Unthresholded Recurrence Plots for Complex-Valued Representations of Narrow Band Signals

Abstract

We address the information content of unthresholded recurrence plots for complex-valued signals admitting a Fourier series representation (including periodic and sampled signals). Unthresholded recurrence plots of complex-valued signals contain the information of two real-valued signals simultaneously and can therefore be used to study the relationship between these signals. The graph theoretic procedure in our recent work [1], which was developed to characterize the uniqueness conditions for real-valued signals, is extended to the class of complex-valued signals. The special properties of complex signal representations provide alternative ways to employ unthresholded recurrence plots on narrow band signals. Examples and an application from EEG analysis clarify the results.