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Introduction to DSP - time domain processing: correlation

Correlation is a maximum when two signals are similar in shape, and are in phase (or 'unshifted' with respect to each other).

Correlation is a measure of the similarity between two signals as a function of time shift between them

correlation can detect where 2 signals are similar

The diagram shows two similar signals.

When the two signals are similar in shape and unshifted with respect to each other, their product is all positive. This is like constructive interference, where the peaks add and the troughs subtract to emphasise each other. The area under this curve gives the value of the correlation function at point zero, and this is a large value.

As one signal is shifted with respect to the other, the signals go out of phase - the peaks no longer coincide, so the product can have negative going parts. This is a bit like destructive interference, where the troughs cancel the peaks. The area under this curve gives the value of the correlation function at the value of the shift. The negative going parts of the curve now cancel some of the positive going parts, so the correlation function is smaller.

The largest value of the correlation function shows when the two signals were similar in shape and unshifted with respect to each other (or 'in phase'). The breadth of the correlation function - where it has significant value - shows for how long the signals remain similar.

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