Generation of Non-Gaussian Wide-Sense Stationary Random Processes with Desired PSDs and PDFs

Milad Johnny

doi:10.4236/jsip.2012.34056

Abstract

This paper describes a new method to generate discrete signals with arbitrary power spectral density (PSD) and first order probability density function (PDF) without any limitation on PDFs and PSDs. The first approximation has been achieved by using a nonlinear transform function. At the second stage the desired PDF was approximated by a number of symmetric PDFs with defined variance. Each one provides a part of energy from total signal with different ratios of remained desired PSD. These symmetric PDFs defined by sinusoidal components with random amplitude, frequency and phase variables. Both analytic results and examples are included. The proposed scheme has been proved to be useful in simulations involving non-Gaussian processes with specific PSDs and PDFs.

Highlights

Generating and representing of a Gaussian variable with desired power spectral density (PSD) is an easy job
This paper describes a new method to generate discrete signals with arbitrary power spectral density (PSD) and first order probability density function (PDF) without any limitation on PDFs and PSDs
To represent and generate this process we need determining a nonlinear transform function to convert Gaussian distribution of t to Rayleigh PDF, the PDFs of the amplitude and frequency can be calculated after the first approximation of desired PSD

Summary

Introduction

The assumption of an infinitely divisible PDF may be restrictive too. We divide desired PDF with a number of symmetric and infinitely divisible ones that these PDFs depend on the first estimation. In contradiction to [8] there is not any restriction on the PDF.

Definition and Properties

One Dimensional Real Signal

E A2 1

Conclusion