Time-varying spectral analysis in exercise and sport science

We discuss the application of time-frequency analysis to biomechanical-type signals, and in particular to signals that would be encountered in the study of rotation rates of bicycle pedaling. We simulate a number of such signals and study how well they are represented by various time-frequency methods. We show that time-frequency representations track very well the instantaneous frequency even when there are very fast changes. In addition, we do a correlation analysis between time-series whose instantaneous frequency is changing and show that the traditional correlation coefficient is insufficient to characterize the correlations. We instead show that the correlation coefficient should be evaluated directly from the instantaneous frequencies of the time series, which can be easily estimated from their time-frequency distributions