convolution of Gaussian pulses

[purnapragna]

What is the final result if i convolve two Gaussian pulses i.e.,
\[e^{-t^2}*e^{-t^2}=\]?
If i convolve for \[n\] times what is the result?

thnx

purna!\]

 

[sivani_vs]

it will be again gaussian I suppose. but i didnot understand the term n times.

 

[flatulent]

One interesting thing is that if you convolve a large number of randomly shaped pulses the result will tend towards gaussian as the number of them becomes larger.

You can prove the gaussian pulse example by knowing that convolution in one domain is multiplication in the other.