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.
KeywordsAttenuation Steam Autocorrelation Convolution Sine
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