Page 218 - Anatomy of a Robot

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DIGITAL SIGNAL PROCESSING (DSP) 203
DISTORTION
The antialias filter itself will distort the very signals we are trying to measure. This
occurs because most signals are a mixture of different frequency waveforms. Only pure
sine waves contain single-frequency waveforms. Even a pure sine wave signal will get
distorted some by a filter, but signals composed of several frequency waveforms will
get distorted all the more because the different frequencies are treated differently by the
filter. We will see that even distortion can be used to our advantage if the distortion can
be predicted.
Over the years, the design of antialias filters has settled on a couple of good solu-
tions that designers can live with. A good filter will have a steep rolloff and a deep stop-
band, as shown in Figure 8-7.

ROLLOFF
The rolloff is the slope of the frequency response between the passband and the stop-
band. With an operational amplifier and a couple of components like an inductor and a
capacitor, it’s possible to get a 12 db/octave rolloff. This means that for every doubling
of the frequency, the filter attenuates the signals by a factor of 4.

STOPBAND

For a low-pass antialias filter, the stopband covers those higher frequencies that the low-
pass filter is supposed to eliminate. The stopband is the area to the right of the rolloff
curve that is dramatically lower than the low-pass frequency part of the curve.
As a rule of thumb, if the S/N ratio for the signals of interest is 40 db, we would want
all the actual high-frequency noise in the stopband to be 40 db or better down in the
stopband, such as Figure 8-7.

Good Anti-alias Filter

0.0 0.1 0.2 0.3 0.4 0.5
0 db
-20 db
-40 db
-60 db
-80 db
-100 db
-120 db

FIGURE 8-7 An imperfect but realizable antialias filter