AUTHORS: Stevan Berber
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ABSTRACT: Continuous density functions and their truncated versions are widely used in engineering practice. However, limited work was dedicated to the theoretical analysis and presentation in closed forms of truncated density functions of discrete random variables. The derivations of exponential, uniform and Gaussian discrete and truncated density functions and related moments, as well as their applications in the theory of discrete time stochastic processes and for the modelling of communication systems, is presented in this paper. Some imprecise solutions and common mistakes in the existing books related to discrete time stochastic signals analysis are presented and rigorous mathematical solutions are offered.
KEYWORDS: truncated densities, Gaussian truncated discrete density, exponential truncated density, moments of truncated densities
REFERENCES:[1] H. M. Hayes, Statistical Digital Signal Processing and Modelling”, John Wiley & Sons, 1996.
[2] D. A. Poularkis “Discrete Random Signal Processing and Filtering Primer with MATLAB”, CRC Press, Boca Raton, 2009
[3] Berber, M. S.., Probability of Error Derivatives for Binary and Chaos-Based CDMA Systems in Wide-Band Channels. IEEE Trans. on Wireless Communications 13/10, 2014, pp. 5596–5606.
[4] Lo, C. M., W. Lam, H., Error probability of binary phase shift keying in Nakagami-m fading channel with phase noise, Electronics Letters 36, 2000, pp. 1773–1774.
[5] Eng. T., Milstein L. B., Partially Coherent DSSS Performance in Frequency Selective Multipath Fading, IEEE Trans. on Comm. 45, 1997, pp. 110–118.
[6] Richards, M. A., Coherent Integration Loss Due to White Gaussian Phase Noise, IEEE Signal Processing Letter 10, 2003, pp. 208- 210.
[7] Polprasert, C., Ritcey, J. A., A Nakagami Fading Phase Difference Distribution and its Impact on BER Performance, IEEE Trans. on Wirel.Comm. 7, 2008, pp. 110–118.
[8] Song, X. F., Cheng, Y. J., Al-Dhahir, N., Xu, Z., Subcarrier Phase-Shift Keying Systems With Phase Errors in Lognormal Turbulence Channels. Journal of Lightwave Technology 33, 2015, pp. 1896–1904.
[9] Chandra, A., Patra, A., Bose, C., Performance analysis of PSK systems with phase error in fading channels: A survey, Physical Communication 4, 2011, pp. 63–82.
[10] Roy, D., The Discrete Normal Distribution. Communications in Statistics – Theory and Methods 32:10, 2003, pp. 1871–1883.
[11] Xekalaki, E., Hazard Functions and Life Distributions in Discrete Time. Communications in Statistics – Theory and Methods 12:21, 1983, pp. 25–2509.
[12] Roy, D., Desgupta, T., A Discretizing Approach for Evaluating Reliability of Complex Systems Under Stress-Strength Model, IEEE Trans. on Reliability, 50:2, 2001, pp. 145–150.
[13] Roy, D., Discrete Rayleigh Distribution. IEEE Trans. on Reliab., 53:2, 2004, pp. 255–256.
[14] Ho, K., Cheng, K. H., A two-dimensional Fibonacci buddy system for dynamic resource management in a partitionable mesh. Aerospace and Electronics Conference, NAECON, Proceedings of the IEEE, 1, 1997, pp. 195–201.
[15] Ansanullah, M, A Characteristic Property of the Exponential Distribution. The Annals of Statistics 5:3, 1977, pp. 580 – 583.
[16] Seo, J. I., Kang, S. B., Notes on the exponential half logistic distribution, Applied Mathematical Modelling 39, 2015, pp. 6491–6500.
[17] Raschke, M., Modeling of magnitude distributions by the generalized truncated exponential distribution, Journal of Seismology 19, 2015, pp. 265–271.
[18] Giurcaneanu, C. D., Abeywickrama, R. V., Berber, S. , Performance Analysis for a ChaosBased CDMA System in Wide-Band Channel, The Journal of Engineering, 2015, pp. 9.
