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

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.