Instantaneous counting of components in nonstationary signals

In the case of multicomponent AM-FM signals, one bottleneck of mode extraction methods such as synchrosqueezing, is that the reconstruction of the individual components assumes some prior knowledge about their number. In order to reduce supervision, an entropy-based time-frequency method had been previously proposed for automatically estimating the instantaneous number of such components. An analytic treatment of this approach is first given, assessing its performance and limitations, in particular with respect to the Rényi entropy order and the amplitude ratio. Based on this analysis, an iterative strategy is then proposed, that is shown to be effective in the case of unequal amplitudes and applicable to real data signals with a moderate level of noise.