Random Processes With Power Law Spectral Density (2206.12722v3)

Abstract: A statistical model of discrete finite length random processes with negative power law spectral densities is presented. The definition of terms is followed by a description of the spectral density trend. An algorithmic construction of random process, and a short block of computer code is given to implement the construction of the random process. The relationship between the second order properties of the random processes and the parameters of the construction is developed and demonstrated. The paper ends with a demonstration of the connection between the frequency of the random process sign changes and the power law exponent.