1/f NOISE, INTERMITTENCY AND CLUSTERING POISON PROCESS

Abstract

This paper presents an extended mathematical base for the interpretation of cluster processes in introducing an intermittent stochastic process; this is characterized by clusters of events being separated by distinct breaks so-called intermissions. The spectral features of such an intermittent process are investigated for the case that either intermission δ or duration of cluster τc is power-law distributed like tz. Correspondingly, a spectral shape like 1/fb(z) is found; a pure 1/f shape (b=1) is obtained for z = -2. The most striking result is the dependence of exponent b(z) on quotient δ/τc: we obtain b≤2 for δ > τc and b≤ 1 for δ < τc. This behavior is explained by mutual time relations between clusters which cannot be neglected in case intermissions are small in comparison to duration of clusters (δ < τc). The conditions under which superimposed intermittent processes converge to the clustering Poisson process exhibiting 1/f noise are investigated. Possible applications are discussed for 1/f noise in neuronal spike trains, ionic channels, on-off intermittency and semiconductors.