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Farrow Structure for Variable Delay FIR Filters

Evaluate polynomial in $ \Delta$ using Horner's rule:

$\displaystyle {\hat X}_{n-\Delta}(z) = X + \Delta\left[C_1 X
+ \Delta\left[C_2 X +
+ \Delta\left[C_3 X + \cdots \right]\right]\right],
$

$ \Rightarrow$ filter structure becomes
\epsfig{file=eps/farrow.eps,width=1.1\textwidth }
As delay $ \Delta$ varies, ``basis filters'' $ C_k(z)$ remain fixed
$ \Rightarrow$ very convenient for changing $ \Delta$ over time


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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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