Periodic signals always go smoothly to zero at their boundaries. Random ``snippets'' of signals typically do not.
As a result, discontinuous signal boundaries produce a ``smearing'' of the frequency content estimation of the DFT.
One way to reduce some of these problems is to multiply the extracted audio signal x[n] by time-domain functions which themselves go smoothly to zero at their edges.
From the heterodyning interpretation of the DFT above, this would mean that the very narrow-band lowpass filter (which corresponds to a rectangular window) is replaced by the frequency-domain correlate of the new time-domain window.
It turns out that in all cases, smooth time-domain windows result in less-narrow frequency-domain filters (in which case more spurious surrounding spectral components might leak into an estimate of a sinusoidal weight).
At the same time, however, the smooth time-domain window greatly minimizes the amount of spectral ``splatter'' across the spectrum and promotes a more accurate frequency estimation.
A wide variety of windows have been investigated and reported for just this purpose.