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Simple analytically solvable models are proposed exhibiting 1/f spectrum in wide range of frequency. The signals of the models consist of pulses (point process) which interevent times fluctuate about some average value, obeying an autoregressive process with very small damping. The power spectrum of the process can be expressed by the Hooge formula. The proposed models reveal possible origin of 1/f noise, i.e., random increments of the time intervals between pulses or interevent time of the process (Brownian motion in the time axis).
Noise of stochastic processes whose power spectrum scales at low frequencies, $f$, as $1/f$ appears in such diverse systems that it is considered universal. However, there have been a small number of instances from completely unrelated fields, e.g.,
We propose a generalization of the Ornstein-Uhlenbeck process in 1+1 dimensions which is the product of a temporal Ornstein-Uhlenbeck process with a spatial one and has exponentially decaying autocorrelation. The generalized Langevin equation of the
Here we present a model for a small system combined with an explicit entropy bath that is comparably small. The dynamics of the model is defined by a simple matrix, M. Each row of M corresponds to a macrostate of the system, e.g. net alignment, while
The power spectrum of quantum dot fluorescence exhibits $1/f^beta$ noise, related to the intermittency of these nanosystems. As in other systems exhibiting $1/f$ noise, this power spectrum is not integrable at low frequencies, which appears to imply
Internal mechanism leading to the emergence of the widely occurring 1/f noise still remains an open issue. In this paper we investigate the distinction between internal time of the system and the physical time as a source of 1/f noise. After demonstr