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Zero Padding in the Time Domain

Unlike time-domain interpolation [270], ideal spectral interpolation is very easy to implement in practice by means of zero padding in the time domain. That is,

$\textstyle \parbox{0.8\textwidth}{\emph{Zero padding} in the time domain corresponds to \emph{ideal
interpolation} in the frequency domain.}$
Since the frequency axis (the unit circle in the $ z$ plane) is finite in length, ideal interpolation can be implemented exactly to within numerical round-off error. This is quite different from ideal (band-limited) time-domain interpolation, in which the interpolation kernel is sinc$ (\pi f_st)$ ; the sinc function extends to plus and minus infinity in time, so it can never be implemented exactly in practice.3.9

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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
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Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University