The power spectrum of a generalized random telegraph signal with special reference to 1/f noise

Abstract

A random telegraph signal (RTS) is regarded as a random succession of non-overlapping, rectangular pulses separated by gaps. Besides the switching amplitude, an RTS is defined by the lifetime of the pulse and by the gap, both of which are exponentially distributed. Such an RTS can be generalized for arbitrarily distributed pulse lifetime and gap. By replacing the pulse with a cluster of non-overlapping events, a new approach to derive the power spectrum of such a generalized RTS is presented. For a power-law distributed cluster size, the power spectrum exhibits 1/f noise only depending on the mean cluster lifetime and on the mean gap. The total power of the generalized RTS shows an aging effect.