Figure 1
From: The sleep EEG envelope is a novel, neuronal firing-based human biomarker
The principle of EEG envelope spectrum analysis. (A) Shows a simulated EEG signal, consisting of the sum of a 2 Hz sinusoid modulated by a 0.2 Hz carrier frequency, a 12 Hz sinusoid modulated by a 1 Hz carrier frequency, and pink noise. Overlain blue and red lines show the instantaneous amplitude or envelope (modulus of the Hilbert transform) of the delta (1–4 Hz) and sigma (10–16 Hz) frequency ranges, respectively. (B) Shows the power spectral density of the original signal (left) and the delta (middle) and sigma (right) envelopes. Note that the carrier frequencies are accurately recovered from spectral analysis of the envelopes (with some impurities due to added noise and the fact that the modulus of the Hilbert transform of a modulated signal is not fully sinusoidal). The spectrum of the envelope reveals periodic fluctuations in the amplitude of higher-frequency activities.
