NeuroAnalyzer tutorials: Plot spectrum

using NeuroAnalyzer
using Plots
eeg = load("files/eeg.hdf");

Spectral energy: \[ E_s = \vert X(t) \vert^2 \] \(X(t)\): Fourier transform of \(x(t)\)

Spectral density: describes the distribution of power into frequency components composing that signal.

Methods of estimating power:

• Welch periodogram
• Bartlett’s method
• multitaper
• wavelets

Welch periodogram

Welch’s method (periodogram): split signal into smaller windows, compute PSD for each window and finally average all individual power spectra.

Periodogram has high variance = noisy spectrogram

• no tapering: highest noise (high variance)
• single taper spectrum: less of noise, but still low resolution

Plot Welch PSD:

plot_psd(eeg,
         ch="Fp1")

Fast Fourier transform

Plot FFT PSD:

plot_psd(eeg,
         ch="Fp1",
         method=:fft)

Short time Fourier transform

For PSD, short time Fourier transform is like the Welch’s method.

Plot short time Fourier transform PSD:

plot_psd(eeg,
         ch="Fp1",
         method=:stft)

Multi-taper

Fourier transform is performed several times, each times on data tapered using a different taper.

Plot multi-taper PSD:

plot_psd(eeg,
         ch="Fp1",
         method=:mt)

(!) To calculate recommended number of tapers, use ntapers():

plot_psd(eeg,
         ch="Fp1",
         method=:mt,
         nt=ntapers(eeg, df=1))

where df is the frequency resolution (bandwidth) – smallest distance between frequency peaks that we want to observe (e.g. 1 Hz).

Morlet wavelet

Plot Morlet wavelet PSD:

plot_psd(eeg,
         ch="Fp1",
         method=:mw)

Scaling axes

Plot PSD, scale x-axis:

plot_psd(eeg,
         ch="Fp1",
         ax=:loglin)

Multi-channel spectrum

Plot multi-channel PSD:

plot_psd(eeg,
         ch=["Fp1", "Fp2", "F3", "F4"])

Butterfly plot of multi-channel PSD:

plot_psd(eeg,
         ch=["Fp1", "Fp2", "F3", "F4"],
         type=:butterfly)

Plot multi-channel PSD, mean ± 95CI:

plot_psd(eeg,
         ch=["Fp1", "Fp2", "F3", "F4"],
         type=:mean)

Plot PSD 3d waterfall:

plot_psd(eeg,
         ch=["Fp1", "Fp2", "F3", "F4"],
         method=:mw,
         type=:w3d)

Plot PSD 3d surface:

plot_psd(eeg,
         ch=["Fp1", "Fp2", "F3", "F4"],
         type=:s3d)

Topographical map of PSD

Plot topomap of PSDs:

plot_psd(eeg,
         ch="eeg",
         type=:topo)

Phase spectral density

Plot phase spectral density:

plot_phsd(eeg,
          ch="eeg")

(!) For plot_phsd(), the same plot types are available as for plot_psd().