A problem about the FFT of Gauss pulse

[mvamjs]

     I write a programme to computed the fourier transform of a function .But now I meet a problem .We know a gauss
pulse f(t)=exp(-(t/a)^2),thus the amplitude spectrum is F(w)=(pi^(1/2))*a*exp(-(w*a/2)^2),it is also a gauss
function and the phase spectrum is zero.But I used labview FFT. vi to simulate this process .The amplitude spectrum
is right but the phase spectrum is not zero,why? Can someone help me.

[johnsold]

I noticed that the phase values seemed to be changing rapidly and by increments near pi.  I added an Unwrap Phase VI and found that the phase seems to be much better behaved (although not constant) when viewed that way.

As for why the phase does not match your expectations, I do not have a good answer.

I moved several unvarying calcuations outside the For loop - no need to repeat them when the result does not change. I also replaced your formula nodes with native LV functiosn to see if the effects were due to some roundoff or numerical calculation effects.  The results are about the same.  I tried changing the 1E15 to 1, again looking for numerical effects but did not find anything.

Lynn

[Darin.K]

Keep in mind that the FFT is not approximating the Fourier Transform of the input waveform, but rather the FT of the periodically extended waveform. The Gaussian pulse has finite amplitude over infinite time so a discrete approximation is not going to exactly match the continuous result.

An alternative could be numeric approximation of the Fourier Transform integral.