#### 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].

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Farrow Structure Coefficients

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Polynomials in the Delay