Farrow Structure Coefficients

Beginning with a restatement of Eq. (4.9),

we can express each FIR coefficient as a vector expression:

Making a row-vector out of the FIR coefficients gives

or

We may now choose a set of parameter values over which an optimum approximation is desired, yielding the matrix equation

where

Equation (4.11) may be solved for the polynomial-coefficient matrix by usual least-squares methods. For example, in the unweighted case, with , we have

Note that this formulation is valid for finding the Farrow coefficients of any th-order variable FIR filter parametrized by a single variable . Lagrange interpolation is a special case corresponding to a particular choice of .

In MATLAB, the function `fdesign.fracdelay` can be used to design
Farrow structures for fractional delay.

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