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Lagrange Interpolation Coefficients
Orders 1, 2, and 3

\begin{displaymath}
\begin{array}{\vert\vert r\vert\vert c\vert c\vert c\vert c\vert}
\hline
h_\Delta{Order} & h_\Delta(0) & h_\Delta(1) & h_\Delta(2) & h_\Delta(3) \\
\hline
\hline
N=1 & 1-\Delta & \Delta & & \\
\hline
N=2 & \frac{(\Delta-1)(\Delta-2)}{2} & -\Delta(\Delta-2) & \frac{\Delta(\Delta-1)}{2} & \\
\hline
N=3 & -\frac{(\Delta-1)(\Delta-2)(\Delta-3)}{6} & \frac{\Delta(\Delta-2)(\Delta-3)}{2} & -\frac{\Delta(\Delta-1)(\Delta-3)}{2} &
\frac{\Delta(\Delta-1)(\Delta-2)}{6} \\
\hline
\end{array}\end{displaymath}


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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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