On moment of velocity for signal analysis

The instantaneous frequency (IF) of a signal is a well-defined quantity that is widely used for analysing non-stationary signals. However, often in practice, IF as a function of time can possess large spikes and negative values. Moreover, IF is very sensitive to noise, limiting its range of practical application. Due to these deficiencies, we introduce the concept of moment of velocity (MoV) for signal analysis. As a case study, we compare the performance of MoV to a standard Hilbert transform-based approach for R-wave identification in human electrocardiogram signals, demonstrating that our approach is more robust to noise. We examine characteristic heartbeats obtained from the MIT-BIH Arrhythmia database. A detection error rate of 0.07%, a positive predictive value of 99.97%, and a sensitivity of 99.95% are achieved against analysis results from the database.