WEBVTT 00:00:00.000 --> 00:00:03.680 Welcome back to CSE 316 — Data Communication and Networking. 00:00:03.730 --> 00:00:09.200 This is the detailed video version of Session 4, and today we touch physics. 00:00:09.250 --> 00:00:18.200 It runs about an hour and three quarters, in five sections, and it is meant to be watched the way you would use a textbook chapter — in pieces, with the pause button, with a calculator beside you, and again before an exam. 00:00:23.200 --> 00:00:29.080 There is a checkpoint at the end of each section so you can tell whether to go on or go back. 00:00:29.130 --> 00:00:31.960 Here is the shape of it. 00:00:32.010 --> 00:00:40.960 We start by being precise about signals: analog against digital, periodic against nonperiodic, and the sine wave with its three knobs. 00:00:41.310 --> 00:00:44.860 Learn about period, frequency and wavelength. 00:00:44.910 --> 00:00:50.230 Then the two ways to look at any signal — the time domain and the frequency domain. 00:00:50.280 --> 00:00:56.570 After that we cross to the digital side: bit rate, bit length, signal levels etc. 00:00:56.620 --> 00:01:00.640 And at the end, the answer to a question I am about to ask you. 00:01:00.690 --> 00:01:07.017 Do not just watch the worked examples — pause and do them. 00:01:07.067 --> 00:01:11.847 Before any definition, here is the fact this session explains. 00:01:11.897 --> 00:01:20.847 The most perfect signal we own — a single pure sine wave, infinitely smooth, mathematically flawless, the cleanest thing in this whole subject — carries exactly zero information. 00:01:25.197 --> 00:01:26.407 Why? 00:01:26.457 --> 00:01:34.487 Pause the video and commit to a sentence; write it down somewhere. 00:01:34.537 --> 00:01:38.517 A wrong sentence is fine — committing to one is the point. 00:01:38.567 --> 00:01:47.517 Here is the shape of the answer, so you know what you are building towards: a pure sine wave is a single spike in the frequency domain, so its bandwidth is f minus f — zero — and a signal with zero bandwidth cannot change unpredictably. 00:01:53.577 --> 00:01:58.977 Section five proves that in one subtraction and grades your sentence against it. 00:01:59.027 --> 00:02:02.747 The question is not a riddle for its own sake. 00:02:02.797 --> 00:02:11.747 To answer it you need everything this session teaches: the three knobs of a sine wave, the two ways of looking at a signal, and the word bandwidth used exactly. 00:02:12.797 --> 00:02:19.937 That is the session objective — own the physical layer's vocabulary well enough that this question becomes easy. 00:02:19.987 --> 00:02:26.322 Everything between here and the last section builds it. 00:02:26.372 --> 00:02:27.652 Section one. 00:02:27.702 --> 00:02:31.592 Signals — analog, digital, and the sine wave. 00:02:31.642 --> 00:02:39.192 Before anything can be measured, the vocabulary has to be exact: what travels, and what shape it takes on the wire. 00:02:39.242 --> 00:02:46.406 Two axes of classification, and then the simplest signal there is. 00:02:46.456 --> 00:02:52.656 Two words this chapter refuses to blur, so let us be careful with them from the first minute. 00:02:52.706 --> 00:02:58.096 An analog signal has infinitely many intensity levels over time. 00:02:58.146 --> 00:03:05.086 Moving from value A to value B, it passes through every value on the path — it cannot jump. 00:03:05.136 --> 00:03:10.406 The output of a microphone is an analog signal; so is the old telephone line. 00:03:10.456 --> 00:03:14.256 Smooth, continuous, no steps anywhere. 00:03:14.306 --> 00:03:18.436 A digital signal is the opposite personality. 00:03:18.486 --> 00:03:26.806 It can take only a limited number of defined values — call the count L — and it jumps between them; nothing in between has a meaning. 00:03:26.856 --> 00:03:31.776 The receiver only ever asks one question: which level am I looking at? 00:03:31.826 --> 00:03:34.386 And notice that I did not say two levels. 