As a test, I am trying to compute the real component of the Fourier transform of a cosine function:
f(t) = cos(2pix)
I expect a result like this:
F(w) = (1/2) * [delta(w+1)+delta(w-1)]
Re(F(w)) = (1/2) * [delta(w+1)+delta(w-1)]
When I do the transform, the output histogram has a range on the x-axis from 0 to 100. The shape of the output looks correct: all bins have zero entries except for two bins with content = 0.5. But the x-axis should range from -1 to +1, not 0 to 100.
What is the prescription for rescaling the x-axis of the “real” transformed histogram? I see a prescription in the tutorial for “magnitude” and “phase” transformed histograms, but not for “real” or “imaginary” transformed histograms: root.cern.ch/root/html/tutorials/fft/FFT.C.html