  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.
