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

Milad Johnny

Electrical and Communication Engineering, Tehran, Iran.

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.

Keywords

Asymmetrical PDF; Signal Representation; Ergodicity; Gaussian Variables; Non-Infinity Devisable; Stealth Objects

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	O. Wright and W. Wright, “Flying-Machine,” US Patent No. 821393, 1906.
[2]	J. K. Wu, “Two Problems of Computer Mechanics Program System,” Proceedings of Finite Element Analysis and CAD, Peking University Press, Beijing, 1994, pp. 9-15.
[3]	B. Liu and D. Munson, “Generation of a Random Sequence Having a Jointly Specified Marginal Distribution and Autocovariance,” IEEE Transaction on Acoustic, Speech and Signal Processing, Vol. 30, 1982, pp. 973-983.
[4]	R. Ortega, A. Loria and R. Kelly, “A Semiglobally Stable Output Feedback PI2D Regulator for Robot Manipulators,” IEEE Transactions on Automatic Control, Vol. 40, No. 8, 1995, pp. 1432-1436. doi:10.1109/9.402235
[5]	E. Wit and J. McClure, “Statistics for Microarrays: Design, Analysis, and Inference,” 5th Edition, John Wiley & Sons Ltd., Chichester, 2004.
[6]	A. S. Prasad, “Clinical and Biochemical Spectrum of Zinc Deficiency in Human Subjects,” In: A. S. Prasad, Ed., Clinical, Biochemical and Nutritional Aspects of Trace Elements, Alan R. Liss, Inc., New York, 1982, pp. 5-15.
[7]	B. M. S. Giambastiani, “Evoluzione Idrologica ed Idrogeologica Della Pineta di San Vitale (Ravenna),” Ph.D. Thesis, Bologna University, Bologna, 2007.
[8]	S. Kay, “Representation and Generation of Non-Gaussian Wide-Sense Stationary Random Processes With Arbitrary PSDs and a Class of PDF,” IEEE Transaction on Signal Processing, Vol. 58. No. 7, 2010, pp. 3448-3458. doi:10.1109/TSP.2010.2046437
[9]	G. L. Wise, A. P. Traganitis and J. B. Thomas, “The Effect of a Memory Less Nonlinearity on the Spectrum of a Random Process,” IEEE Transactions on Information Theory, Vol. 23, No. 1, 1977, pp. 84-89.
[10]	Bendat and Piersol, “Random Data, Analysis and Measurement Procedures,” 3rd Edition, Wiley, New York, 2000.