PMC

Amplitude of the second harmonic with amplitude modulation (AM) and residual amplitude modulation (RAM) is greater than that without AM or RAM in (a), so we can learn that the profile with AM and RAM can be adjusted to the profile without AM or RAM. Relationships between the amplitude of the second harmonic and the modulation index m are given in (b,c) by solid lines, so we can learn that not only can the profile be adjusted, the value of the modulation index for the adjustment can be obtained.

A Illustration of AM and FM. A modulating signal (0.01 Hz) is utilized to modulate the faster “carrier” sine wave (14 Hz) by means of alteration of carrier amplitude (i.e. AM) or frequency (i.e. FM). B Amplitude or frequency modulated sine wave combined with white noise to simulate an artificial LFP. The simulated LFP was filtered in the beta band (β, black line) and both instantaneous amplitude (IA, red line) and frequency (IF, blue line) were extracted through Hilbert transform. Bottom, cross-correlation function (Xcorr) calculated between instantaneous amplitude and instantaneous frequency. C, D Boxplots representing the distribution of the logarithmic variance of instantaneous amplitude (AM, red) and the variance of instantaneous frequency (FM, blue), as a function (C) of the AM index (k_AM) or (D) or the FM index (k_AM). In the boxplots, the central black line indicates the median, the central black square indicates the mean and the box limits indicate the 25th and 75th percentiles. Whiskers at ±1.5 interquartile range. As expected, changing the AM does not affect the FM and viceversa, showing that AM and FM are mathematically independent concepts.

Stimulus generation, experimental paradigm, and behavioral results. A, AM stimulus generation. The left panel shows the modulation spectra used to generate AM envelops. The line color codes for different modulation spectra. An example of each AM envelope is shown in the middle panel. We filtered the AM envelopes through a bandpass filter of 1–30 Hz and then modulated broadband white noise with the AM envelopes to create AM stimuli. An example waveform of the AM stimuli with a 1/f modulation spectrum of exponent 1 is shown in the upper right panel. The spectrogram of the example AM stimulus is shown in the lower right panel. B, Modulation spectra of AM stimuli. We extracted amplitude envelopes of each AM stimulus and then converted the envelopes to modulation spectra for each AM type. It can be seen that the trends of the prior modulation spectra were preserved in the modulation spectra of the AM stimuli. C, Examples of prior AM envelopes and the AM envelopes from the AM stimuli. The upper row shows examples of the prior AM envelopes and the lower row shows the AM envelopes extracted from the AM stimuli. D, Experimental paradigm for presenting AM stimuli during EEG recording. E, Box plot of behavioral data. D-prime values were calculated to quantify the performance of tone detection. The thin black line indicates the threshold of significance (α level of 0.01) derived from a permutation test (for more details, see Results). F, Local SNR of tones in the AM stimuli. We calculated local SNRs using temporal windows of different sizes. The line color codes for different AM types as in A. G, Correlation between behavioral data and local SNR. The dashed line represents the threshold of significance (α level of 0.01) derived from a permutation test (for more details, see Results). The results show that the shorter the temporal window is, the better the local SNR explains the behavioral performance. The error bars in F, G represent ±1 SE over participants. The AM stimuli can be found in the OSF project folder https://osf.io/yp4k3/.

Phase-amplitude coupling and phase-slope index. A1–A4 PAC between AM and FU in patient 6, right hemisphere (Group O). Enhanced PAC (Z-score ≥ 2) was observed between FU theta/alpha phase and AM low gamma frequency amplitude when viewing faces. No enhanced PAC was observed when viewing mosaics. B Overlap between PSI and the area of enhanced PAC. Red area indicates modulation directionality from FU theta phase towards AM low gamma amplitude. Blue area indicates modulation directionality from AM low gamma amplitude towards FU alpha phase. C1–4 PAC between HI and PH in patient 9, right hemisphere (Group M). Enhanced PAC (Z-score ≥ 2) was calculated between PH alpha/beta phase and HI high gamma amplitude when viewing faces. No enhanced PAC was observed when viewing mosaics. D Overlap between PSI and the area of enhanced PAC. Red area indicates modulation directionality from PH alpha/beta phase towards HI high gamma amplitude. Blue areas indicate modulation directionality from HI high gamma amplitude towards PH alpha phase