Farrow Structure for Variable Delay FIR Filters

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

$${\hat X}_{n-\Delta}(z) = C_0 X + \Delta\left[C_1 X + \Delta\left[C_2 X + \cdots + \Delta\left[C_3 X + \cdots \right]\right]\right],$$

$\Rightarrow$ filter structure becomes

As delay $\Delta$ varies, ``basis filters'' $C_k(z)$ remain fixed
$\Rightarrow$ very convenient for changing $\Delta$ over time