Gibbs-like phenomena in chaos-based frequency modulated signals

This paper investigates the problem of spectral singularities in frequency modulated signals where the modulating signal is a chaotic PAM. We analyze the properties of the spectrum when the duration of the pulses of modulating signal tends to infinity, in order to exclude the presence of any kind of periodicity. Such a spectrum is analytically known for all frequencies with the exception of a countable number of points, at which Gibbs-like peaks are nevertheless highlighted by simulations and measurements. We here concentrate on these points, and prove their link with the underlying chaotic dynamic giving also a method to approximate their height.