Take the 2-minute tour ×  I'm trying to understand a few
concepts about Fourier Transforms (mainly in the context of
signal processing).  Let's suppose a signal is sampled at 10kHz
and that the FFT size is 1000. If 1000 samples are processed
through this FFT (real only, assuming rectangular window), and
if we take the amplitude of the result (first half only and
discarding the phase), this gives 500 bins of width 10Hz (except
the first one), since the maximum/Nyquist frequency is 5000Hz.
• bin 0, centered at 0Hz goes from 0Hz to 5Hz   • bin 1,
centered at 10Hz goes from 5Hz to 15Hz   • bin 2, centered at
20Hz goes from 15Hz to 25Hz   • bin 3, centered at 30Hz goes
from 25Hz to 35Hz   • (and so on...)  Although such a spectrum
can be plotted as a line, I tend to think of this as a
histogram, some sort of "integral" (I'm using this term loosely,
feel free to correct me), representing the energy falling within
the range of each bin.  Following this, if the goal was to find
the energy corresponding to a wider