Bakalis, E.; Lugli, F.; Zerbetto, F. Daughter Coloured Noises: The Legacy of Their Mother White Noises Drawn from Different Probability Distributions. Fractal Fract.2023, 7, 600.
Bakalis, E.; Lugli, F.; Zerbetto, F. Daughter Coloured Noises: The Legacy of Their Mother White Noises Drawn from Different Probability Distributions. Fractal Fract. 2023, 7, 600.
Bakalis, E.; Lugli, F.; Zerbetto, F. Daughter Coloured Noises: The Legacy of Their Mother White Noises Drawn from Different Probability Distributions. Fractal Fract.2023, 7, 600.
Bakalis, E.; Lugli, F.; Zerbetto, F. Daughter Coloured Noises: The Legacy of Their Mother White Noises Drawn from Different Probability Distributions. Fractal Fract. 2023, 7, 600.
Abstract
White noise is fundamentally linked to many processes, it has a flat power spectral density and a delta-correlated autocorrelation. Operators acting on white noise can result in coloured noise, whether they operate in the time domain, like fractional calculus, or in the frequency domain, like spectral processing.
We investigate whether any of the white noise properties remain in the coloured noises produced
by the action of an operator. For a coloured noise, which drives a physical system, we provide evidence to pinpoint the mother process from which it came. We demonstrate the existence of two indices, that is,
kurtosis and codifference, whose values can categorise coloured noises according to their mother process. Four different mother processes are used in this study: Gaussian, Laplace, Cauchy, and Uniform white noise distributions. The mother process determines the kurtosis value of the coloured noises that are produced. It maintains its value for Gaussian, never converges for Cauchy, and takes values for Laplace and Uniform that are within a range of its white noise value. In addition, the codifference function maintains its value for zero lag-time essentially constant around the value of the corresponding white noise.
Keywords
white noises; probability distributions; fractional calculus; colours of noise; classification of noises; kurtosis; codifference
Subject
Physical Sciences, Other
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
