On the normality and accuracy of simulated random processes

✍ Scribed by J.-N. Yang

• Publisher: Elsevier Science
• Year: 1973
• Tongue: English
• Weight: 608 KB
• Volume: 26
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/s0022-460x(73)80196-8

✦ Synopsis

Efficient methods of simulating stationary and non-stationary random processes and envelopes, by using a series of sine or cosine functions or by using the fast Fourier transform, have been proposed previously. Without applying the central limit theorem, it is shown in this paper that the simulated random processes are asymptotically Gaussian processes as the number of terms, N, of sine or cosine functions approaches infinity. The accuracy of the first-order probability densities of the simulated random processes is investigated by using the fast Fourier transform. Numerical results are computed with respect to the variation of the number of terms, N, of sine or cosine functions used for simulation. It is shown that within the practical range of N, such as 500, the accuracy is remarkably satisfactory even outside the region of 3 standard deviations. The investigation of the accuracy of the second-order probabi!ity densities by applying the fast Fourier transform is also described in detail. The study of accuracy presented herein is of vital importance in determining the applicability and practicality of methods of simulation.