Scaling properties of signals as origin of 1/f noise

Abstract: There are several mathematical models yielding 1/f noise. For example, 1/f spectrum can be obtained from stochastic sequence of pulses having power-law distribution of pulse durations or from nonlinear stochastic differential equations. We show that a couple of seemingly different models exhibiting 1/f spectrum are due to the similar scaling properties of the signals. In addition, we demonstrate a connection between signals with the power-law behavior of the power spectral density generated by the nonlinear stochastic differential equations and modeled by a sequence of random different pulses. An approximation of solutions of the nonlinear stochastic differential equations by the sequence of pulses correctly reproduces the power-law parts of the probability density function and of the power spectral density. This connection provides further insights into the origin of 1/f noise.