# Understanding FFT bin resolution

For a signal sampled at $f_s$, the frequency resolution (or "bin width") for an $N$ point FFT is $f_s/N$. Does this mean that the $k$th bin will contain energy from sinusoids within $0.5f_s/N$ on either side of the center frequency of that bin (ignoring spectral leakage for now)? Is this energy averaged? Is it the same as taking a $2N$ point FFT and then averaging every two bins?

• You can't "ignore spectral leakage for now", because that is exactly the point here. – chirlu Sep 9 '13 at 2:21
• @chirlu Does a longer FFT length imply lesser leakage from $f_1$ into $f_2$? – user5400 Sep 9 '13 at 4:02
• Not necessarily. See hotpaw2 answer below: the "leakage" is given by a Sinc function which in turn is determined by the FFT length. Since the Sinc function isn't monotonous, leakage at certain frequencies can actually increase with FFT length – Hilmar Sep 9 '13 at 14:47
• is N the number of samples in time series? – user16307 Oct 20 '15 at 14:02