01 September 2016

Correlation vs Convolution

This is a basic relationship in DSP.

When we talk about similarity between signals, we normally talk about "correlation".
When we talk about filtering, in the time domain that's a "convolution".

Correlation and convolution are basically the same thing.
The only difference is that correlation is a convolution by the inverted (or flipped) version of the same signal in the time domain:

y(n) = h(n)*x(n) --> convolution
y(n)=h(n)*x(-n) -> correlation

In Matlab/Octave that would be:

y = conv( h, x) for convolution


y = conv( h, flip(x)) for correlation.

In the frequency domain, the operation of flipping in the time domain translates into the "conjugate" version of the transform, that is with an inverted sign for its imaginary part.

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