Polynomials in the Delay

A more parametric approach is to formulate each filter coefficient $h_\Delta(n)$ as a polynomial in the desired delay $\Delta$ :

$$h_\Delta(n) \isdefs \sum_{m=0}^{N_c}c_n(m)\Delta^m, \quad n=0,1,2,\ldots,N \protect$$ (5.9)

Taking the z transform of this expression leads to the interesting and useful Farrow structure for variable FIR filters [135].