem of frequency estimation in non-stationary data. Although they can estimate the power of a signal in a given time interval and in a given frequency band, these tools have two drawbacks that make them less valuable in certain situations. First, due to their interdependent time and frequency resolutions, improving the accuracy in one domain means decreasing it in the other one. Second, it is difficult to use this kind of approach to estimate the instantaneous frequency of a specific oscillatory component. A solution to these two limitations is provided by adaptive frequency tracking algorithms. Typically, these algorithms use a time-varying filter (a band-pass or notch filter in most cases) to extract an oscillation, and an adaptive mechanism to estimate its instantaneous frequency. The main objective of the first part of the present thesis is to develop such a scheme for adaptive frequency tracking, the single frequency tracker. This algorithm compares favorably with existing methods for frequency tracking in terms of bias, variance and convergence speed. The most distinguishing feature of this adaptive algorithm is that it maximizes the oscillatory behavior at its output. Furthermore, due to its specific time-varying band-pass filter, it does not introduce any distortion in the extracted component. This scheme is also extended to tackle certain situations, namely the presence of several oscillations in a single signal, the related issue of harmonic components, and the availability of more than one signal with the oscillation of interest. The first extension is aimed at tracking several components simultaneously. The basic idea is to use one tracker to estimate the instantaneous frequency of each oscillation. The second extension uses the additional information contained in several signals to achieve better overall performance. Specifically, it computes separately instantaneous frequency estimates for all available signals which are then combined with weights minimizing the estimation variance. The third extension, which is based on an idea similar to the first one and uses the same weighting procedure as the second one, takes into account the harmonic structure of a signal to improve the estimation performance. A non-causal iterative method for offline processing is also developed in order to enhance an initial frequency trajectory by using future information in addition to past information. Like the single frequency tracker, this method aims at maximizing the oscillatory behavior at the output. Any approach can be used to obtain the initial trajectory. In the second part of this dissertation, the schemes for adaptive frequency tracking developed in the first part are applied to electroencephalographic and electrcardiographic data. In a first study, the single frequency tracker is used to analyze interactions between neuronal oscillations in different frequency bands, known as cross-frequency couplings, during a visual evoked potential experiment with illusory contour stimuli. With this adaptive approach ensuring that meaningful phase information is extracted, the differences in coupling strength between stimuli with and without illusory contours are more clearly highlighted than with traditional methods based on predefined filter-banks. In addition, the adaptive scheme leads to the detection of differences in instantaneous frequency. In a second study, two organization measures are derived from the harmonic extension. They are based on the power repartition in the frequency domain for the first one and on the phase relation between harmonic components for the second one. These measures, computed from the surface electrocardiogram, are shown to help predicting the outcome of catheter ablation of persistent atrial fibrillation. The proposed adaptive frequency tracking schemes are also applied to signals recorded in the field of sport sciences in order to illustrate their potential uses. To summarize, the present thesis introduces several algorithms for adaptive frequency tracking. These algorithms are presented in full detail and they are then applied to practical situations. In particular, they are shown to improve the detection of coupling mechanisms in brain activity and to provide relevant organization measures for atrial fibrillation.
EPFL2012
