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First-Order Allpass Interpolation


\begin{eqnarray*}
{\hat x}(n-\Delta) \mathrel{\stackrel{\mathrm{\Delta}}{=}}y(n) &=& \eta \cdot x(n) + x(n-1) - \eta \cdot y(n-1) \\
&=& \eta \cdot \left[ x(n) - y(n-1)\right] + x(n-1)
\end{eqnarray*}

$\displaystyle H(z) = \frac{\eta + z^{-1}}{1 + \eta z^{-1}}
$

Intuitively, ramping the coefficients of the allpass gradually ``grows'' or ``hides'' one sample of delay. This tells us how to handle resets when crossing sample boundaries (sufficiently slowly).


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``Bandlimited Interpolation, Fractional Delay Filtering, and Optimal FIR Filter Design'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2014-03-24 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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