Convolution and Impulse Signals

[cshum00]

I am a little confused about convolutions.

I know that convolution is the multiplication and then integral of the two signals. The confusion starts at the commutative property. If i try to change the time-shift from signal to another for any 2 general functions or equations the commutative property doesn't work out.

for example:
let x(t) = sin(t)
and h(t) = t^2

If you try to convolve the signals above with the commutative property you get 2 different results.

However, the convolution's commutative property does work out if h(t) were to be a impulse function. So, does it mean that convolution is only an integral between an impulse signal and a generic signal and not two generic signals? (which is the part i am confused because i have seen examples of convolving 2 different signals)

 

[marcusl]

I'm not sure what you are referring to. This article shows how convolutions are symmetric
http://en.wikipedia.org/wiki/Convolution"
Scroll down to "Definitions" for the commutative property.