Complex demodulation (CDM) has been proposed as a method for the analysis of high- and low-frequency variabilities of heart rate and blood pressure under non-stationary conditions. In contrast to power spectral analysis, CDM provides time-dependent changes in signal amplitude and frequency on a continuous basis and may yield insights into short-term alterations in autonomic regulation. In particular, CDM may be uniquely suited for quantifying changes in respiratory sinus arrhythmia (RSA) at the onset of acute physical or mental stress conditions. In a simulation analysis we generated R-R interval time series within a normal physiological range that represented different typical sources of non-stationarity present during varying stress. Sources of non-stationarity included abrupt changes in a) mean level (from 1000 to 500 ms within 60 sec), b) oscillatory amplitude (from 50 to 10 ms), c) oscillatory frequency (from 0.2 to 0.4 Hz), and d) a combination of the above. In general, CDM-estimated amplitude and frequency accurately reproduced characteristics of the simulation data under all conditions, even after substantial noise and a 0.09 Hz oscillation were added. However, during some transitions CDM estimates fluctuated around the true values for up to 15 sec before they stabilized. Compared to CDM, power spectral analysis results were less informative since they did not allow the disentangling of unique contributions of distinct amplitudes and frequencies at different time points. Our analyses indicate that CDM provides a powerful means of continuously assessing time-dependent changes in RSA during varying physical or mental stress. CDM may also hold promise for a range of physiological and environmental non-steady state conditions where rapid dynamic alterations in autonomic control are likely to occur.