Phase-rectified signal averaging detects quasi-periodicities in non-stationary data

We present an efficient technique for the study of quasi-periodic oscillations in noisy, non-stationary signals, which allows the assessment of system dynamics despite phase resetting and noise. It is based on the definition of anchor points in the signal (in the simplest case increases or decreases of the signal) which are used to align (i.e., phase-rectify) the oscillatory fluctuations followed by an averaging of the surroundings of the anchor points. We give theoretical arguments for the advantage of the technique, termed phase-rectified signal averaging (PRSA), over conventional spectral analysis and show in a numerical test using surrogate heartbeat data that the threshold intensity for the detection of additional quasi-periodic components is approximately 75% lower with PRSA. With the use of different anchor point criteria PRSA is capable of separately analysing quasi-periodicities that occur during increasing or decreasing parts of the signal. We point to a variety of applications in the analysis of medical, biological, and geophysical data containing quasi-periodicities besides non-stationarities and 1/f1/f noise.