%This uses the FFT to compute F[\frac{e^{-t^2/2}}{\sqrt{2\pi}}]=e^{-\omega^2/2}=e^{-2\pi^2f^2}$.
%Assuming: \frac{e^{-t^2/2}}{\sqrt{2\pi}}\approx 0 for |t|>4 since \frac{e^{-4^2/2}}{\sqrt{2\pi}}=0.00013 and
%Assuming: e^{-2\pi^2f^2}\approx 0 for |f|>0.6 since e^{-2\pi^20.6^2}=0.00082.
%Using the above assumptions, we have the following:
%T=2(4)=8 and Delta f=1/8=0.125; and F=2(0.6)=1.2 and Delta t=1/1.2.
%N=TF=(8)(1.2)=9.6. Round N up to 10 by rounding F up to 1.25 and Delta t down to 1/1.25=0.8.
clear;T=[-4:0.8:3.2];F=[-0.625:0.125:0.5];X=exp(-T.*T/2)/sqrt(2*pi);FX=exp(-2*pi*pi*F.*F);
FY=fftshift(abs(fft(X)))/1.25;plot(F,FX,'o',F,FY,'+'),grid on,title('Exact: blue circles. Computed: red crosses.')
