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A method to upsample insufficiently sampled experimental time series ofpseudo-periodic signals is proposed. The result is an estimate of thepseudo-periodic cycle underlying the signal. This hypersampling requires asufficiently sampled reference signal that defines the pseudo-periodicdynamics. The time series and reference signal are combined by projecting thetime series values to the analytic phase of the reference signal. The resultingestimate of the pseudo-periodic cycle has a considerably higher effectivesampling rate than the time series. The procedure is applied to time series ofMRI images of the human brain. As a result, the effective sampling rate couldbe increased by three orders of magnitude. This allows for capturing thewaveforms of the very fast cerebral pulse waves traversing the brain.Hypersampling is numerically compared to the more commonly used retrospectivegating. An outlook regarding EEG and optical recordings of brain activity asthe reference signal is provided.

Hypersampling of pseudo-periodic signals by analytic phase projection