Mathematical Preliminaries: Power Spectral Densities of Random Data and Noise
In this chapter techniques for determining the power spectral density (PSD) of random data and random signals derived from the data will be presented. There exists a complete theory for determining the spectral content of random signals [1 2 3 4]. However, the general theory involves a knowledge of probability distributions, and is restricted in application only to stationary, or wide-sense stationary random signals. The condition of stationarity is violated for random binary non-return-to-zero (NRZ) data, and the general theory cannot be directly applied to the problem at hand. However, an NRZ data stream in not totally random; such signals are termed cyclo-stationary because their statistics are cyclic. There exists a well defined structure in the data such that the absolute value of the signal in the bit period T is precisely known — only its polarity is random. Therefore it is reasonable to assume that the representation of this random data stream in the frequency domain can be obtained directly by applying the definitions of the Fourier series and Fourier transform, and problems with nonstationarity can be averted.
KeywordsPower Spectral Density Random Data Clock Signal Random Signal Sample Function
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- Wilbur B. Davenport, Jr. and William L. Root. An Introduction to the Theory of Random Signals and NoiseIEEE Press, New York, 1987. IEEE PRESS edition of a book published by McGraw Hill Book Company in 1958 under the same title.Google Scholar
- Athanasios Papoulis. Probability Random Variables and Stochastic Processes. McGraw Hill, New York, 1965.Google Scholar
- Richard E. Mortensen. Random Signals and Systems. John Wiley & Sons, New York, 1987.Google Scholar
- W. R. Bennett. Statistics of regenerative digital transmission. Bell Syst. Tech. J. 37(6):1501–1542, November 1958.Google Scholar
- R. C. Titsworth and L. R. Welch. Power spectra of signals modulated by random and pseudorandom sequences. Technical Report 32–140, Jet Propulsions Laboratory, Pasadena, Calif., October 1961.Google Scholar
- William H. Hayt, Jr. and Jack E. Kemmerly. Engineering Circuit Analysis. McGraw Hill, Inc., New York, third edition, 1978.Google Scholar
- Mischa Schwartz. Information Transmission Modulation and Noise. McGraw Hill, Inc., New York, third edition, 1980.Google Scholar
- Frederic de Coulon. Signal Theory and Processing. Artech House, Inc., Dedham MA, 1986. Translation ofTheorie et Traitement des Signauxoriginally published in French as volume VI of theTraité d’Electricitéby The Presses Polytechniques Romandes, Lausanne, Switzerland. ©1984.Google Scholar
- K. Shanmugam. Digital and Analog Communication Systems. John Wiley & Sons, New York, 1979.Google Scholar
- William C. Lindsey and Marvin K. Simon. Telecommunication Systems Engineering. Dover Publications Inc., New York, 1991. Dover edition first published in 1991 is an unabridged, unaltered republication of the work first published by Prentice-Hall, Inc., Englewood Cliffs, N.J., 1973 in its “Prentice-Hall Information and System Science Series.”.Google Scholar