Time-Frequency Characterization of Interdependencies in Nonstationary Signals: Application to Epileptic EEG

Abstract

For the past decades, numerous works have been dedicated to the development of signal processing methods aimed at measuring the degree of association between electroencephalographic (EEG) signals. This interdependency parameter, which may be defined in various ways, is often used to characterize a functional coupling between different brain structures or regions during either normal or pathological processes. In this paper, we focus on the time-frequency characterization of the interdependency between signals. Particularly, we propose a novel estimator of the linear relationship between nonstationary signals based on the cross correlation of narrow band filtered signals. This estimator is compared to a more classical estimator based on the coherence function. In a simulation framework, results show that it may exhibit better statistical performances (bias and variance or mean square error) when a priori knowledge about time delay between signals is available. On real data (intracerebral EEG signals), results show that this estimator may also enhance the readability of the time-frequency representation of relationship and, thus, can improve the interpretation of nonstationary interdependencies in EEG signals. Finally, we illustrate the importance of characterizing the relationship in both time and frequency domains by comparing with frequency-independent methods (linear and nonlinear).

Seizure characterisation using frequency-dependent multivariate dynamics

“…This activity may possibly be reflected in the second or third largest eigenvalue of the multivariate technique, where correlations orthogonal to those in the largest eigenvalue are found, (corresponding to correlations between certain subsystems, [8]). The linear cross-correlation for two band-filtered channels were examined for different time lags, with a strong relationship found for a frequency band around 30Hz, [19].…”

“…In the case of MEG signals, a limited study consisting of three patients was performed, using wavelets to determine cross-correlations over different frequencies and calculate the time lag between different brain regions, [18]. The application of the coherence function and cross-correlation between different frequency bands, defined by a continuous filter bank was also used to explore the time-frequency dependence of epileptic seizure data, [19].…”

Analysis of the Phase Locking Index for Measuring of Interdependency of Cortical Signals Recorded in the EEG

“…However, we assume that it remains within a subband of width Ω for a given time period. Furthermore, we assume that the power spectrum of the background signal of analyze the interdependencies between areas q , the EEG is typically bandpass filtered [6], [13]. Since the exact value of 0 f depends on the state of the brain and is a priori unknown, the EEG is typically decomposed into multiple overlapping subbands, e.g.…”

“…For simplicity we use equal SNR for both sources. We take 100 Hz s f = and 2 Hz s f = Ω = , which is a commonly used bandwidth for EEG analysis [4], [13]. Furthermore, we assume that The results are shown for the mean of the PLI in Fig.…”

Time-varying model identification for time–frequency feature extraction from EEG data

“…Conventionally, the basis functions have been chosen to be Chebyshev and Legendre polynomials, prolate spheroidal sequences which are the best approximation to bandlimited functions [2], [4], [12]- [13] and wavelet basis that have a distinctive property of multi-resolution in both the time and frequency domains [3], [14]- [15]. Basis expansion methods have been widely applied to solve various engineering problems.…”