Correlation

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Correlation

Correlation is a technique that is very similar in mechanism to
convolution, with one subtle difference.

The correlation integral is given by

While this may appear to be similar to equation (1) with some changes
of variable, unlike convolution where

is time reversed, in correlation this is not the case. The integral
thus no longer represents the output of a filter driven by an
input signal. Rather it is a tool used to measure the similarity
between two signals. A large correlation value (positive or
negative) represents a strong similarity between the two
signals, while a value near zero represents little
similarity. The delay value,

allows this comparison to be made on two signals at
different delay separations.

Using the correlation tool

compare a number of signals with a unit pulse shape, noting the
maximum values that you can obtain, and the delay at which these
values occur. For all signals that you correlate, except for
those signals incorporating impulses, the maximum value that you
will obtain will be found by those signals similar in shape to
the one you are correlating with. This is because correlation
identifies the similarity between the two signals.

If a signal is correlated with itself, a process known as
autocorrelation, then the maximum value of the correlation can
be found at a time shift of 0. Verify this yourself for any
signals that you wish to test out. For the correlation between
two different signals, known as cross-correlation, this is not
necessarily the case.

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