1. Design FIR Windowing a. LPF 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 -70 -60 -50 -40 -30 -20 -10 0 Frequency (kHz) Magnitude (dB) Magnitude Response (dB) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 Frequency (kHz) Phase (radians) Phase Response 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 -70 -60 -50 -40 -30 -20 -10 0 Frequency (kHz) Magnitude (dB) Magnitude Response (dB) and Phase Response -17.6204 -15.1124 -12.6044 -10.0964 -7.5884 -5.0804 -2.5724 -0.0644 Phase (radians) Ossy Anita P ( 1203 1210 ) Jatayu Aghar ( 1203 1210 ) Yahya Rais ( 1203 1210 ) Ahmad A’an N ( 1203 1210 )
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Jul 16, 2015
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1. Design FIR Windowing
a. LPF
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-70
-60
-50
-40
-30
-20
-10
0
Frequency (kHz)
Magnitu
de (
dB
)
Magnitude Response (dB)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
Frequency (kHz)
Phase (
radia
ns)
Phase Response
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-70
-60
-50
-40
-30
-20
-10
0
Frequency (kHz)
Magnitu
de (
dB
)
Magnitude Response (dB) and Phase Response
-17.6204
-15.1124
-12.6044
-10.0964
-7.5884
-5.0804
-2.5724
-0.0644
Phase (
radia
ns)
Ossy Anita P ( 1203 1210 ) Jatayu Aghar ( 1203 1210 ) Yahya Rais ( 1203 1210 )
Ahmad A’an N ( 1203 1210 )
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Time (mseconds)
Am
plit
ude
Impulse Response
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
0
0.2
0.4
0.6
0.8
1
Time (mseconds)
Am
plit
ude
Step Response
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5
-1
-0.5
0
0.5
1
Real Part
Imagin
ary
Part
16
Pole/Zero Plot
Numerator :
b. HPF
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-70
-60
-50
-40
-30
-20
-10
0
Frequency (kHz)
Magnitu
de (
dB
)
Magnitude Response (dB)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
2
Frequency (kHz)
Phase (
radia
ns)
Phase Response
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-70
-60
-50
-40
-30
-20
-10
0
Frequency (kHz)
Magnitu
de (
dB
)
Magnitude Response (dB) and Phase Response
-19.3654
-16.3708
-13.3762
-10.3816
-7.3871
-4.3925
-1.3979
1.5967
Phase (
radia
ns)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
Time (mseconds)
Am
plit
ude
Impulse Response
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Time (mseconds)
Am
plit
ude
Step Response
Numerator :
c. BPF
-4 -3 -2 -1 0 1 2 3 4
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Real Part
Imagin
ary
Part
16
Pole/Zero Plot
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-70
-60
-50
-40
-30
-20
-10
0
Frequency (kHz)
Magnitu
de (
dB
)
Magnitude Response (dB)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
2
Frequency (kHz)
Phase (
radia
ns)
Phase Response
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-70
-60
-50
-40
-30
-20
-10
0
Frequency (kHz)
Magnitu
de (
dB
)
Magnitude Response (dB) and Phase Response
-19.5793
-16.5402
-13.501
-10.4618
-7.4227
-4.3835
-1.3444
1.6948
Phase (
radia
ns)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Time (mseconds)
Am
plit
ude
Impulse Response
Numerator :
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Time (mseconds)
Am
plit
ude
Step Response
-4 -3 -2 -1 0 1 2 3 4
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Real Part
Imagin
ary
Part
16
Pole/Zero Plot
2. Design FIR Least Square a. LPF
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-60
-50
-40
-30
-20
-10
0
Frequency (kHz)
Magnitu
de (
dB
)
Magnitude Response (dB)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
Frequency (kHz)
Phase (
radia
ns)
Phase Response
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-60
-50
-40
-30
-20
-10
0
Frequency (kHz)
Magnitu
de (
dB
)
Magnitude Response (dB) and Phase Response
-16.3004
-13.6109
-10.9214
-8.232
-5.5425
-2.8531
-0.1636
Phase (
radia
ns)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
Time (mseconds)
Am
plit
ude
Impulse Response
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
0
0.2
0.4
0.6
0.8
1
1.2
Time (mseconds)
Am
plit
ude
Step Response
-1 0 1 2 3 4 5 6 7
-1.5
-1
-0.5
0
0.5
1
1.5
Real Part
Imagin
ary
Part
16
Pole/Zero Plot
Numerator :
b. HPF
