Spike Spectra for Recurrences

A novel kind of power spectrum is constructed, the inter-spike spectrum, which transforms any signal into its spike-frequency domain. This method clearly shows the apparent cycles in the data and overcomes the problems for spike-train-like signals when using the obvious idea of Fourier-transforming it. We invent this instructive approach with the idea of transforming the τ-recurrence rate of a recurrence plot (RP), which often has a spiky appearance. The τ-recurrence rate is the density of recurrence points along diagonals of the RP, which are parallel to the main diagonal with a distance of τ. In this context the inter-spike spectrum can be interpreted as a nonlinear power spectrum of a potentially high dimensional system which constitutes the RP. The proposed measure is robust to noise and is able to detect and analyze bifurcations.