I used a matrix to calculate the fourier transform of a lorentzian and it did generate a decaying exponential but that was followed by the mirror image of the exponential going up. I am referring to the real part of the exponential. If I use an fft instead I also see this. Shouldn't the result be just a decaying exponential? Also the fft shows an imaginary component whereas my matrix does not. I don't think there should be an imaginary component since the lorentzian is an even function centered at zero. Perhaps the fft does not treat it as centered at zero. So I have two questions, one is why is the exponential going up in the second half of the real part and why does the fft show an imaginary part that the matrix method does not show?