Electrophysiological signals such as the EEG, MEG, or LFPs have been extensively studied over the last decades, and elaborate signal processing algorithms have been developed for their analysis. Many of these methods are based on time-frequency decomposition to account for the signals’ spectral properties while maintaining their temporal dynamics. However, the data typically exhibit intra- and interindividual variability. Existing algorithms often do not take into account this variability, for instance by using fixed frequency bands. This shortcoming has inspired us to develop a new robust and flexible method for time-frequency analysis and signal feature extraction using the novel smooth natural Gaussian extension (snaGe) model. The model is nonlinear, and its parameters are interpretable. We propose an algorithm to derive initial parameters based on dynamic programming for nonlinear fitting and describe an iterative refinement scheme to robustly fit high-order models. We further present distance functions to be able to compare different instances of our model. The method’s functionality and robustness are demonstrated using simulated as well as real data. The snaGe model is a general tool allowing for a wide range of applications in biomedical data analysis. 1. Introduction Electrophysiological brain signals are widely studied to get insights into the inner function of the brain. The electro-encephalogram (EEG), as an example, has been analyzed for decades and is particularly popular because of its noninvasiveness, wide availability, relatively small cost and excellent temporal resolution which enables capturing the fast neural dynamics. Because it is known that electrophysiological brain signals exhibit important spectral characteristics, frequency transforms are often applied. However, since in general brain signals do not possess the statistical property of stationarity, time-frequency transforms are of special interest. Such methods are able to represent a given signal jointly in the time-frequency domain, called its time-frequency representation (TFR). Thereby the signal’s spectral components can be analyzed in relation to its temporal dynamics. In a wide sense, TFRs can be interpreted as images containing complex pixel intensities in general. An important feature of biological signals, and particularly brain signals, is their inter- and intraindividual variability. That is, under fixed experimental conditions, the obtained signals exhibit heterogeneousness not only between groups of subjects, but also between subjects within the same
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