Signals Complex Waves and Harmonics Sine Wave Square Wave Saw tooth Wave Conversion/Signal Formatting Character Coding

1. EE334: Communication Systems

2. 2
review
Signals
Complex Waves and Harmonics
Sine Wave
Square Wave
Saw tooth Wave
Conversion/Signal Formatting
Character Coding

3. 3

4. 4
Formatting
• Character coding
• Sampling
• Quantization
• Pulse Code Modulation(PCM)

5. Formatting and Transmission of
baseband signal
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6. 6
Input Signal
1. Textual
2. Digital
3. Analog

7. Different Conversion Scheme

8. 1. Digital to Digital conversion
• done

9. 2. Analog to Digital Conversion
(Codec)
First Step: Pulse Amplitude Modulation (PAM)
• According to Nyquist
theorem, the sampling
rate must be at least
two times the frequency
to ensure the accurate
reproduction of the
original signal.
K. Salah

10. Second step: Quantized PAM Signal
Quantizing Using Sign and Magnitude
K. Salah

11. Third Step: Pulse Code Modulation
(PCM)
Remember this
Out of each sample, Telephone companies only uses the upper 7 bits. The lower bit (bit0)
is always assumed to be 0. For example, samplingvalues:
+024  +024, +038  +038,
+025  +024, +039  +038
This is not affecting sampling values much.
In transmission, the most significant bit is used for control purposes, as we will see later.
K. Salah

12. From Analog to PCM digital signal
K. Salah

13. Sample Theorem
Need for sampling:
In analog signal, distortion is produced, and it
is difficult to recover the signal, However it is
easy to do so in digital signal.
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14. Sampling Theorem(contd.)
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15. Sampling(contd.)
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16. 16
Impulse Sampling
Use of Impulse:
At a particular point, we get a sample.
When any function is multiplied by impulse
function at t=xsec, we get a sample of that
function at x sec.
If we want to recover complete signal we have to
multiply by impulse train.

17. Impulse sampling(contd.)
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18. Impulse sampling : Using convolution
property
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20. 20

21. 21

22. Natural Sampling
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23. 23

24. Sampling Theorem using frequency
shifting property of Fourier Transform
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25. 25

26. Under and over sampling
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27. Over and under sampling
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28. Aliasing
Aliasing refers to an effect that causes different
signals to become indistinguishable (or aliases
of one another) when sampled. It also refers to
the distortion that results when the signal
reconstructed from samples is different from the
original continuous signal.
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29. Aliasing
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30. 30

31. Use of Filters
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32. Use of Filters
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33. Converting bit into samples
• Quantizing
• Similar concept to pixelization.
• Breaks wave into pieces, assigns a value in a
particular range
• 8-bit range allows for 256 possible sample
levels
• More bits means greater detail, fewer bits
means less detail

34. Quantization/Digitizing/PCM
Uniform Quantization
Non uniform Quantization
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35. Analog to Digital Conversion
(Sampling)
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36. 36

37. 37

38. 38

39. PCM

40. PCM

41. PCM

42. 42

43. 43

44. Non-Uniform Uniform
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45. Non Uniform Quantization
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46. 46

47. Companding
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48. Quantization Levels
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49. PCM
PCM uses a sampling rate of 8000 samples per
second.
Each sample is an 8 bit sample resulting in a
digital rate of 64,000 bps (8 x 8000).

50. 50
• n=number of pulses(bit)
• L=M=number of levels=2^n
• Step size= 2A/M
• s0=m^2(t)

51. Quantization Error
• Analog voice data must be translated into a
series of binary digits before they can be
transmitted.
• With Pulse Code Modulation (PCM), the
amplitude of the sound wave is sampled at
regular intervals and translated into a binary
number.
• The difference between the original analog
signal and the translated digital signal is called
quantizing error.

52. 3. Digital to Analog Modulation
(Modem)
K. Salah

53. 4. Analog to analog Conversion

54. Amplitude Modulation
K. Salah

55. Frequency Modulation
K. Salah

56. Structure of Telephone System
• End office, known also as
local central office
• Local loops (twisted pairs,
analog signaling)
• Trunks (fiber optics or
microwave, mostly digital)
• Intermediate switches
K. Salah

57. Need for A/D and D/A conversions
• Modem converts D/A signals
• Codec converts A/D signals
K. Salah

58. 58
Question of Lecture
• What is the difference between time and frequency
domain?
• Any complex waveform is composed of?
• A square wave is composed of?
• A saw tooth wave is composed of?
• Prove that sine wave is composed of main frequency and all
harmonics using Fourier series?
• Prove that square wave is composed of main frequency and
all odd harmonics using Fourier series?
• Read what is ASCII coding?
• What is M-ary pulse modulation

59. Asssignment#1
Due Date: 21Feb, 2014
1. Prove through Fourier series that sine waveform
is a fundamental waveform?
2. What is the harmonic composition of a square
wave?
3. Draw and explain the basic communication
system taking PSTN as an exemplary network?
4. What is m-ary pulse modulation?
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