The major aim of our study is to demonstrate that a concerted combination of time-variant, frequency-selective, linear and nonlinear analysis approaches can be beneficially used for the analysis of heart rate variability (HRV) in epileptic patients to reveal premonitory information regarding an imminent seizure and to provide more information on the mechanisms leading to changes of the autonomic nervous system. The quest is to demonstrate that the combined approach gains new insights into specific short-term patterns in HRV during preictal, ictal, and postictal periods in epileptic children. The continuous Morlet-wavelet transform was used to explore the time-frequency characteristics of the HRV using spectrogram, phase-locking, band-power and quadratic phase coupling analyses. These results are completed by time-variant characteristics derived from a signal-adaptive approach. Advanced empirical mode decomposition was utilized to separate out certain HRV components, in particular blood-pressure-related Mayer waves (≈0.1 Hz) and respiratory sinus arrhythmia (≈0.3 Hz). Their time-variant nonlinear predictability was analyzed using local estimations of the largest Lyapunov exponent (point prediction error). Approximately 80-100 s before the seizure onset timing and coordination of both HRV components can be observed. A higher degree of synchronization is found and with it a higher predictability of the HRV. All investigated linear and nonlinear analyses contribute with a specific importance to these results.

Repetitive flicker stimulation (photic driving) offers the possibility to study the properties and coupling characteristics of stimulation-sensitive neuronal oscillators by means of the MEG/EEG analysis. With flicker frequencies in the region of the individual alpha band frequency, the dynamics of the entrainment process of the alpha oscillation, as well as the dynamics of the accompanying gamma oscillations and the coupling between the oscillations, are investigated by means of an appropriate combination of time-variant analysis methods. The Hilbert and the Gabor transformation reveal time-variant properties (frequency entrainment, phase locking, and n:m synchronization) of the entrainment process in the whole frequency range. Additionally, time-variant partial directed coherence is applied to identify ocular saccadic interferences and to study the directed information transfer between the recording sites of the simultaneously derived MEG/EEG data during the entrainment. The MEG data is the focus of this methodological study as the entrainment effects of the alpha oscillation are stronger in MEG than in the EEG. The occipital brain region (visual cortex) was mainly investigated and the dynamics of the alpha entrainment quantified. It can be shown that at the beginning of this entrainment, a transient, strongly phase-locked "40-Hz" gamma oscillation occurs.

SummaryObjectives: This review outlines the method -ological fundamentals of the most frequently used non-parametric time-frequency analysis techniques in biomedicine and their main properties, as well as providing decision aids concerning their applications.Methods: The short-term Fourier transform (STFT), the Gabor transform (GT), the S-transform (ST), the continuous Morlet wavelet transform (CMWT), and the Hilbert transform (HT) are introduced as linear transforms by using a unified concept of the time-frequency representation which is based on a standardized analytic signal. The Wigner-Ville dis -tribution (WVD) serves as an example of the ‘quadratic transforms’ class. The combination of WVD and GT with the matching pursuit (MP) decomposition and that of the HT with the empirical mode decomposition (EMD) are explained; these belong to the class of signal-adaptive approaches.Results: Similarities between linear transforms are demonstrated and differences with regard to the time-frequency resolution and interference (cross) terms are presented in detail. By means of simulated signals the effects of different time-frequency resolutions of the GT, CMWT, and WVD as well as the resolution-related properties of the inter -ference (cross) terms are shown. The method-inherent drawbacks and their consequences for the application of the time-frequency techniques are demonstrated by instantaneous amplitude, frequency and phase measures and related time-frequency representations (spectrogram, scalogram, time-frequency distribution, phase-locking maps) of measured magnetoencephalographic (MEG) signals.Conclusions: The appropriate selection of a method and its parameter settings will ensure readability of the time-frequency representations and reliability of results. When the time-frequency characteristics of a signal strongly correspond with the time-frequency resolution of the analysis then a method may be considered ‘optimal’. The MP-based signal-adaptive approaches are preferred as these provide an appropriate time-frequency resolution for all frequencies while simultaneously reducing interference (cross) terms.

Short-time Fourier transform (STFT), Gabor transform (GT), wavelet transform (WT), and the Wigner-Ville distribution (WVD) are just some examples of time-frequency analysis methods which are frequently applied in biomedical signal analysis. However, all of these methods have their individual drawbacks. The STFT, GT, and WT have a time-frequency resolution that is determined by algorithm parameters and the WVD is contaminated by cross terms. In 1993, Mallat and Zhang introduced the matching pursuit (MP) algorithm that decomposes a signal into a sum of atoms and uses a cross-term free pseudo-WVD to generate a data-adaptive power distribution in the time-frequency space. Thus, it solved some of the problems of the GT and WT but lacks phase information that is crucial e.g., for synchronization analysis. We introduce a new time-frequency analysis method that combines the MP with a pseudo-GT. Therefore, the signal is decomposed into a set of Gabor atoms. Afterward, each atom is analyzed with a Gabor analysis, where the time-domain gaussian window of the analysis matches that of the specific atom envelope. A superposition of the single time-frequency planes gives the final result. This is the first time that a complete analysis of the complex time-frequency plane can be performed in a fully data-adaptive and frequency-selective manner. We demonstrate the capabilities of our approach on a simulation and on real-life magnetoencephalogram data.