  Objective. In neuroscience, time-frequency analysis has been used to get
insight into brain rhythms from brain recordings. In event-related protocols,
one applies it to investigate how the brain responds to a stimulation repeated
over many trials. In this framework, three measures have been considered: the
amplitude of the transform for each single trial averaged across trials,
avgAMP; inter-trial phase coherence, ITC; and the power of the evoked potential
transform, POWavg. These three measures are sensitive to different aspects of
event-related responses, ITC and POWavg sharing a common sensitivity to phase
resetting phenomena. Methods. In the present manuscript, we further
investigated the connection between ITC and POWavg using theoretical
calculations, a simulation study and analysis of experimental data. Results. We
derived exact expressions for the relationship between POWavg and ITC in the
particular case of the S-transform of an oscillatory signal. In the more
general case, we showed that POWavg and ITC are connected through a
relationship that roughly reads $\mathrm{POWavg} \approx \mathrm{avgAMP}^2
\times \mathrm{ITC}^2$. This result was confirmed on simulations. We finally
compared the theoretical prediction with results from real data. Conclusion. We
showed that POWavg and ITC are related through an approximate, simple
relationship that also involves avgAMP. Significance. The presented
relationship between POWavg, ITC, and avgAMP confirms previous empirical
evidence and provides a novel perspective to investigate evoked brain rhythms.
It may provide a significant refinement to the neuroscientific toolbox for
studying evoked oscillations.
