#### Farrow Structure

Taking the *z* transform of Eq.(4.9) yields

Since is an th-order FIR filter, at least one of the must be th order, so that we need . A typical choice is .

Such a parametrization of a variable filter as a polynomial in
*fixed* filters is called a *Farrow structure*
[134,502]. When the polynomial Eq.(4.10) is
evaluated using *Horner's rule*,^{5.5} the efficient structure of
Fig.4.19 is obtained. Derivations of Farrow-structure
coefficients for Lagrange fractional-delay filtering are introduced in
[502, §3.3.7].

As we will see in the next section, Lagrange interpolation can be implemented exactly by the Farrow structure when . For , approximations that do not satisfy the exact interpolation property can be computed [148].

**Next Section:**

Farrow Structure Coefficients

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Polynomials in the Delay