00:03:34.436 --> 00:03:41.506 Often it is just 1 and 0 — but nothing stops us defining four, eight, or sixteen levels. 00:03:41.556 --> 00:03:46.176 What that buys, and what it costs, is settled later in this session. 00:03:46.226 --> 00:03:50.006 Now the sentence that keeps the two words apart. 00:03:50.056 --> 00:03:54.786 Data is the information; a signal is its shape on the wire. 00:03:54.836 --> 00:03:59.976 They are different things — and either kind of data can ride either kind of signal. 00:04:00.026 --> 00:04:07.026 Analog data can become a digital signal: that is what happened when your voice was digitized in Session 1. 00:04:07.076 --> 00:04:10.216 Digital data can become an analog signal too. 00:04:10.266 --> 00:04:19.216 Keep that cross-over in your pocket; it is Forouzan section 3.1, and it is the kind of distinction the exam checks with a one-line true-or-false. 00:04:22.818 --> 00:04:26.988 One more axis, and then the vocabulary is complete. 00:04:27.038 --> 00:04:35.988 A periodic signal completes a pattern in a measurable time frame — that time frame is called the period — and then repeats it, cycle after identical cycle, for as long as you care to watch. 00:04:40.078 --> 00:04:42.848 Know one cycle and you know them all. 00:04:42.898 --> 00:04:49.028 A nonperiodic signal changes without any pattern or cycle that ever repeats. 00:04:49.078 --> 00:04:51.718 A spoken sentence is nonperiodic. 00:04:51.768 --> 00:04:55.448 Every file you have ever downloaded is nonperiodic. 00:04:55.498 --> 00:04:58.988 Nothing about its past guarantees its future. 00:04:59.038 --> 00:05:07.988 Now cross the two axes and note the pairing that data communications actually uses: periodic ANALOG signals — because they are simple and cheap to generate and need little bandwidth — and nonperiodic DIGITAL signals, because they can carry data. 00:05:15.508 --> 00:05:19.628 This session covers both halves of that pairing, in that order. 00:05:19.678 --> 00:05:25.298 And a related question: why would a periodic DIGITAL signal be useless for carrying data? 00:05:25.348 --> 00:05:31.768 Think about what 'repeats identically forever' means for a signal that is supposed to be telling you something. 00:05:31.818 --> 00:05:40.348 It has the same answer as the question from minute one, and slide 37 gives both. 00:05:40.398 --> 00:05:45.858 The simplest signal there is — the periodic analog signal called the sine wave. 00:05:45.908 --> 00:05:49.808 For this one, watch rather than listen. 00:05:49.858 --> 00:05:53.668 One wave, three knobs, thirty-five seconds. 00:05:53.718 --> 00:06:01.968 Watch each knob move on its own: first the wave gets taller without getting faster. 00:06:02.018 --> 00:06:10.968 Then it gets faster without getting taller. 00:06:11.318 --> 00:06:20.268 Then it slides sideways without doing either. 00:06:20.618 --> 00:06:26.718 Three independent controls, and the whole of the next slide is just naming them. 00:06:26.768 --> 00:06:35.718 If any of the three moves surprised you, play it again before you go on — the clip is thirty-five seconds and the names mean nothing without the picture. 00:06:39.915 --> 00:06:42.625 You watched the clip — now in words. 00:06:42.675 --> 00:06:47.065 Three knobs describe every sine wave there is, completely. 00:06:47.115 --> 00:06:50.575 Amplitude, written A: how tall. 00:06:50.625 --> 00:06:53.515 The value of the signal's highest intensity. 00:06:53.565 --> 00:06:57.585 On a wire that is a voltage; in the air it is a pressure. 00:06:57.635 --> 00:07:01.245 Turn it up and the wave is louder — not faster. 00:07:01.295 --> 00:07:03.695 Louder, not faster. 00:07:03.745 --> 00:07:07.555 Frequency, written f: how often. 00:07:07.605 --> 00:07:12.445 Cycles per second, measured in hertz (named after Heinrich Hertz). 