Discrete frequency tracking in nonstationary signals using joint order statistics technique

In this communication we present a method for detecting periodicities which are superimposed on noisy and possibly discontinuous trends. This problem is encountered in practice whenever the baseline of the signal is susceptible of unpredictable variations. The discrete frequency estimate of periodicities superimposed on large trends is done by counting the extrema of the signal. The robustness of the method is provided by observing the variations of a pair of order statistics (a joint order statistic envelope) of the signal. The simultaneous change of sign of these variations correspond to extrema. We show how this yet unresolved problem can be, in extremis, reduced to a known and resolved problem of the removal of smooth trends.