1. ## Fourier transform

The problem is:

Find the fourier transform of:

$\displaystyle f(t)=\int{cos(t)*e^{-t^2}}$

My question is: can i solve this problem using convolution, and how? I have some problems understanding when to apply convolution, can I choose
$\displaystyle f(t)=g(t)*h(t)$ with $\displaystyle g(t)=cos(t)$ and $\displaystyle h(t)=e^{-t^2}$, and then say that $\displaystyle F(f) = F(g*h) = \sqrt{2*Pi}*F(g)*F(h)$ ?
Or is this completely wrong?

2. Originally Posted by dreamsound
The problem is:

Find the fourier transform of:

$\displaystyle f(t)=\int{cos(t)*e^{-t^2}}$

My question is: can i solve this problem using convolution, and how? I have some problems understanding when to apply convolution, can I choose
$\displaystyle f(t)=g(t)*h(t)$ with $\displaystyle g(t)=cos(t)$ and $\displaystyle h(t)=e^{-t^2}$, and then say that $\displaystyle F(f) = F(g*h) = \sqrt{2*Pi}*F(g)*F(h)$ ?
Or is this completely wrong?
Is $\displaystyle f(t)=\int{cos(t)*e^{-t^2}}$ meant to repesent the convolution of $\displaystyle \cos(t)$ and $\displaystyle e^{-t^2}$ ? (Your notation is poor if that's the case). If so, there is a standard operational theorem for finding the Fourier transform of the convolution of two functions.

Otherwise, please post the question exactly as it's worded and with the exact notation used.

3. Sorry, i now see that my notation might be confusing.

A better notation is:
$\displaystyle f(t)=\int{cos(t)e^{-t^2}}$
i.e. it's just ordinary multiplication...