Nonstationarity of deterministic signals: when to use frequency estimation algorithms under real-time constraints
Résumé
Signals are ubiquitous in engineering fields and have a common classification by their statistical properties with respect to time. In practice, engineers are faced with a choice to use a frequency estimation algorithm (one that assumes fixed-time representations, e.g. the FFT) or a time-frequency estimation algorithm (one that does not assume a fixed time representation e.g., empirical mode decomposition) depending on the nonstationarity of the signal. In this study, we quantize the trade off between accuracies and computational burden for real-time sinusoidal parameter extraction of frequency estimators for deterministic signals with varying degrees of nonstationarity. Additionally, we demonstrate the implications for different nonstationary signals of different statistical kinds: stationarity about the mean (or linear trend); stationarity about the variance; time-invariance of the autocovariance; and wide-sense stationarity. Lastly, we benchmark on synthetic and experimental signals frequently seen around material characterization in metals: one where a very low-stress solicitation is performed in very high cycle fatigue tests, and two, in acoustic material characterization seen in nonlinear ultrasound, non-destructive testing.