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
1.2
1
0.8
1.2
1
0.8
0.6
0.4
0.2
Heuristic Method
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
TIA Approach
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
0.8
1.2
1
0.8
0.6
0.4
0.2
HTGA Approach
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
Method of Tang et al.
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normailzed Frequency
Fig. 10 Frequency responses of band stop filter by using the Heuristic approach and the methods 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
1.4360 0.2052
1.6119 0.2191
1.9418 0.2350
5.2165 0.6949
Table 5
Design Results for Band Pass Filter
L2-norm Pass-band performance
error
(Ripple magnitude)
j
0.9896
H ( e ) 1.004
(0.0147)
j
0.9806
H ( e ) 1.000
(0.0194)
j
0.9760
H ( e ) 1.000
(0.0234)
j
0.8956
H ( e ) 1.000
(0.1044)
Stop-band performance
(Ripple magnitude)
j
H ( e ) 0.0627
(0.0627)
j
H ( e ) 0.0658
(0.0658)
j
H ( e ) 0.0711
(0.0711)
j
H ( e ) 0.1772
(0.1772)
Method
Heuristic
Approach
TIA Approach
[21]
HTGA
Approach [23]
Method of Tang
et al. [10]
L1-norm
error
3.7699 0.4532
4.1275 0.4752
4.5504 0.4824
6.6072 0.7903
Table 6
Design Results for Band Stop Filter
L2-norm Pass-band performance
error
(Ripple magnitude)
j
0.9652
H ( e ) 1.008
(0.0434)
j
0.9560
H ( e ) 1.000
(0.0440)
j
0.9563
H ( e ) 1.000
(0.0437)
j
0.8920
H ( e ) 1.000
(0.1080)
Stop-band performance
(Ripple magnitude)
j
H ( e ) 0.1060
(0.1060)
j
H ( e ) 0.1171
(0.1171)
j
H ( e ) 0.1013
(0.1013)
j
H ( e ) 0.1726
(0.1726)
E-ISSN: 2224-3488 134 Issue 3, Volume 8, July 2012