Effective Bandwidths of Broadband Chaotic Signals

We propose and study a new definition for the effective bandwidths of the broadband chaotic signals, which sums up only those discrete spectral segments of the chaos power spectrum accounting for 80% of the total power. Compared to the definitions used conventionally, which tend to overestimate the effective bandwidths of the chaotic signals, the proposed definition measures only the bandwidths that possess significant amounts of power in the chaos spectra. With the proposed definition, the broadband chaos states can be clearly distinguished from the narrowband periodic oscillation states, based on just the values of the effective bandwidths measured. In this paper, the bandwidths of the dynamical states generated with an optically injected semiconductor laser under different definitions are studied and compared. To demonstrate the usefulness of the proposed definition in applications, such as ranging using chaos, the relations between the chaos bandwidths and the peak to sidelobe levels of the autocorrelations of the chaotic signals are also investigated.