A First Course in Statistics for Signal Analysis pp 175-196 | Cite as

# Discrete Signals and Their Computer Simulations

Chapter

## Abstract

Given an arbitrary power spectrum, our ability to simulate the corresponding stationary random signals, using only the random number generator which produces, say, discrete white noise, depends on the observation that in some sense all stationary random signals can be approximated by superpositions of random harmonic oscillations desciribed in Example 4.1.2. The observation itself is not obvious at all and, of course, the key to applying it is in the details: In what is sense the approximation meant? What is the precise algorithm for obtaining such an approximation?

## Keywords

Power Spectrum White Noise Spectral Representation Random Number Generator Power Spectrum Density
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## References

- 40.See Section 3.1 or, e.g., M. Denker and W. A. Woyczyński,
*Introductory Statistics and Random Phenomena: Uncertainty, Compexity, and Chaotic Behavior in Engineering and Science*, Birkhäuser Boston, Cambridge, MA, 1998.Google Scholar - 41.See, e.g., G. B. Folland,
*Real Analysis*, Wiley, New York, 1984.MATHGoogle Scholar - 42.A step proving the existence of an
*infinite*such sequence requires an application of the so-called Kolmogorov extension theorem; see, e.g., P. Billingsley,*Probability and Measure*, Wiley, New York, 1986.MATHGoogle Scholar - 44.See, e.g., G. B. Folland,
*Real Analysis*, Wiley, New York, 1984.MATHGoogle Scholar

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© Birkhäuser Boston 2006