This is just a curious doubt. What is the statistical significance of convolution? For instance, we define the auto correlation in terms of expectation as R(u) = E(X.Xu). Similarly, do we have any expression for convolution of two signals? Can I have it as something like (sorry, if it is completely absurd): Conv(Xu, Yv) = E(Xu-v.Yu) - Krishna

# Convolution

Started by ●April 11, 2006

Reply by ●April 11, 20062006-04-11

krishna_sun82 skrev:> This is just a curious doubt. What is the statistical significance of > convolution? For instance, we define the auto correlation in terms of > expectation as > R(u) = E(X.Xu). > Similarly, do we have any expression for convolution of two signals? Can I > have it as something like (sorry, if it is completely absurd): > Conv(Xu, Yv) = E(Xu-v.Yu)Formally, yes, convolution and correlation are similar operations. The only difference is that in convolution, the direction of one of the signals is reverted. Convolution between a random variable and a deterministic function serves the purpose of modifying the temporal correlation between samples in a random sequence. This is the key behind whitening filters and ARMA modelling. I can't remember, off the top of my head, that the convolution between two random variables serve any particular purpose, though. Rune

Reply by ●April 11, 20062006-04-11

Something that is probably of interest would be the convolution of pdfs of two random variables which would be the joint pdf of X+Y, whereX, Y are random variables. Regarding the original question, it is common to see correlation and convolution as similar operations especially while coding. You may have single function for both operations but in the case of convolution one of the input arrays would be mirrored Nithin