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

Milad Johnny
2012 Journal of Signal and Information Processing  
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
more » ... ed PSD. These symmetric PDFs defined by sinusoidal components with random amplitude, frequency and phase variables. Both analytic results and examples areincluded. The proposed scheme has been proved to be useful in simulations involving non-Gaussian processes with specific PSDs and PDFs. Figure 2. Nonlinear transform function converting non zero mean Gaussian PDF to Rayleigh random process. Figure 3. Generated Rayleigh random process after applying g(t) on Gaussian PDF. Figure 4. Power spectral density synthesizing. Figure 5. First order probability density function of Z[n], red line depicts Rayleigh PDF.
doi:10.4236/jsip.2012.34056 fatcat:ywdzwknk6bhmrmpbpi4yuswfrm