5. Spectrum analysis and time-frequency analysis

Resting-state EEG: without stimulation. Task-state EEG: There are stimuli and tasks.

Spectrum Analysis: Does not contain time information. Time-frequency analysis: time + frequency joint method.

5.1 Spectrum Estimation

5.1.1 Basic concepts

Time series signal: For example, the EEG signal recorded continuously in a certain channel can be characterized as the change of signal amplitude (or other quantity) relative to time in the time domain , or as signal power (or other quantity) in the frequency domain value) distribution along the frequency variation .

Frequency: The basic parameter describing the periodic activity of the oscillatory waveform in unit time. The unit is Hertz (HZ), which is one cycle per second.

Spectrum: the distribution curve of the power, amplitude or phase of the time series signal along the frequency in the frequency domain.

Spectrum estimation: An estimation method that transforms a time-domain signal into a frequency-domain spectrum. The purpose is to observe the frequency peak of the corresponding period to detect the periodicity of the signal.

When choosing a sampling rate be sure to choose twice the frequency of most interest.

5.1.2 Spectrum Estimation Method: Periodogram

Because the ultra-low frequency is meaningless, but it will weaken other waves, as shown in the upper right corner. So add a log, and then become the following picture.

5.1.3 Spectrum estimation method: Welch method

The purpose of windowing is to emphasize the signal in the middle and ignore the signals on both sides.

After windowing, the periodograms of each segment are added on average.

It can be seen that the variance of the periodogram is very large; the waveform of the Welch method is very prominent, and a relatively smooth power spectrum can be obtained.