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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).
\includegraphics[width=0.9\twidth]{eps/tlagrange-5-ar}
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.
\includegraphics[width=0.9\twidth]{eps/tlagrange-5-pd}
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.
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