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414 Chapter 8 IIR FILTER DESIGN
Now we can determine H a(s).
α = 1 ɛ + √1+ 1 ɛ 2 =4.1702
(
N
a =0.5
√ α − N√ )
1/α =0.3646
(
N
b =0.5
√ α + N√ )
1/α =1.0644
There are four poles for H a(s):
[ π
p 0,3 =(aΩ c) cos
2 + π ] [ π
± (bΩ c) sin
8 2 + π ]
= −0.0877 ± j0.6179
8
Hence
[ π
p 1,2 =(aΩ c) cos
2 + 3π ] [ π
± (bΩ c) sin
8
2 + 3π ]
= −0.2117 ± j0.2559
8
H a(s) =
0.03829
{ }} {
K
0.89125 × .1103 × .3895
=
3∏
(s 2 +0.1754s +0.3895) (s 2 +0.4234s +0.1103)
(s − p k )
k=0
Note that the numerator is such that
H a(j0) =
1
√
1+ɛ
2 =0.89125
□
8.3.8 MATLAB IMPLEMENTATION
Using the U chb1ap function, we provide a function called afd chb1 to
design an analog Chebyshev-II lowpass filter, given its specifications. This
is shown below and uses the procedure described in Example 8.5.
function [b,a] = afd_chb1(Wp,Ws,Rp,As);
% Analog Lowpass Filter Design: Chebyshev-1
% -----------------------------------------
% [b,a] = afd_chb1(Wp,Ws,Rp,As);
% b = Numerator coefficients of Ha(s)
% a = Denominator coefficients of Ha(s)
% Wp = Passband edge frequency in rad/sec; Wp > 0
% Ws = Stopband edge frequency in rad/sec; Ws > Wp > 0
% Rp = Passband ripple in +dB; (Rp > 0)
% As = Stopband attenuation in +dB; (As > 0)
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