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Class of perfect 1/f noise and the low-frequency cutoff paradox.

The low-frequency cutoff paradox occurring in 1/f processes has been revisited in a recent Letter [M. Niemann, H. Kantz, and E. Barkai, Phys. Rev. Lett. 110, 140603 (2013)]. A model of independent pulses exhibiting an integrable 1/f(β) power spectrum with β>1 explains this paradox. In this paper we explore a complementary possibility based on the use of multiplicative models to generate integrable 1/f(β) processes. Three distinct types of models are considered. One of the most used methods of generating 1/f processes based on correlated pulses is among these models. Consequently we find that, contrary to what is generally thought, the low-frequency cutoff is not necessary to avoid the postulated divergence in a wide variety of processes.