Variable FIR Interpolating Filter

Basic idea: Each FIR filter coefficient $h_n$ becomes a polynomial in the delay parameter $\Delta$:

$$\begin{eqnarray*} h_\Delta(n) &\mathrel{\stackrel{\mathrm{\Delta}}{=}}& \sum_{m=... ...el{\stackrel{\mathrm{\Delta}}{=}}& \sum_{m=0}^P C_m(z) \Delta^m \end{eqnarray*}$$

• More generally: $H_\Delta(x) = \sum_m \alpha(\Delta)C_m(z)$
  where $\alpha(\Delta)$ is provided by a table lookup
• Basic idea applies to any one-parameter filter variation
• Also applies to time-varying filters ( $\Delta\leftarrow t$)