1. Introduction to Telecommunication
M J Khan
Lecture 07

2. Menu
• Frequency and frequency domain
• Fourier Transform
• Discrete Fourier Transform (DFT)
• Signal Encoding Techniques
• Bit Encoding Techniques

3. Frequency
• Frequency is the rate of change with respect
to time.
• Change in a short span of time means high
frequency.
• Change over a long span of time means low
frequency.

4. Time domain VS Frequency domain

5. Time domain VS Frequency domain
A complete sine wave in the time domain
can be represented by one single spike in
the frequency domain.

6. Time domain VS Frequency domain
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-10
-5
0
5
10
0 10 20 30 40 50 60 70 80 90 100
0
1
2
3
4
5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-10
-5
0
5
10

7. Time domain VS Frequency domain
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-10
-5
0
5
10
0 10 20 30 40 50 60 70 80 90 100
0
1
2
3
4
5

8. Time domain VS Frequency domain
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-10
-5
0
5
10
0 10 20 30 40 50 60 70 80 90 100
0
1
2
3
4
5

9. Fourier Analysis
Fourier analysis is a tool that changes a time
domain signal to a frequency domain signal
and vice versa.

10. Fourier Series
Every composite periodic signal can be
represented with a series of sine and cosine
functions. The functions are integral
harmonics of the fundamental frequency “f”
of the composite signal. Using the series we
can decompose any periodic signal into its
harmonics.

11. Fourier Transform
Fourier Transform gives the frequency
domain of a non-periodic time domain signal.

12. Discrete Fourier Transform (DFT)
We are living digital age where every signal
is
• Sampled
• Of finite extent
The DFT is the sampled Fourier Transform.
1
0
/2
)()(
N
t
Nstj
etfsF

13. Inverse DFT
In similar fashion we can transform
frequency domain to time domain
1
0
/2
)(
1
)(
N
s
Nstj
esF
N
tf

14. Example
Let
]123543[)(tf
1
0
/2
)()(
N
t
Nstj
etfsF
We know
By Applying we get
]5.1962i1.0000-0205.1962i-1.0000-18[)(sF

15. Frequency Analysis
For more visit the web link
http://www.fourier-series.com/fourierseries2/DFT_tutorial.html

16. Signal Encoding Techniques
• Digital Data Analog Signal
• Analog Data Analog Signal
• Analog Data Digital Signal

17. Digital Data Analog Signal

18. Digital Data Analog Signals

19. Digital Data Analog Signals

20. Amplitude Shift Keying

21. Frequency Shift Keying

22. Phase Shift Keying

23. Phase Shift Keying

24. 4-PSK

25. 8-PSK

26. Quadrature amplitude modulation is a
combination of ASK and PSK so that a
maximum contrast between each signal
unit (bit, dibit, tribit, and so on) is
achieved.
Note:

27. The 4-QAM and 8-QAM collections

28. Time domain for an 8-QAM signal

29. 16-QAM collections

30. Bit and baud

31. Bit and baud rate comparison
Modulation Units Bits/Baud Baud rate Bit Rate
ASK, FSK, 2-PSK Bit 1 N N
4-PSK, 4-QAM Dibit 2 N 2N
8-PSK, 8-QAM Tribit 3 N 3N
16-QAM Quadbit 4 N 4N
32-QAM Pentabit 5 N 5N
64-QAM Hexabit 6 N 6N
128-QAM Septabit 7 N 7N
256-QAM Octabit 8 N 8N

32. Analog Data Analog Signals
Amplitude Modulation (AM)
Frequency Modulation (FM)
Phase Modulation (PM)

33. Analog Data Analog Signal

34. Analog Data Analog Signal

35. Amplitude Modulation

36. Angle Modulation

37. Analog Data Digital Signal

38. Pulse Code Modulation

39. Pulse Code Modulation
PCM involves following steps
1. Sampling
2. Quantization
3. Coding

40. 15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Analog Signal
Time (seconds)
L
e
v
e
l
s

41. Nyquist Sampling Theorem

42. Nyquist Sampling
Theorem
Fs = Fc/2

43. Nyquist Sampling
Theorem
Fs = Fc/2

44. Nyquist Sampling
Theorem
Fs = Fc

45. Nyquist Sampling
Theorem
Fs = Fc

46. Nyquist Sampling
Theorem
Fs = 1.5*Fc

47. Nyquist Sampling
Theorem
Fs = 1.5*Fc

48. Nyquist Sampling
Theorem
Fs = 2*Fc

49. Nyquist Sampling
Theorem
Fs = 2*Fc

50. Nyquist Sampling
Theorem
Fs = 4*Fc

51. Nyquist Sampling
Theorem
Fs = 4*Fc

52. Nyquist Sampling
Theorem
Fs = 6*Fc

53. Nyquist Sampling
Theorem
Fs = 6*Fc

54. 15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Sampling
Time (seconds)
L
e
v
e
l
s

55. 15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Quantization
Time (seconds)
L
e
v
e
l
s

56. 15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
After Sampling
Time (seconds)
L
e
v
e
l
s

57. 15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
After Quantization
Time (seconds)
L
e
v
e
l
s

58. 15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
0011
0100
0111
1000
1001
1010
1011
1011
1011
1010
1001
10001000
0111
10001000
1000
0110
Coding
Time (seconds)
L
e
v
e
l
s

59. Delta Modulation

60. Pulse Code Modulation
Delta Modulation involves following
steps
1. Step up or Step down
2. Coding

61. 15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Analog Signal
Time (seconds)
L
e
v
e
l
s

62. 15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Follow the Difference
Time (seconds)
L
e
v
e
l
s

63. 15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Coding
1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 0 0
Time (seconds)
L
e
v
e
l
s

64. Bit Encoding

65. 1 0 1 0 1 1 0 01
Unipolar NRZ
NRZ-Inverted
(Differential
Encoding)
Bipolar
Encoding
Differential
Manchester
Encoding
Polar NRZ
Manchester
Encoding