00:07:12.495 --> 00:07:18.495 And frequency has a twin: the period, T — the seconds one cycle takes. 00:07:18.545 --> 00:07:20.635 T equals one over f. 00:07:20.685 --> 00:07:29.635 Say both aloud — seconds per cycle, cycles per second — and you can hear that they are one fact, two ways up. 00:07:29.765 --> 00:07:38.075 Phase, written phi: where the first cycle starts — the wave's position relative to time zero. 00:07:38.125 --> 00:07:44.105 Measured in degrees or radians, and the exchange rate is 360 degrees to two pi radians. 00:07:44.155 --> 00:07:49.885 A 360-degree shift is one whole period, which is no shift at all. 00:07:49.935 --> 00:07:56.495 And now two extremes worth filing away; they look like trivia and are not. 00:07:56.545 --> 00:07:58.275 First: f equals zero. 00:07:58.325 --> 00:08:03.725 A signal that never changes — a flat DC line, with an infinite period. 00:08:03.775 --> 00:08:11.485 Second: a signal that could change instantaneously — a perfectly vertical edge — has infinite frequency. 00:08:11.535 --> 00:08:20.485 File the flat line especially. Its relative is the pure sine wave from minute one: both perfectly predictable, and both therefore silent. 00:08:21.045 --> 00:08:27.605 Here is the demonstration: the signal playground on the course page — three sliders, one wave. 00:08:27.655 --> 00:08:33.585 The house rule: one slider at a time, and predict every readout before you move anything. 00:08:33.635 --> 00:08:39.885 Try the preset that doubles f — the period readout halves, T equals one over f, live. 00:08:39.935 --> 00:08:47.485 Then drag amplitude from zero to five volts and ask first: does the period readout change? 00:08:47.535 --> 00:08:48.755 It must not. 00:08:48.805 --> 00:08:54.215 Then the 90-degree head start — same wave, same period, shifted start. 00:08:54.265 --> 00:09:03.215 And end on the preset called DC, f equals zero: a flat line, T equals infinity, and the readout says no change, no information. 00:09:03.765 --> 00:09:09.595 Remember the flat line. 00:09:09.835 --> 00:09:11.155 First checkpoint. 00:09:11.205 --> 00:09:15.915 Pause the video and answer these three on paper, without scrolling back. 00:09:15.965 --> 00:09:17.175 One. 00:09:17.225 --> 00:09:23.375 A signal moves from one value to another by passing through every value in between. 00:09:23.425 --> 00:09:25.225 Analog or digital? 00:09:25.275 --> 00:09:26.435 Two. 00:09:26.485 --> 00:09:32.445 Name the three knobs that fully describe a sine wave — and the twin of frequency. 00:09:32.495 --> 00:09:33.665 Three. 00:09:33.715 --> 00:09:35.245 A sine wave's frequency is zero. 00:09:35.295 --> 00:09:39.965 What does it look like, and what is its period? 00:09:40.015 --> 00:09:44.065 Pause now. 00:09:44.115 --> 00:09:45.555 Answers. 00:09:45.605 --> 00:09:48.135 The first: analog. 00:09:48.185 --> 00:09:56.735 Infinitely many levels, and it cannot jump; a digital signal jumps between defined levels and nothing in between has a meaning. 00:09:56.785 --> 00:10:04.685 The second: amplitude, frequency and phase — and frequency's twin is the period, T equals one over f, seconds per cycle. 00:10:04.735 --> 00:10:07.225 The third: a flat DC line. 00:10:07.275 --> 00:10:10.905 It never completes a cycle, so its period is infinite. 00:10:10.955 --> 00:10:19.905 If you hesitated on that one, go back to the two extremes before section two — they are about to start earning money. 00:10:23.180 --> 00:10:24.480 Section two. 00:10:24.530 --> 00:10:28.460 Period, frequency, wavelength — the arithmetic. 00:10:28.510 --> 00:10:31.430 This is the first calculator work of the course. 00:10:31.480 --> 00:10:38.950 None of it is deep, and all of it is exactly where marks are lost — powers of ten, routed carelessly. 00:10:39.000 --> 00:10:47.950 So we route them carefully, twice, and then add the one formula that puts the wave into space. 