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
![$ {\underline{\Delta}}^T=[\Delta_0,\Delta_1,\ldots,\Delta_L]$](http://www.dsprelated.com/josimages_new/pasp/img1093.png)
over which an optimum approximation is desired, yielding
the
matrix equation
 |
(5.11) |
where
![$\displaystyle \mathbf{H}_{\underline{\Delta}}\isdefs \left[\begin{array}{c} \un...
...elta_0}^T \\ [2pt] \vdots \\ [2pt] \underline{h}_{\Delta_L}^T\end{array}\right]$](http://www.dsprelated.com/josimages_new/pasp/img1095.png)
and
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

.
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