TABLE OF CONTENTS In Chapter 8, we covered those advanced analyzer functions that might reasonably be used in the diagnostics of particular sets of problems. The functions discussed in this chapter are available on many modern FFT spectrum analyzers, but are rarely used. They were put into a separate chapter in order that a diagnostician could refer to them when the normal avenues of attack do not work on a particular problem.
Both the autocorrelation and the cross-correlation functions are time domain properties. Since they turn out to be inverse FFTs of frequency domain properties, their calculation can be easily implemented in an FFT spectrum analyzer. The autocorrelation function is a single-channel property; the cross-correlation function, described below, requires a dual-channel analyzer for implementation.
The autocorrelation function, which compares the similarity of a time domain function A( t) to replications of itself delayed by a time constant ?, is given by the equation
where P is the period of the signal. Note the difficulty one would have in calculating the property in the time domain (integration) compared to the ease with which it can be processed in the frequency domain (simply an inverse FFT of the averaged power spectra). The fact that the averaged power spectra is used should be a hint that the autocorrelation function, like coherence, is an averaged rather than an instantaneous function.
One of the main uses of the autocorrelation function at the present time is to check a signal for periodicity. Suppose...
