Valuable property when used in a feedback loop

The amplitude response of Lagrange interpolation is always less than 1 when the desired delay $D$ lies within the middle half of the coefficient span [511, p. 92]:

$$\begin{eqnarray*} && \frac{N-1}{2} \le D \le \frac{N+1}{2}\quad\mbox{($N$\ odd)}\\ && \frac{N}{2}-1 \le D \le \frac{N}{2}+1\quad\mbox{($N$\ even)} \end{eqnarray*}$$

Note that even-order interpolators have a two-sample ``passive'' range, while odd-order interpolators have only a one-sample passive range.