The most widely used approach in the physical sciences for characterizing a random process is via a power spectral density, that is, the decomposition of the signals defined by a random process into their constituent sinusoidal components. The power spectral density for a random process has been introduced in Chapter 7. This chapter extends the discussion of a power spectral density with the definition of the cross power spectral density and the consideration of the power spectral density of a sum of random processes. The power spectral density of a periodic pulse train, signalling random processes, quantization error signals, shot noise random processes, 1/f noise, and a correlated jittered random process are established. Further theory and results for the power spectral density, consistent with the approach taken, can be found in Howard (2002).
Consider a random process defined on [0, T ], with a signal sample space
that is based on the sample space S of experimental outcomes underpinning the random process. The sample space S defines a random variable Ω with a probability mass function for the countable case and a probability density function for the uncountable case.
In terms ...