Order 5 over a range of fractional delays

Figures 4.17 and 4.18 show amplitude response and phase delay, respectively, for 5th-order Lagrange interpolation, evaluated over a range of requested delays between $2$ and $3$ samples in steps of $0.1$ samples. Note that the vertical scale in Fig.4.17 spans $100$ dB while that in Fig.4.15 needed less than $9$ dB, again due to the constrained zero at half the sampling rate for odd-order interpolators at the half-sample point.

Figure 4.17: Amplitude responses, Lagrange interpolation, order 5, for the range of requested delays $[2.0 : 0.1 : 3.0]$ , with $2.495$ and $2.505$ included as well (see next plot for why).

Figure 4.18: Phase delays, Lagrange interpolation, order 5, for the range of requested delays $[2.0 : 0.1 : 3.0]$ , with $2.495$ and $2.505$ included as well.

Notice in Fig.4.18 how suddenly the phase-delay curves near 2.5 samples delay jump to an integer number of samples as a function of frequency near half the sample rate. The curve for $2.495$ samples swings down to 2 samples delay, while the curve for $2.505$ samples goes up to 3 samples delay at half the sample rate. Since the gain is zero at half the sample rate when the requested delay is $2.5$ samples, the phase delay may be considered to be exactly $2.5$ samples at all frequencies in that special case.