I am attempting to numerically invert the characteristic function F(y) of the normal distribution using the FFT. I have discretised the integral into a form consistent with FFT. As a first step I am computing this integral by calculating the sums (i.e. not using the FFT). My problem is that when I increase the number of terms N in the sum, the plot of the approximate PDF f(x) gets thinner and thinner and obviously does not approach the true PDF. I am not sure if I have made an error in the mathematics or in the code (please see attached file).
Any help would be appreciated,
Attachment: Question.nb, URL: ,