13.3 Time-frequency analysis of EEG

EEG signals are complex, non-stationary brain waves that traditional Fourier analysis can't fully capture. Time-frequency techniques like short-time Fourier transform and wavelet transform offer better ways to analyze these signals, revealing both frequency and temporal information.

These methods create visual representations called spectrograms and scalograms, which show how EEG frequencies change over time. This helps identify important brain events, like evoked potentials or seizures, and characterize different brain states more accurately than standard Fourier analysis.

Fourier Analysis and EEG Signals

Limitations of traditional Fourier analysis

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• Assumes signal stationarity but EEG signals often have statistical properties that change over time making them non-stationary
• Provides only frequency information losing temporal information and cannot localize frequency components in time
• Unsuitable for capturing transient events as rapid changes in EEG signals may be missed (spikes, bursts)

Time-Frequency Analysis Techniques

Application of short-time Fourier transform

• Divides the signal into short segments (epochs) and applies Fourier transform to each segment
• Provides time-frequency representation with a spectrogram as a visual representation of STFT
  • Time on x-axis, frequency on y-axis, amplitude as color or intensity (heat map)
• Has fixed time and frequency resolution determined by window size and overlap leading to a trade-off between time and frequency resolution (Heisenberg uncertainty principle)

Implementation of wavelet transform techniques

• Uses wavelets as basis functions that are localized in both time and frequency (Morlet, Mexican hat)
• Continuous Wavelet Transform (CWT) computes wavelet coefficients at all scales and positions providing high resolution in both time and frequency
• Discrete Wavelet Transform (DWT) decomposes signal into discrete wavelet coefficients using dyadic scales and positions making it more computationally efficient than CWT
• Allows for multi-resolution analysis capturing both low and high-frequency components
  • Provides good temporal resolution for high frequencies and good frequency resolution for low frequencies (Zoom-in, zoom-out)

Interpretation of time-frequency representations

• Spectrogram (STFT) identifies time-localized frequency components and detects transient events and changes in frequency content over time
• Scalogram (Wavelet Transform) represents wavelet coefficients in time-frequency domain identifying localized time-frequency components at different scales
  • Detects transient events (P300, N400) and oscillatory patterns (alpha, beta, gamma)
• Identify dominant frequencies and their temporal evolution
• Detect event-related changes in EEG activity
  1. Transient responses, such as evoked potentials (VEP, AEP)
  2. Changes in oscillatory patterns, such as event-related synchronization/desynchronization (ERD/ERS)
• Characterize non-stationary behavior of EEG signals (sleep stages, epileptic seizures)