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

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1 Author(s)
Halford, D. ; National Bureau of Standards, Boulder, Colo.

Any class of reasonable time-dependent perturbations occurring at random, under certain internal contraints, generates random noise having a spectral density varying as |f|αover 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 A2(τ). P(τ) is the lifetime probability desity. A2(τ) is a mean square amplitude of perturbations having lifetime τ. For a given class, |f|αand |f|α0are the frequency-smoothed laws in the limits of infinite and zero frequencies, respectively. Any reasonable perturbation has α≤ - 2 and α0≥ 0. To generate random noise having an |f|αlaw over an arbitrarily large range of f from a subclass chosen from any class characterized by αand α0, it is necessary that α≤ α ≤ α0. For α< α < α0, it is necessary and sufficient that such subclasses satisfy the condition, P(τ)A2(τ) ≈ Bτ- α - 3with B constant, over a suitable range of τ, and that P(τ)A2(τ) not be larger than Bτ- α - 3outside the range. This general mechanical model is of immediate value in the formulation and criticism of specific physical models of |f|αnoise, including flicker noise, and in computer simulation of |f|αnoise.

Published in:

Proceedings of the IEEE  (Volume:56 ,  Issue: 3 )