Analysis of Random Signals

Consider a random signal sensed by a probe and recorded by a measuring system as shown in Figure 1.8. Though it is impossible to collect this signal manually, modern instruments can collect such a signal with considerable amount of accuracy in both magnitude and time. The simplest quantities that must be determined from this signal are the mean, the RMS value and the cross-correlation with a second signal . The relationships between the signal and the reduced quantities are given by:

Mean:
RMS:
Cross-correlation:

If the signals are directly stored in the memory of a computer in digital form, the integrals appearing above can be evaluated using computer programs.

For example, the numerical evaluation of an integral proceeds as

or,

In (i) and (ii) where