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