Mean spectral phase and detection of masked periodic signals in chaotic carriers

In the analysis of chaos, conventional frequency-spectrum analysis has largely been overlooked in development of novel `non-linear time series analysis`. In particular, the phase information of chaos in the frequency spectrum has received comparatively little attention. Here the authors present an analysis of the spectral phase of chaos by means of averaged Fourier spectra for the representative Lorenz and Ro`ssler chaotic system models. It is demonstrated that a random distribution of the phase in the frequency domain is obtained from one shot of chaotic data. From averaging the chaotic spectrum over many observations it is revealed that the random phase distribution converges to zero in the mean-phase spectrum. It is also demonstrated that, by utilising the zero mean-phase property, the non-zero phase associated with very small periodic signals hidden in chaotic spectrum allows their identification within the chaos.