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 and samples in steps of samples. Note that the vertical scale in Fig.4.17 spans dB while that in Fig.4.15 needed less than 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 , with and included as well (see next plot for why).

Figure 4.18: Phase delays, Lagrange interpolation, order 5, for the range of requested delays , with and 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 samples swings down to 2 samples delay, while the curve for 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 samples, the phase delay may be considered to be exactly samples at all frequencies in that special case.