Page 158 - Analog and Digital Filter Design
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Highpass Filters
are on a unit circle, the denominators in the equations are equal to one. There-
fore the poles are in the same place. as shown in Figure 5.10.
Fourth-Order Butterworth Highpass
Pole Locations
The difference is that the zeroes that were at infinity in the lowpass design have
now moved to the S-plane origin. In other words. the filter does not pass DC.
Scaling nornialized highpass pole and zero locations is easy: simply multiply
them by 2nE. The zeroes stay at the origin, but the poles move outwards away
from the origin just as they did in the case of lowpass filters. This is shown in
Figure 5.1 1.
'\
New pole
location '
',\
'\
\ Zero
Original pole * unchanged
-0
Figure 5.1 1
Frequency Scaling of Pole
Location in S-Plane
