Estimation of time delay between EEG signals for epileptic focus localization: statistical error considerations.

Area of Science:

• Neuroscience
• Signal Processing
• Biomedical Engineering

Background:

• Accurate time delay estimation is crucial for analyzing neural connectivity using electroencephalogram (EEG) signals.
• Existing methods for time delay estimation in EEG may have limitations in variance and applicability.

Purpose of the Study:

• To theoretically analyze the variance of time delay estimates between two EEG signals using the phase spectrum method.
• To derive explicit theoretical formulae for this variance and compare them with simulation results.

Main Methods:

• Theoretical derivation of variance formulae for time delay estimation.
• Computer simulations to compare theoretical formulae with experimentally derived results.
• Analysis of factors influencing variance, including frequency range, data segments, and signal coherence.

Main Results:

• Explicit theoretical formulae for the variance of time delay estimates were obtained.
• Variance is inversely proportional to the frequency range, number of data segments, and coherence between EEG signals.
• Derived formulae are applicable to non-Gaussian and narrow-band EEG-like data.

Conclusions:

• The theoretical formulae provide an accurate assessment of time delay estimation variance in EEG signals.
• Understanding these variance factors can improve the reliability of neural connectivity analyses.
• A minimum-variance estimate for time delay is also proposed.