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thus no longer represents the output of a filter driven by an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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