1. Net 222: Communications and networks fundamentals (Practical Part)
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Tutorial 2 : Chapter 3 Data & computer communications

2. Revision
Trigonometric Functions
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3. Revision (Cont.) Trigonometric Functions
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4. Revision (Cont.)
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5. Revision (Cont.)
Logarithms
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6. Revision (Cont.) General Sine Wave
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7. Revision (Cont.)
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8. Revision (Cont.)
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9. Revision (Cont.)
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10. Revision (Cont.)
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11. Revision (Cont.)
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12. Chapter 3 (Data & computer communications)
3.2
3.3
3.4
3.5
3.6
3.7
3.16
3.17
3.18
3.19
3.21
3 more question on ch3.
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13. Question
3.1)
a) For the multipoint configuration, only one device at a time can transmit. Why?
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14. Answer
If two devices transmit at the same time, their signals will be on the medium at the same time, interfering with each other; i.e., their signals will overlap and become garbled.
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15. Question
3.2)
A signal has a fundamental frequency 1000 Hz what is it's period?
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16. Answer Period = 1/1000 = 0.001 s (×103) = 1 ms.
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17. Question 3.3) Express the following in the simplest form you can:
a) sin(2π ft -π ) + sin(2π ft +π)
b) sin 2π ft + sin(2π ft -π )
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18. Answer
Using: 
Sin (A+B)=sin (A) cos (B) + cos (A) sin (B)
Sin (A- B) = sin (A) cos (B) - cos (A) sin (B) a)
= sin 2ft . cos  - cos 2ft . sin  + sin 2ft . cos  + cos 2ft . sin 
= -2 sin 2ft OR
Using
Sin(A+B) + Sin(A-B) = 2 sin (A) cos (B) 
= 2 sin (2ft) . cos 
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19. Answer(Cont.) b) = sin 2ft + sin 2ft . cos  + cos 2ft . sin  = 0
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20. Question
3.4)
Sound may be modeled as a sinusoidal function. Compare the relative frequency and wavelength of musical note. Use 330 m/s as the speed of sound and the following frequencies for the musical scale
Note C D E F G A B
Frequency
264
297
330
352
396
440
495
528
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21. Answer Note Frequency Frequency deference Wavelength C D E F G A B 264
297
330
352
390
440
495
528
Frequency deference 33 22 44 55
Wavelength
1.25
1.11 1
0.93
0.83
0.75
0.67
0.63
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22. Question
3.5)
If the solid curve in Figure 3.17 represents sin(2t), what does the dotted curve represent? That is, the dotted curve can he written in the form
A sin (2ft +  ); what are A, f and  ?
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23. Answer 2 sin(4πt + π ); A = 2, f = 2,  = π
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24. Question
3.6)
Decompose the signal (1+0.1cos 5t) cos 100t into a linear combination of sinusoidal, function amplitude ,frequency, and phase of each component
hint: use the identity for cos a cos b .
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25. Answer = cos 100t + 0.1 cos 5t cos 100t.
From the trigonometric identity
cos a cos b = (1/2)[ cos(a+b) + cos(a–b) ]
, this equation can be rewritten as the linear combination of three sinusoids
cos 100t cos 105t cos 95t
A=1
F=15.96
=0
A=0.05
F=16.72
=0
A=0.05
F=15.13
=0
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26. Question 3.7) Find the period of the function f(t) =(10 cos t )2?
 3.7)
Find the period of the function f(t) =(10 cos t )2?
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27. Answer cos a cos b = (1/2) [ cos(a+b) + cos(a–b) ]
f(t) = 50 cos 2t + 50
The period of cos(2t) is π and therefore the period of f(t) is π .
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28. Question
3.16)
A digital signaling system is required to operate at bps.
a- if a signal element encodes a 4-bit word, what is the minimum required bandwidth of the channel?
b- Repeat part (a) for the case of 8-bit words.
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29. Answer Using Nyquist's equation: C = 2B log2M We have C = 9600 bps
a. log2M = 4, because a signal element encodes a 4-bit word
Therefore, C = 9600 = 2B × 4, and B = 1200 Hz
b = 2B × 8, and B = 600 Hz
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30. Question
3.17)
What is the thermal noise level of a channel with a bandwidth of 10 kHz carrying 1000 watts of power operating at 50°C?
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31. Answer N = 1.38 × 10–23 × (50 + 273.15) = 445.947× 10–23 watts/Hz
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32. Question
3.18)
Given the narrow (usable) audio bandwidth of a telephone transmission facility, a nominal SNR of 56dB (400,000), and a certain level of distortion,
a. What is the theoretical maximum channel capacity (kbps) of traditional telephone lines?s
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33. Answer
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34. Question
3.19)
Consider a channel with a 1-MHz capacity and an SNR of 63.
a. What is the upper limit to the data rate that the channel can carry?
b. The result of part (a) is the upper limit. However, as a practical matter, better error performance will be achieved at a lower data rate. Assume we choose a data rate of 2/3 the maximum theoretical limit. How many signal levels are needed to achieve this data rate?
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35. Answer
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36. Question
3.21)
Given a channel with an intended capacity of 20 Mbps, the bandwidth of the channel is 3 MHz. Assuming white thermal noise, what signal-to- noise ratio is required to achieve this capacity?
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37. Answer
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38. Question 1- find the bandwidth for the signal:
(4/π)[ sin(2πft) + (1/3)sin(2π(3f)t) + (1/5)sin(2π(5f)t) +(1/7)sin(2π(7f)t) ]
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39. Answer
Bandwidth = 7f-f=6f
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40. Question
2- a signal with a bandwidth of 2000 Hz is composed of two sine waves. the first one has a frequency of 100 Hz with a maximum amplitude of 20, the second one has a maximum amplitude of 5. draw the frequency spectrum
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41. Answer B=2000 F=100 B=fh-fL 2000=fh-100=2100Hz
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42. Question 3- find the DC component of the following signal.
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43. Answer
DC component =13
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44. The End
Any Questions ?
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