- 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.

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