# 10POWER SPECTRAL DENSITY THEORY

## 10.1 INTRODUCTION

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).

## 10.2 POWER SPECTRAL DENSITY THEORY

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 ...

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