Digital Filters - Digital Signal Processing: A Practitioner's Approach - page 55

0

-50

< --- r = 0.3

-100

< --- r = 0.95

-150

-200

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Figure 3.11 Phase of a first-order all-pass filter

0

< --- r = 0.95

-100

< --- r = 0.3

-200

-300

-400

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Figure 3.12 Phase of a second-order all-pass filter

The phase shown in Figure 3.11 is for a real-pole filter. Notice the sensitivity of r in
controlling phase, and notice that between 50 samples/cycle and 4 samples/cycle
the filter is very effective at controlling the phase. Figure 3.12 shows the phase of a
complex all-pass filter and its sensitivity to the radial pole position.

3.5.1 Interpolation of Data Using an APF
A typical data acquisition system with more than one signal has the structure given
in Figure 3.13. This structure is chosen for economy and to make best use of the
A/D converter's bandwidth.

Figure 3.13 Phase shift in the data acquisition