Heuristic Search Method for Digital IIR Filter Design - WSEAS

Magnitude
Magnitude
Magnitude
Magnitude
WSEAS TRANSACTIONS on SIGNAL PROCESSING
Ranjit Kaur, Manjeet Singh Patterh,
J. S. Dhillon, Damanpreet Singh
Table 2
Prescribed Design Conditions on LP, HP, BP and BS Filters.
Filter type Pass-band Stop-band Maximum Value of H( , x)
Low-Pass
High-Pass
Band-Pass
Band-Stop
0 0. 2
0 .3
1
0 .8
0 0. 7
1
0 0. 25
0.4 0. 6
0 .75
1
0 0. 25
0 .75 0.4 0. 6
1
1.2
1
Heuristic Method
1.2
1
TIA Approach
0.8
0.8
0.6
0.4
0.2
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normailzed Frequency
0.6
0.4
0.2
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normailzed Frequency
1.2
1
HTGA Approach
1.2
1
Method of Tang et al.
0.8
0.8
0.6
0.4
0.2
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normailzed Frequency
0.6
0.4
0.2
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normailzed Frequency
Fig. 7 Frequency responses of low pass filter using the Heuristic approach and the method given in [21], [23] and [10] respectively.
Method
Heuristic
Approach
TIA Approach
[21]
HTGA
Approach [23]
Method of Tang
et al.[10]
L1-norm
error
4.1145 0.4107
4.2162 0.4380
4.2511 0.4213
4.3395 0.5389
Table 3
Design Results for Low Pass Filter.
L2-norm Pass-band performance
error
(Ripple magnitude)
j
0.9246
H ( e ) 1.011
(0.0871)
j
0.9012
H ( e ) 1.000
(0.0988)
j
0.9004
H ( e ) 1.000
(0.0996)
j
0.8870
H ( e ) 1.009
(0.1139)
Stop-band performance
(Ripple magnitude)
j
H ( e ) 0.1238
(0.1238)
j
H ( e ) 0.1243
(0.1243)
j
H ( e ) 0.1247
(0.1247)
j
H ( e ) 0.1802
(0.1802)
E-ISSN: 2224-3488 132 Issue 3, Volume 8, July 2012