TABLE OF CONTENTS As we discussed, the power density spectrum ? ff( ?) of a continuing waveform f( t) is equal to the Fourier transform of 
ff( ?), the autocorrelation function of f( t). The autocorrelation function is the time average
For theoretical analysis, we thus first determine the autocorrelation function of a waveform in order to determine its power density spectrum. A problem with determining the autocorrelation function is that the waveform f( t) is rarely known in sufficient detail to determine the desired average analytically as an integration over time as given by Eq. (5.70). We thus require a subterfuge.
First note that the time average of a waveform is just dependent on the fraction of time that the waveform has certain values and is not dependent on the time order at which these values occur. For example, the time average of a rectangular waveform that jumps between the values zero and A is equal to A times the fraction of time that the value of the waveform is A irrespective of the times at which the waveform jumps between zero and A. As another example, the time average of sin( ? t + ) is zero no matter what the value of ? or . Observe then that it is only necessary to know certain general characteristics of a waveform in order to determine its average. Specifically, we note that the...
