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416 Chapter 8 IIR FILTER DESIGN
Magnitude Response
Magnitude in dB
1
0.8913
0
1
|H|
decibels
16
0.1585
0
0 0.2 0.3 0.5
Analog frequency in π units
30
0 0.2 0.3 0.5
Analog frequency in π units
1
Phase Response
0.2
Impulse Response
0.5
0.15
radians
0
ha(t)
0.1
0.05
−0.5
0
−1
0 0.2 0.3 0.5
Analog frequency in π units
−0.05
0 10 20 30 40
time in seconds
FIGURE 8.16 Chebyshev-I analog filter in Example 8.6
A Chebyshev-II filter is related to the Chebyshev-I filter through a
simple transformation. It has a monotone passband and an equiripple
stopband, which implies that this filter has both poles and zeros in the
s-plane. Therefore the group delay characteristics are better (and the
phase response more linear) in the passband than the Chebyshev-I prototype.
If we replace the term ɛ 2 T 2 N (Ω/Ω c)in(8.52) by its reciprocal and
also the argument x =Ω/Ω c by its reciprocal, we obtain the magnitudesquared
response of Chebyshev-II as
|H a (jΩ)| 2 =
1
1+[ɛ 2 T 2 N (Ω c/Ω)] −1 (8.60)
One approach to designing a Chebyshev-II filter is to design the corresponding
Chebyshev-I first and then apply these transformations. We will
not discuss the details of this filter but will use a function from MATLAB
to design a Chebyshev-II filter.
8.3.9 MATLAB IMPLEMENTATION
MATLAB provides a function called [z,p,k]=cheb2ap(N,As) to design a
normalized Chebyshev-II analog prototype filter of order N and passband
ripple As and that returns zeros in z array, poles in p array, and the gain
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