# Implementing the basic Fourier-Transformation

Hi there!

I'm currently plaing around with sage and I'm really excited about it.

I'd love to do my computations at university and home with a neat opensource-tool instead of the higly prices closed competitors.

Now, the problem I am facing is the symbolif computation of a fourier transformation.

Below is my current naive approach (I'm still learning fourier and complex mathematics, but with large interest!)

```
x,w,f_0,t = var("x,w,f_0,t")
w = 2*pi*f_0
x(t) = sin(w*t)
integrate(x*exp(-I*w*t),t, -oo, oo)
```

which results in the following (obviously equal) result:

```
integrate(e^(-2*I*pi*f_0*t)*sin(2*pi*f_0*t), t, -Infinity, +Infinity)
```

My expectiation would be an equation without the t (since it has been substituted through integration) and an floating f_0 which I can set according to my desired sine frequency.

Please, could someone tell me, what exactly I am missing here?

Greetings Jakob