Relationship between Cross-Correlation and Convolution

[tomizzo]

Hi there,

I've recently been looking into applications of cross-correlation in the context of signal processing. I've noticed that the mathematical operations that yield the cross correlation between two signals is very similar to the operations in calculating the convolution of a signal and system.

Referring to Wikipedia, it looks like the only difference between the cross-correlation and convolution operation is the sign in which one of the functions is horizontally shifted.

My question: Is there a meaningful difference between the mathematical operations in calculating the cross-correlation vs convolution, or is the primary difference the interpretation of the result (i.e. cross-correlation shows similarity between signals while convolution is typically used for computing a system output based upon its impulse response and an inputted signal)?

Thanks!

 

[mathman]

Both involve the integration of the product of two functions related to signal distribution, but they are different.

 

[ytht100]

Just my short input, may not be correct:
Not very sure what you meant "meaningful difference", but your judgements of the only mathematical difference between them and the physical interpretation are correct.