Fourier Transform of Gaussian

Problem

The Fourier transform of the Gaussian e^(-a*x^2) is sqrt(pi/a) * e^(-omega^2/(4a)).

Since the transform is real and positive, its magnitude equals its value. Given a > 0 and the angular frequency omega, return that magnitude.

Hint

A Gaussian transforms to a Gaussian: wider in x means narrower in frequency.

case 1

in: [1,0]

expected: 1.7724538509055159

case 2

in: [1,1]

expected: 1.380388447043143

case 3

in: [4,0]

expected: 0.8862269254527579

case 4

in: [0.25,2]

expected: 0.06492724936026344

Starter codePython

def gaussian_ft_magnitude(a, omega):
    # Your code here
    pass

4 test cases · run your code against them in the editor