easy way to convolve a function

thomitsu

Hallo there!

I was wondering wether there is an easy way to convolve a function with itself.
For example is ther an easy formula or something that gives directly the result?
thanks in advance

thomitsu

for example, for correlation...

The correlation of a function with itself is called its autocorrelation
In this case the correlation theorem becomes
the transform pair
– This is the Wiener-Khinchin Theorem
Corr(g,g)↔G( f )G*( f ) = G( f )^2

Is there something like that for convolution???

mathman

I don't know if it helps any, but take the Fourier transform of the function, square the transform, and take the inverse transform of the result.

thomitsu

Oh god! This is so complicated( my function is a squared bessel function)!! I will try it though.thank you so much!