What causes broadening or finite width of harmonic peaks in a Fourier transform?
If a signal is perfectly periodic (i.e. repeats exactly after a period T) and infinitely long, we might expect its Fourier transform to have infinitey narrow peaks at frequency f = 1/T and the other harmonics 2f, 3f etc. When we sample such a signal and use a program to calculate the Fourier transform, we obtain peaks of finite width. (If we sample a signal with vibrato we might see even broader peaks, but let’s restrict this to a strictly periodic signal.) In fact, we could get very narrow peaks if we did one of two things. First, we could use a very long signal and a very long sample window for the transform. This would give narrow peaks, going to zero width as the signal and window length approached infinity. Second, we could use a window whose length was exactly an integral number of periods nT. (Of course, without having performed a Fourier transform on a very long sample we don’t know exactly what T is…) In practice, we rarely do either of these: even if the software used for t
