Page 90 - Analog and Digital Filter Design

87
Poles and Zeroes

The pole-zero diagram for such an Inverse Chebyshev filter is shown in Figure
3.2. The 3dB cutoff point for a filter with these pole positions is 0.47233radls.

1 Q"

Figure 3.2
Pole Zero Diagram for Inverse -' 0
Chebyshev Filter

One of the most obvious differences is that the poles are nowhere near the unit
circle. This is because of the way in which their positions are calculated, to give
a stopband rather than the 3 dB attenuation point, starting at w = 1. When cor-
rected to give a 3dB point at w = 1, the pole and zero positions change. The
zeroes move to k~2.8228, the poles become -1.1342 and -0.4666 kfl.917. These
are plotted as shown in Figure 3.3.

I

Figure 3.3
Normalized Inverse Chebyshev
Pole Zero Diagram