Implementing the basic Fourier-Transformation
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?