Pules Detection Using Cross
Correlation
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Summary
Accurate timing of acoustic pulses can be carried out by comparing
them with a template pulse of similar shape. We have set up a
crosscorrelation timing procedure for the signals detected by the ORE
UVM at 3Mile Slough.
Description
To the eye, it is often easy to distinguish special features in the graph
of a function  a bump, a series of bumps, a signal "turning on" or
"turning off." It is not quite as easy to make a computer program do
the same thing. Cross correlation is a mathematical way of shifting a
template shape along a signal waveform, to determine at what position
the two signals line up best. The technique is to calculate the
crosscorrelation as a function of the shift of the template. It is
maximum where the two signals correlate best.
Mathematics
Consider a signal waveform s(t), represented in the computer by an
array of length ns, and a template (or replica) waveform r(t), of length
nr. The crosscorrelation function c(tau) is defined by