I'm trying to do an FFT of some data (a Gaussian pulse), but I'm finding a strange result. The real and imaginary components of the resultant FFT alternate in sign every index of the array. The absolute values of the arrays, however, are continuous. So, I get something that looks like this:
Does anybody have an idea on what is causing this? Thanks!
Alternating signs in the frequency domain corresponds to an exp(j*pi*n) complex factor which by the shift theorem corresponds to a time domain circular shift of N/2 samples. Looking at your time domain Gaussian pulse you should notice that the peak indeed appears at N/2 instead of index 0.
Shifting back your time domain Gaussian pulse with fftshift should give you a pulse centered at 0 whose frequency domain representation does not have this sign alternation.
