The Power Spectral Density The power spectral density is widely used to characterize random processes in electronic and communication systems. One common application of the power spectral density is to characterize the noise in a system. From such a characterization the noise power, and hence, the system signal to noise ratio, can be evaluated. This chapter gives a detailed justification of the two distinct, but equivalent ways of defining the power spectral density. | Principles of Random Signal Analysis and Low Noise Design The Power Spectral Density and Its Applications. Roy M. Howard Copyright 2002 John Wiley Sons Inc. ISBN 0-471-22617-3 3 The Power Spectral Density INTRODUCTION The power spectral density is widely used to characterize random processes in electronic and communication systems. One common application of the power spectral density is to characterize the noise in a system. From such a characterization the noise power and hence the system signal to noise ratio can be evaluated. This chapter gives a detailed justification of the two distinct but equivalent ways of defining the power spectral density. The first is via decomposition as given by the Fourier transform of signals comprising the random process the second is through the Fourier transform of the time averaged autocorrelation function of waveforms comprising the random process. The first approach is used in later chapters and facilitates analysis to a greater degree than the second. Finally the relationship between the power spectral density and autocorrelation function as stated by the Wiener -Khintchine theorem is justified. A brief historical account of the development of the theory underlying the power spectral density can be found in Gardner 1988 pp. 12f . Relative Power Measures In the following sections the concepts of signal power and signal power spectral density are introduced and used. Strictly speaking the concepts are that of relative signal power and relative signal power spectral density as signals typically have units that lead to relative not absolute power measures. To simplify terminology the word relative is dropped. The best justification for the use of relative power measures is the signal to noise ratio which is defined as the signal power divided by the noise power. Provided both the 59 60 THE POWER SPECTRAL DENSITY signal and noise have the same units for example watts or volts squared it does not matter whether relative .
