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Although classical spectral analysis is a natural approach to characteriselinear systems, it cannot describe a chaotic dynamics. Here, we propose theordinal spectrum, a method based on a spectral transformation of symbolicsequences, to characterise the complexity of a time series. In contrasts withother nonlinear mapping functions (e.g. the state-space reconstruction) theproposed representation is a natural approach to distinguish, in a frequencydomain, a chaotic behavior. We test the method in different synthetic andreal-world data. Our results suggest that the proposed approach may provide newinsights into the non-linear oscillations observed in different real data.

Ordinal spectrum: a frequency domain characterization of complex time series