## Section12.7Using Technology to Calculate and Graph Fourier Transforms

The code below will allow you to calculate and plot the Fourier transform of an input function of your choice. The default input function is the Gaussian $$f(x)=e^{-x^2}\text{.}$$

pretty_print_default(True)
k=var('k')
f=exp(-x^2)
F=1/sqrt(2*pi)*integrate(f*exp(-i*k*x),x,-infinity,infinity)
F

plot(F,(k,-5,5))


You might also want to try the Fourier transform calculator at Wolfram Alpha. 1

www.wolframalpha.com/input/?i=Fourier+transform+calculator