# Convolution

Started by April 11, 2006
```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
```
```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

```
```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

```