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When I take the Continuous Fourier transform of a function, I get back a very nice magnitude and phase.

When I try the exact same thing with a FFT I get back a very nice magnitude, but my phase is highly erratic. Most of the time, it is just oscillates in between two values every point (eg -[tex]\pi[/tex] and [tex]\pi[/tex] or does this on a slope. I am using the atan2 function.

If I unwrap this, the phase will go to ridiculously huge numbers.

Can someone explain if why this happens and more importantly if and how I can make the discrete phase match the continuous phase?