# The science of pearson product moment correlation coefficient

I need to compare two sound signals for similarity, I took cross-correlation of both the signals and I got a cross-correlation signal, now I intend to use pearson correlation coeff formula to get the coeff out of it, by looking to the below formula it seems that I dont need to explicitly perform the cross-correlation since the formula takes both the signal arrays in the form of x and y, and it seems that the formula does both the things 1) perform the cross-correlation 2) calculate the correlation coeff. Am I right in understanding it?

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Of course, this assumes you know what you are doing: i.e. this assumes that $X_i$ and $Y_i$ are samples of some random variable, and that you are interested in getting a scalar correlation. If you are dealing instead with a temporal correlation function, that's other thing.