Page 221 - Anatomy of a Robot

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206 CHAPTER EIGHT
Amplitude
1.6
1.4
1.2
1
x 0.8
0.6
0.4
0.2
0
0 5 Time 10
FIGURE 8-10 The step input response of the second-order analog filter

To get the stopband down to 40 db at the Nyquist Frequency with this filter, we’d
have to increase the sampling rate by a factor of 10 or so (3 octaves ).
If we concatenate 2 such analog filters, we would get a 24 db per octave rolloff
and it would only be something less than 2 octaves to achieve the same results:

(2 octaves 24 db/octave 8 db) 40 db

To get the stopband down 40 db at the Nyquist Frequency with this filter, we’d
have to increase the sampling rate by a factor of 3.7 or so: (2 octaves ).
This would be a good trade-off since the analog filters are relatively inexpensive,
and the DSP filters can be expensive, depending on the technology used.
If we concatenate 3 such analog filters, we would get a 36 db per octave rolloff
and it would only be something more than 1 octave to achieve the same results:

(1 octave 36 db/octave 4 db) 40 db

To get the stopband down 40 db at the Nyquist Frequency with this filter, we’d
have to increase the sampling rate by a factor of 2.1 or so: (1 octave ). This, too,
would be a good trade-off. Details about analog filters can be found at
http://my.integritynet.com.au/purdic/lcfilters.htm and at www.freqdev.com/guide/
FDIGuide.pdf.