Farrow Structure
Taking the z transform of Eq.(4.9) yields
Since






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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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].
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Farrow Structure Coefficients
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Polynomials in the Delay