Curved structures in recurrence plots: The role of the sampling time

We give a theoretical explanation of the formation of the curved macropatterns in the recurrence plots of sinusoidal signals, with nonstationarity in the phase or in the frequency. We show that the large time scales observed and the curved structures are the artificial product of the discretization of the signal. Recurrence plots are highly sensitive to the phase error introduced by the sampling, and we show that this characteristic can be used to detect very small (similar to 0.5%) phase or frequency shifts of the carrier frequency.