A Simple Method to Generate a Stationary Random Process with Arbitrary Desired Probability Density Function and Autocorrelation

Authors

  • Tariq Tashan Electrical Engineering Department, College of Engineering, Mustansiriyah University, Baghdad, Iraq Author
  • Maher K. Mahmood Al-Azawi Retired Professor, Electrical Engineering Department, College of Engineering, Mustansiriyah University, Baghdad, Iraq 3Retired Professor, University Author
  • Jafar W. Abdul Sadah Retired Professor, University of Baghdad, Baghdad, Iraq Author

DOI:

https://doi.org/10.31272/ajece.43

Keywords:

ACF, PDF, Correlation shaping filter, Non-Gaussian noise generation, Stationary random process

Abstract

A stationary random process with a desired Probability Density Function (PDF) and Autocorrelation Function (ACF) is generated in this paper. These two required properties are achieved simultaneously using a simple design procedure. The proposed method consists of a digital filter followed by non-linear function. The digital filter is designed to shape the ACF, while the non-linear function is designed to produce the desired PDF at the final output. A simple polynomial form is used to represent the nonlinear function and a simple non-recursive linear phase digital filter is used. Six scenarios are considered, that combine two types of ACF and three types of PDF. Computer simulation results show that the required properties are achieved with high accuracy using Chi-Square goodness of fit test.

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Published

2026-08-30

Issue

Vol. 2 No. 01 (2026): Academic Journal of Electrical and Computer Engineering (AJECE)

Section

Articles

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Copyright (c) 2026 Tariq Tashan, Maher K. Mahmood Al-Azawi, Jafar W. Abdul Sadah (Author)

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