Fourier transform of a Gaussian is not a Gaussian, but thats wrong! - Python

Question

I am trying to utilize Numpy\'s fft function, however when I give the function a simple gausian function the fft of that gausian function is not a gausian, its close but its

Answer 1

Your result is not even close to a Gaussian, not even one split into two halves.

To get the result you expect, you will have to position your own Gaussian with the center at index 0, and the result will also be positioned that way. Try the following code:

from pylab import *
N = 128
x = r_[arange(0, 5, 5./N), arange(-5, 0, 5./N)]
y = exp(-x*x)
y_fft = fft(y) / sqrt(2 * N)
plot(r_[y[N:], y[:N]])
plot(r_[y_fft[N:], y_fft[:N]])
show()

The plot commands split the arrays in two halfs and swap them to get a nicer picture.