  A method to upsample insufficiently sampled experimental time series of
pseudo-periodic signals is proposed. The result is an estimate of the
pseudo-periodic cycle underlying the signal. This hypersampling requires a
sufficiently sampled reference signal that defines the pseudo-periodic
dynamics. The time series and reference signal are combined by projecting the
time series values to the analytic phase of the reference signal. The resulting
estimate of the pseudo-periodic cycle has a considerably higher effective
sampling rate than the time series. The procedure is applied to time series of
MRI images of the human brain. As a result, the effective sampling rate could
be increased by three orders of magnitude. This allows for capturing the
waveforms of the very fast cerebral pulse waves traversing the brain.
Hypersampling is numerically compared to the more commonly used retrospective
gating. An outlook regarding EEG and optical recordings of brain activity as
the reference signal is provided.
