Page 281 - Analog and Digital Filter Design

278 Analog and Digital Filter Design

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P Network N Network
Order Pole Pole Error (Rads) Rejection

4 12.18077 2.137451 0.148336 22.57 dB
0.467847 0.082097
6 19.2 19302 4.706894 0.028565 36.9 dB
1.657275 0.6034
0.212454 0.052031

8 26.089973 7.271928 0.005501 51.21 dB
3.148916 1.4602 14
0.68483 1 0.31757
0.137515 0.038329
10 32.885954 9.758666 0.001059 65.52dB
4.706895 2.493038
1.353589 0.738777
0.401117 0.2 12454
0.102473 0.030408

12 39.64303 1 12.180766 0.000204 79.82dB
6.255099 3.59243
2.137452 1.28692
Table 9.17
0.777049 0.467847
Quadrature Pole 0.278363 0.15987
Locations 0.082097 0.025225
(WbIWa = 100)
Angle = 1.560796 rads-' or 89.427065 degrees
Q= 0.43883 K= 5.991589 K = 1.570836 <~~/~o
100
=
The pole locations are given by the equation:

CIZ and SIZ are the elliptic sine and cosine functions. Also,

4i+l
.
K
tLi = - for all i = 0, . . n - 1, where the order is n.
2n
This produces a set of poles Po, PI, and so on.

K is the complete elliptic integral, of modulus k, where k + sin 0, and a very
simple C program can be found to do this. A" is the complete elliptic integral,