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-70
-60
-50
-40
-30
-20
-10
0
Frequency (kHz)
Magnitu
de (
dB
)
Magnitude Response (dB)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-6
-4
-2
0
2
4
Frequency (kHz)
Phase (
radia
ns)
Phase Response
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-70
-60
-50
-40
-30
-20
-10
0
Frequency (kHz)
Magnitu
de (
dB
)
Magnitude Response (dB) and Phase Response
-6.6552
-5.0873
-3.5193
-1.9514
-0.3834
1.1846
2.7525
4.3205
Phase (
radia
ns)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Time (mseconds)
Am
plit
ude
Impulse Response
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
Time (mseconds)
Am
plit
ude
Step Response
Numerator :
c. BPF
-1 0 1 2 3 4 5 6 7
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
16
Real Part
Imagin
ary
Part
Pole/Zero Plot
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-60
-50
-40
-30
-20
-10
0
Frequency (kHz)
Magnitu
de (
dB
)
Magnitude Response (dB)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-16
-14
-12
-10
-8
-6
-4
-2
0
Frequency (kHz)
Phase (
radia
ns)
Phase Response
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-60
-50
-40
-30
-20
-10
0
Frequency (kHz)
Magnitu
de (
dB
)
Magnitude Response (dB) and Phase Response
-15.8421
-13.1514
-10.4607
-7.77
-5.0792
-2.3885
0.3022
Phase (
radia
ns)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
Time (mseconds)
Am
plit
ude
Impulse Response
Numerator :
3. Design IIR
a. Butterworth
-3 -2 -1 0 1 2 3
-1
-0.5
0
0.5
1
Real Part
Imagin
ary
Part
16
Pole/Zero Plot
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-350
-300
-250
-200
-150
-100
-50
0
Frequency (kHz)
Magnitu
de (
dB
)
Magnitude Response (dB)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-20
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
Frequency (kHz)
Phase (
radia
ns)
Phase Response
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-350
-300
-250
-200
-150
-100
-50
0
Frequency (kHz)
Magnitu
de (
dB
)
Magnitude Response (dB) and Phase Response
-19.3397
-16.6085
-13.8774
-11.1462
-8.415
-5.6838
-2.9526
-0.2215
Phase (
radia
ns)
0 0.5 1 1.5 2 2.5 3
-0.02
0
0.02
0.04
0.06
0.08
Time (mseconds)
Am
plit
ude
Impulse Response
0 0.5 1 1.5 2 2.5 3
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Time (mseconds)
Am
plit
ude
Step Response
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
14
Real Part
Imagin
ary
Part
Pole/Zero Plot
b. Analog Prototype Chebychev
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-500
-450
-400
-350
-300
-250
-200
-150
-100
-50
0
Frequency (kHz)
Magnitu
de (
dB
)
Magnitude Response (dB)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-25
-20
-15
-10
-5
0
Frequency (kHz)
Phase (
radia
ns)
Phase Response
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-500
-450
-400
-350
-300
-250
-200
-150
-100
-50
0
Frequency (kHz)
Magnitu
de (
dB
)
Magnitude Response (dB) and Phase Response
-25.5851
-23.0977
-20.6103
-18.1229
-15.6354
-13.148
-10.6606
-8.1732
-5.6858
-3.1984
-0.711
Phase (
radia
ns)
0 20 40 60 80 100
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
Time (mseconds)
Am
plit
ude
Impulse Response
0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
1
1.2
Time (mseconds)
Am
plit
ude
Step Response
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Real Part
Imagin
ary
Part
16
Pole/Zero Plot
c. Elliptical
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
Frequency (kHz)
Magnitu
de (
dB
)
Magnitude Response (dB)
\
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-20
-15
-10
-5
0
Frequency (kHz)
Phase (
radia
ns)
Phase Response
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
Frequency (kHz)
Magnitu
de (
dB
)
Magnitude Response (dB) and Phase Response
-23.3162
-20.9556
-18.5949
-16.2343
-13.8737
-11.5131
-9.1525
-6.7919
-4.4313
-2.0707
0.29
Phase (
radia
ns)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
Time (seconds)
Am
plit
ude
Impulse Response
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
0
0.2
0.4
0.6
0.8
1
Time (seconds)
Am
plit
ude
Step Response
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Real Part
Imagin
ary
Part
Pole/Zero Plot
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