A general mechanical model for |f|αspectral density random noise with special reference to flicker noise 1/|f|

Any class of reasonable time-dependent perturbations occurring at random, under certain internal contraints, generates random noise having a spectral density varying as |f|
^α
over an arbitrarily large range of spectral frequency f only for - 2 ≤ α ≤ 0. A class is the set of all perturbations which are equivalent under some individual indenpendent scaling of amplitute, scaling of time, and translation of time. A subclass is characterized by P(τ) and A
²
(τ). P(τ) is the lifetime probability desity. A
²
(τ) is a mean square amplitude of perturbations having lifetime τ. For a given class, |f|
^α
∞
and |f|
^α
0
are the frequency-smoothed laws in the limits of infinite and zero frequencies, respectively. Any reasonable perturbation has α
∞
≤ - 2 and α
0
≥ 0. To generate random noise having an |f|
^α
law over an arbitrarily large range of f from a subclass chosen from any class characterized by α
∞
and α
0
, it is necessary that α
∞
≤ α ≤ α
0
. For α
∞
< α < α
0
, it is necessary and sufficient that such subclasses satisfy the condition, P(τ)A
²
(τ) ≈ Bτ
^{- α - 3}
with B constant, over a suitable range of τ, and that P(τ)A
²
(τ) not be larger than Bτ
^{- α - 3}
outside the range. This general mechanical model is of immediate value in the formulation and criticism of specific physical models of |f|
^α
noise, including flicker noise, and in computer simulation of |f|
^α
noise.