Random Processes With Power Law Spectral Density

TL;DR

This paper introduces a statistical model for finite-length discrete random processes with negative power law spectral densities, providing an algorithmic construction, implementation code, and analysis of their properties.

Contribution

It presents a novel model and construction method for such processes, linking spectral density parameters to process behavior.

Findings

Established the relationship between spectral density and process sign change frequency

Provided an algorithm and code for generating these processes

Demonstrated how spectral parameters influence process properties

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.