A number fluctuation model generating 1/f pattern (Q1079882)

It is shown that 1/f noise can be described by a special doubly stochastic process. Contrary to most theories, the stochastic process considered here represents a number fluctuation model. The capability of this stochastic model is as follows. Hooge's relation \(S(f)=I^ 2\alpha_ H/N_{TOT}f\) can theoretically be derived. Within the scope of this derivation, \(\alpha_ H\) attains arbitrary values depending on physical conditions. A lower as well as an upper cutoff frequency of 1/f noise can be calculated. In counting statistics, the relative variance of a system exhibiting 1/f noise turns out to be an extremum, its value being much higher than that found in the case of shot noise.