UploadFile_6417

Analog-to-Digital Filter Transformations 441
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 8.28
Digital Chebyshev-II lowpass filter using bilinear transformation
>> OmegaP = (2/T)*tan(wp/2); % Prewarp Prototype Passband freq
>> OmegaS = (2/T)*tan(ws/2); % Prewarp Prototype Stopband freq
>> % Analog Elliptic Prototype Filter Calculation:
>> [cs,ds] = afd_elip(OmegaP,OmegaS,Rp,As);
*** Elliptic Filter Order = 3
>> % Bilinear transformation:
>> [b,a] = bilinear(cs,ds,Fs); [C,B,A] = dir2cas(b,a)
C = 0.1214
B = 1.0000 -1.4211 1.0000
1.0000 1.0000 0
A = 1.0000 -1.4928 0.8612
1.0000 -0.6183 0
The desired filter is a 3rd-order filter with system function
H(z) = 0.1214 ( 1 − 1.4211z −1 + z −2)( 1+z −1)
(1 − 1.4928z −1 +0.8612z −2 )(1− 0.6183z −1 )
The frequency response plots are given in Figure 8.29. Note that the bilinear
transformation has again properly designed the elliptic digital filter. □
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.