The document describes the design of various digital and analog filters including low pass, high pass, and band pass filters using FIR and IIR design methods. It includes magnitude and phase response plots, impulse responses, step responses, and pole-zero plots for filters designed using windowing, least squares, Butterworth, and Chebyshev techniques.

1. 1. Design FIR Windowing
a. LPF
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-10
-20
-30
-40
-50
-60
-70
Frequency (kHz)
Magnitude (dB)
Magnitude Response (dB)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
Frequency (kHz)
Phase (radians)
Phase Response
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-10
-20
-30
-40
-50
-60
-70
Frequency (kHz)
Magnitude (dB)
Magnitude Response (dB) and Phase Response
-0.0644
-2.5724
-5.0804
-7.5884
-10.0964
-12.6044
-15.1124
-17.6204
Phase (radians)
Ossy Anita P ( 1203 1210 )
Jatayu Aghar ( 1203 1210 )
Yahya Rais ( 1203 1210 )
Ahmad A’an N ( 1203 1210 )

2. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.05
Time (mseconds)
Amplitude
Impulse Response
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
1
0.8
0.6
0.4
0.2
0
Time (mseconds)
Amplitude
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
Imaginary Part
16
Pole/Zero Plot

3. Numerator :
b. HPF
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-10
-20
-30
-40
-50
-60
-70
Frequency (kHz)
Magnitude (dB)
Magnitude Response (dB)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
2
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
Frequency (kHz)
Phase (radians)
Phase Response

4. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-10
-20
-30
-40
-50
-60
-70
Frequency (kHz)
Magnitude (dB)
Magnitude Response (dB) and Phase Response
1.5967
-1.3979
-4.3925
-7.3871
-10.3816
-13.3762
-16.3708
-19.3654
Phase (radians)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
0.6
0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
Time (mseconds)
Amplitude
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)
Amplitude
Step Response

5. Pole/Zero Plot
-4 -3 -2 -1 0 1 2 3 4
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
Numerator :
c. BPF
Real Part
Imaginary Part
16
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-10
-20
-30
-40
-50
-60
-70
Frequency (kHz)
Magnitude (dB)
Magnitude Response (dB)

6. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
2
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
Frequency (kHz)
Phase (radians)
Phase Response
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-10
-20
-30
-40
-50
-60
-70
Frequency (kHz)
Magnitude (dB)
Magnitude Response (dB) and Phase Response
1.6948
-1.3444
-4.3835
-7.4227
-10.4618
-13.501
-16.5402
-19.5793
Phase (radians)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
0.4
0.3
0.2
0.1
0
-0.1
-0.2
Time (mseconds)
Amplitude
Impulse Response

7. 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
2
1.5
1
0.5
0
-0.5
-1
-1.5
Numerator :
Time (mseconds)
Amplitude
Step Response
Pole/Zero Plot
-4 -3 -2 -1 0 1 2 3 4
-2
Real Part
Imaginary Part
16

8. 2. Design FIR Least Square
a. LPF
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-10
-20
-30
-40
-50
-60
Frequency (kHz)
Magnitude (dB)
Magnitude Response (dB)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
Frequency (kHz)
Phase (radians)
Phase Response
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-10
-20
-30
-40
-50
-60
Frequency (kHz)
Magnitude (dB)
Magnitude Response (dB) and Phase Response
-0.1636
-2.8531
-5.5425
-8.232
-10.9214
-13.6109
-16.3004
Phase (radians)

9. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
0.6
0.5
0.4
0.3
0.2
0.1
0
-0.1
Time (mseconds)
Amplitude
Impulse Response
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
1.2
1
0.8
0.6
0.4
0.2
0
Time (mseconds)
Amplitude
Step Response
-1 0 1 2 3 4 5 6 7
1.5
1
0.5
0
-0.5
-1
-1.5
Real Part
Imaginary Part
16
Pole/Zero Plot

10. Numerator :
b. HPF
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-10
-20
-30
-40
-50
-60
-70
Frequency (kHz)
Magnitude (dB)
Magnitude Response (dB)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
4
2
0
-2
-4
-6
Frequency (kHz)
Phase (radians)
Phase Response

11. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-10
-20
-30
-40
-50
-60
-70
Frequency (kHz)
Magnitude (dB)
Magnitude Response (dB) and Phase Response
4.3205
2.7525
1.1846
-0.3834
-1.9514
-3.5193
-5.0873
-6.6552
Phase (radians)
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)
Amplitude
Impulse Response
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
Time (mseconds)
Amplitude
Step Response

12. 2
1.5
1
0.5
0
-0.5
-1
-1.5
Numerator :
c. BPF
-1 0 1 2 3 4 5 6 7
-2
16
Real Part
Imaginary Part
Pole/Zero Plot
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-10
-20
-30
-40
-50
-60
Frequency (kHz)
Magnitude (dB)
Magnitude Response (dB)

13. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-2
-4
-6
-8
-10
-12
-14
-16
Frequency (kHz)
Phase (radians)
Phase Response
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-10
-20
-30
-40
-50
-60
Frequency (kHz)
Magnitude (dB)
Magnitude Response (dB) and Phase Response
0.3022
-2.3885
-5.0792
-7.77
-10.4607
-13.1514
-15.8421
Phase (radians)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
Time (mseconds)
Amplitude
Impulse Response

14. Pole/Zero Plot
-3 -2 -1 0 1 2 3
1
0.5
0
-0.5
-1
Numerator :
3. Design IIR
a. Butterworth
Real Part
Imaginary Part
16
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-50
-100
-150
-200
-250
-300
-350
Frequency (kHz)
Magnitude (dB)
Magnitude Response (dB)

15. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
Frequency (kHz)
Phase (radians)
Phase Response
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-50
-100
-150
-200
-250
-300
-350
Frequency (kHz)
Magnitude (dB)
Magnitude Response (dB) and Phase Response
-0.2215
-2.9526
-5.6838
-8.415
-11.1462
-13.8774
-16.6085
-19.3397
Phase (radians)
0 0.5 1 1.5 2 2.5 3
0.08
0.06
0.04
0.02
0
-0.02
Time (mseconds)
Amplitude
Impulse Response

16. 0 0.5 1 1.5 2 2.5 3
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
Time (mseconds)
Amplitude
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
Imaginary Part
Pole/Zero Plot

17. b. Analog Prototype Chebychev
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-50
-100
-150
-200
-250
-300
-350
-400
-450
-500
Frequency (kHz)
Magnitude (dB)
Magnitude Response (dB)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-5
-10
-15
-20
-25
Frequency (kHz)
Phase (radians)
Phase Response
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-50
-100
-150
-200
-250
-300
-350
-400
-450
-500
Frequency (kHz)
Magnitude (dB)
Magnitude Response (dB) and Phase Response
-0.711
-3.1984
-5.6858
-8.1732
-10.6606
-13.148
-15.6354
-18.1229
-20.6103
-23.0977
-25.5851
Phase (radians)

18. 0 20 40 60 80 100
0.25
0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
Time (mseconds)
Amplitude
Impulse Response
0 20 40 60 80 100
1.2
1
0.8
0.6
0.4
0.2
0
Time (mseconds)
Amplitude
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
Imaginary Part
16
Pole/Zero Plot

19. c. Elliptical
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-10
-20
-30
-40
-50
-60
-70
-80
-90
-100
Frequency (kHz)
Magnitude (dB)
Magnitude Response (dB)

20. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-5
-10
-15
-20
Frequency (kHz)
Phase (radians)
Phase Response
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
-10
-20
-30
-40
-50
-60
-70
-80
-90
-100
Frequency (kHz)
Magnitude (dB)
Magnitude Response (dB) and Phase Response
0.29
-2.0707
-4.4313
-6.7919
-9.1525
-11.5131
-13.8737
-16.2343
-18.5949
-20.9556
-23.3162
Phase (radians)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
0.25
0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
Time (seconds)
Amplitude
Impulse Response

21. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
1
0.8
0.6
0.4
0.2
0
Time (seconds)
Amplitude
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
Imaginary Part
Pole/Zero Plot