Sampling — Transcript

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1. 0:00EP 1100 data communication and computer
2. 0:04networks some illustration in this
3. 0:06material are collected from the book by
4. 0:08foron data Communications and networking
5. 0:10published by
6. 0:11mcrill I want to start by distinguishing
7. 0:14two types of signals analog and digital
8. 0:17signals analog signals are continuous in
9. 0:20time and also continuous in amplitude
10. 0:22that means that like giv the figure on
11. 0:24the right that they can be drawn as a
12. 0:26continuous curve as a functional time
13. 0:30digital signals on the other side are
14. 0:32discrete in time so they only exist at
15. 0:34certain points in time and at the points
16. 0:37where they exist they only take one out
17. 0:39of a limited set of amplitude levels if
18. 0:42you look on the right you see that the
19. 0:43signal can take four amplitude levels
20. 0:46the zeroth and what first second and
21. 0:48third
22. 0:49level sampling is the process to go from
23. 0:53an analog signal to a Time discrete
24. 0:56signal we do that by sampling the signal
25. 0:59meaning that we read the signal value at
26. 1:01specific points in time if we do this
27. 1:04correctly we can recover the analog
28. 1:06signal without any information loss but
29. 1:09then we have to obey a certain sampling
30. 1:11rate this is given by a theorem called
31. 1:13the Nyquist theorem it states that you
32. 1:16must sample at least twice as fast as
33. 1:19the highest frequency of the analog
34. 1:21signal so we denote this by FS being the
35. 1:24sampling frequency so it has to be at
36. 1:27least twice as high this frequency often
37. 1:30referred to as a Nyquist frequency or
38. 1:32nist rate the nist frequency is both
39. 1:35sufficient and necessary to recover the
40. 1:38analog signal and there's no gain in
41. 1:40sampling at a higher rate this example
42. 1:42here shows a signal which has Max
43. 1:45frequency n Hertz so we need to sample
44. 1:48it at at least 2 n
45. 1:50Hertz the the interval between two
46. 1:54values is the inverse of the sampling
47. 1:58frequency so in this case it's it's 1/
48. 2:002N seconds by sampling we obtain a
49. 2:04signal which is discreet in time but
50. 2:07still continuous in amplitude the
51. 2:09Nyquist theorum is named after Harry
52. 2:10Nyquist a Swede from verland who
53. 2:13immigrated and was active in United
54. 2:17States sampling gives us a Time
55. 2:20discreete signal but it still is
56. 2:23continuous in amplitude to get a digital
57. 2:25signal we need a signal which only takes
58. 2:29ampl udes from a limited set of
59. 2:31amplitude values we call this
60. 2:34quantization so we select which
61. 2:36amplitude values we should accept in the
62. 2:38digital signal and then we round off
63. 2:42each of the sample values to its closest
64. 2:46level this roundoff gives an information
65. 2:49loss and this process is not
66. 2:51reversible so the important aspect of
67. 2:54quantization is to design it so that
68. 2:57this round of error does not not disturb
69. 3:02the communication for instance if it's a
70. 3:04voice signal that that we we Conta the
71. 3:07roundoff error should not be audible or
72. 3:09at least not disturb the The Voice
73. 3:12communication once we have quantized the
74. 3:14signal to uh a set of finite amplitude
75. 3:18levels then we can represent each
76. 3:20amplitude value by a code word of of
77. 3:22bits so for instance we could take the
78. 3:24zeroth level and represent it by four
79. 3:27zeros we could have a value which
80. 3:29represents
81. 3:30plus 25 molts that could be represented
82. 3:33by
83. 3:3400001 plus 50 molts could be 0 0 1 0 and
84. 3:39minus 25 Mills could be 1 0 0
85. 3:421 the process of going from an analog to
86. 3:46a digital signal is sometimes referred
87. 3:48to as pulse code modulation so it
88. 3:50includes both the sampling and the
89. 3:52quantization the sampling frequency has
90. 3:55to be given by the bandwidth or the
91. 3:56highest frequency of the signal it's us
92. 4:00usually ensured by filtering the signal
93. 4:03so that we know before sampling that the
94. 4:05signal does not have any higher
95. 4:07frequency than the one that we have
96. 4:09designed the sampling for then we decide
97. 4:12how many bits or how many quantization
98. 4:14levels we should have in the signal so
99. 4:16that we get the quality that's
100. 4:17acceptable for the purpose of digitizing
101. 4:20the signal and I said we represent each
102. 4:23digital amplitude value by an electric
103. 4:27signal level so when we want to recover
104. 4:30an analog signal we know that if you get
105. 4:32a certain bit value it should be mapped
106. 4:35into a certain voltage level in the
107. 4:36outgoing signal so for example we could
108. 4:39have 8 bit sample values and they could
109. 4:41represent quantization levels fromus 127
110. 4:45to plus7 for instance for an audio
111. 4:47signal and these levels from - 127 to
112. 4:50plus 127 will in turn also be mapped to
113. 4:54certain voltage levels for the outgoing
114. 4:58signal with the samp a quantization we
115. 5:01go from an analog signal to a digital
116. 5:03signal which has a bit rate that means
117. 5:05that we sample it at the certain
118. 5:07frequency which has units one/ seconds
119. 5:10times the number of bits per sample
120. 5:13measured in bits of course so we get the
121. 5:15unit of bits per second one bit per
122. 5:19second is a very low data rate and
123. 5:21therefore we need prefixes to to mark
124. 5:24that we want to have higher units such
125. 5:26as kilo Mega Giga Tera and so forth
126. 5:32here are some examples of PCM encoded
127. 5:35signals for telephony the bandwidth of
128. 5:37the human voice is below 4 khz so it was
129. 5:41decided to sample at 8 khz it's enough
130. 5:44to represent each sample by eight bits
131. 5:47so the 256 levels that I had in the
132. 5:49previous slide and that give a bit rate
133. 5:51of 64 kilobits per second which has been
134. 5:53the standard digital rate of telepan IM
135. 5:56music CD needs to represent the full
136. 5:58auditory spectrum of the human ear which
137. 6:01is around 20 khz the sampling rate was
138. 6:04decided to be 44.1 khz since the quality
139. 6:07expectation is much higher each sample
140. 6:10is represented by 16bit amplitude values
141. 6:13and that create a data rate per channel
142. 6:16of 76 KOB per second and similarly for
143. 6:20DVD audio there is a whole set of
144. 6:23sampling rates and a resolution of 16 20
145. 6:27or 24 bits per sample giving a data rate
146. 6:31up to
147. 6:324.6 megabits per second per
148. 6:58Channel