I have a characteristic function of a standard normal distribution function exp(-1/2ω^2) and want to use ifft to recover back to its original form in the real space. Imposing the Nyquist relation to the grid sizes in the x- and ω-domains, ∆x · ∆ω ≡ 2π/N is crucial here, but I messed up something in my codes. It would be great if you could teach how to do it.
Here are my codes:
x_min = -10.0; x_max = 10.0;
char_exp_factor = exp((-0.5*(sigma*w).^2));
pdf doesn't look like a normal probability density function at all.