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Analog-to-Digital Filter Transformations 433
1
0.8913
Magnitude Response
1
Phase Response
|H|
π units
0
0.1778
0
0 0.2 0.3 1
frequency in π units
−1
0 0.2 0.3 1
frequency in π units
0
1
Magnitude in dB
15
Group Delay
decibels
15
Samples
10
5
0 0.2 0.3 1
frequency in π units
0
0 0.2 0.3 1
frequency in π units
FIGURE 8.24
Digital elliptic lowpass filter using impulse invariance design
>> % Analog Prototype Specifications: Inverse mapping for frequencies
>> T = 1; % Set T=1
>> OmegaP = wp / T; % Prototype Passband freq
>> OmegaS = ws / T; % Prototype Stopband freq
>> % Analog Elliptic Prototype Filter Calculation:
>> [cs,ds] = afd_elip(OmegaP,OmegaS,Rp,As);
*** Elliptic Filter Order = 3
>> % Impulse Invariance transformation:
>> [b,a] = imp_invr(cs,ds,T); [C,B,A] = dir2par(b,a);
From the frequency response plots in Figure 8.24 we clearly observe that once
again the impulse invariance design technique has failed.
□
The advantages of the impulse invariance mapping are that it is a
stable design and that the frequencies Ω and ω are linearly related. But
the disadvantage is that we should expect some aliasing of the analog
frequency response, and in some cases this aliasing is intolerable.
Consequently, this design method is useful only when the analog filter
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