Fig. 2.

A: schematic derivation of time-frequency representation (TFR). Example LFP segment is band-pass filtered into 2 frequency ranges of interest for amplitude (Signal_amp, red; 20–300 Hz) and for phase (Signal_ph, blue; 7–14 Hz). The spectral power of Signal_amp is calculated with a sliding time window and triggered at every peak of Signal_ph to obtain averaged power of Signal_amp around the peak of Signal_ph. This procedure is repeated for each Signal_amp frequency in 1-Hz steps from 20 to 300 Hz to obtain the full TFR. B: schematic derivation of the modulation index (MI). The first filtering steps are the same as for the TFR. Next, the instantaneous amplitude of Signal_amp and the instantaneous phase of Signal_ph are calculated with the Hilbert transform. The amplitude of Signal_amp is binned according to the phase of Signal_ph. The MI is calculated with the algorithm proposed by Tort et al. (2010). The MI equals 0 when the amplitude is distributed uniformly across the phase cycle (right). C: application of TFR and MI analyses to simulated LFP. Top left: simulated LFP is the sum of 3 spectral components: Signal_ph (10-Hz sine wave), Signal_amp (100-Hz sine wave with amplitude coupled with Signal_ph), and 1/f^α (pink) noise. Top right: MI matrix of simulated LFP. The procedure shown in B was repeated for Signal_ph frequencies ranging from 3 to 60 Hz and Signal_amp frequencies ranging from 30 to 300 Hz. High MI values occurred around a phase frequency of 10 Hz and amplitude frequency of 100 Hz. Bottom: TFRs of simulated LFP with different frequencies for Signal_amp (100 Hz, 50 Hz, and 30 Hz from left to right, respectively). Clear modulation of power occurs around each frequency of Signal_amp synchronized with the peaks and troughs in Signal_ph (bottom left). Note that the range of the y-axes for the right 2 TFRs is different from that for the left TFR to reveal the entire shape of the modulation. No pronounced smearing can be seen in any TFR.