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I'm working on some practice examples and in one of them I'm asked to find the convolution and the correlation of some signal pairs given. I know that correlation , given two signals x(n),g(n), is given by the following : $$Φ_{xg}=x(n)\ast g(-n)$$ where asterisk is convolution. Now is this the same as $$g(n)\ast x(-n)$$

I think I read this somewhere $$Φ_{xy}(n)=Φ_{yx}(-n)$$ So the 2 convolutions give different results. Shouldn't the question specify which correlation I am to calculate? $$Φ_{xy}\\Φ_{yx}$$

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You are correct in noting that cross-correlation is not commutative. If the question says "correlation between two signals $x$ and $g$" then it is usually assumed that you go in that sequence and compute $\Phi_{xg}$.

Or you can choose to say that the question and ambiguous compute both $\Phi_{xg}$ and $\Phi_{gx}.$

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