import scipy.fftpack as Fourier
@interact
def discrete_fourier(f = input_box(default=sum([sin(k*x) for k in range(1,5,2)])), scale = slider(.1,20,.1,5)):
pbegin = -float(pi)*scale
pend = float(pi)*scale
html("<h3>Function plot and its discrete Fourier transform</h3>")
show(plot(f, (x,pbegin, pend), plot_points = 512), figsize = [4,3])
f_vals = [f(x=ind) for ind in srange(pbegin, pend,(pend-pbegin)/512.0)]
my_fft = Fourier.fft(f_vals)
show(list_plot([abs(i) for i in my_fft], plotjoined=True), figsize = [4,3])