00:10:48.410 --> 00:10:53.530 One formula runs this whole section, so let us give it a slide of its own. 00:10:53.580 --> 00:11:02.530 T equals one over f — and, flipped over, f equals one over T. One relationship, two directions, and you must be able to walk it both ways without thinking. 00:11:06.660 --> 00:11:10.330 Read it as period: seconds per cycle. 00:11:10.380 --> 00:11:12.650 The time one full cycle takes. 00:11:12.700 --> 00:11:21.310 Mains electricity in Bangladesh runs at 50 hertz, so one cycle takes one fiftieth of a second — 20 milliseconds. 00:11:21.360 --> 00:11:24.430 We will do that one properly in a moment. 00:11:24.480 --> 00:11:28.330 Read it as frequency: cycles per second. 00:11:28.380 --> 00:11:31.320 How many cycles fit into one second. 00:11:31.370 --> 00:11:36.550 A period of one millisecond means a thousand cycles fit into each second — one kilohertz. 00:11:36.600 --> 00:11:41.340 Say both aloud: seconds per cycle; cycles per second. 00:11:41.390 --> 00:11:44.590 One fact, two ways up. 00:11:44.640 --> 00:11:53.590 Fix either number and the other is fixed too: one kilohertz pairs with one millisecond, one megahertz pairs with one microsecond, ten hertz pairs with one hundred milliseconds. 00:11:57.600 --> 00:12:05.840 Every conversion in this section — and in the weekly online quizzes, and on the midterm — is this line plus powers of ten. 00:12:05.890 --> 00:12:13.750 The powers of ten are where the danger is, which is why the next slide exists. 00:12:14.000 --> 00:12:19.370 Forouzan Examples 3.4 and 3.5, worked in full. 00:12:19.420 --> 00:12:23.500 A signal has a period of 100 milliseconds. 00:12:23.550 --> 00:12:28.980 Express the period in microseconds; express the frequency in kilohertz. 00:12:29.030 --> 00:12:32.700 Two questions, one period, and a trap in each. 00:12:32.750 --> 00:12:36.180 Step one — into seconds first, always. 00:12:36.230 --> 00:12:44.200 One hundred milliseconds is one hundred times ten to the minus three seconds, which is ten to the minus one seconds. 00:12:44.250 --> 00:12:46.490 A tenth of a second. 00:12:46.540 --> 00:12:49.560 Do not move on until the number is in seconds. 00:12:49.610 --> 00:12:51.500 Step two — part (a). 00:12:51.550 --> 00:12:57.740 Ten to the minus one seconds, into microseconds: multiply by ten to the six. 00:12:57.790 --> 00:13:03.450 Ten to the minus one times ten to the six is ten to the five microseconds. 00:13:03.500 --> 00:13:06.660 One hundred thousand microseconds. 00:13:06.710 --> 00:13:12.580 Step three — part (b) starts from seconds too. 00:13:12.630 --> 00:13:18.900 Frequency is one over the period: one over ten to the minus one seconds is ten hertz. 00:13:18.950 --> 00:13:22.440 The signal completes ten cycles every second. 00:13:22.490 --> 00:13:28.080 Step four — ten hertz into kilohertz: multiply by ten to the minus three. 00:13:28.130 --> 00:13:32.720 Ten times ten to the minus three is ten to the minus two kilohertz. 00:13:32.770 --> 00:13:36.250 One hundredth of a kilohertz. 00:13:36.300 --> 00:13:43.340 So the answers: T is ten to the five microseconds, and f is ten to the minus two kilohertz. 00:13:43.390 --> 00:13:50.560 And now the rule that saves you — write it down: route everything through seconds and hertz first. 00:13:50.610 --> 00:13:59.010 Never convert milliseconds directly to kilohertz in your head — that one jump is where a power of ten silently disappears. 00:13:59.060 --> 00:14:01.730 Two safe hops beat one clever one. 00:14:01.780 --> 00:14:10.730 These two examples reappear on quizzes with the numbers filed off — including yours, in this week's online quiz. 00:14:12.183 --> 00:14:13.243 Now you. 00:14:13.293 --> 00:14:16.193 Ninety seconds, on paper, alone. 00:14:16.243 --> 00:14:19.733 Bangladesh mains electricity: 50 hertz. 00:14:19.783 --> 00:14:20.843 US mains: 60 hertz. 00:14:20.893 --> 00:14:23.923 Find the period of each, in milliseconds. 00:14:23.973 --> 00:14:32.923 And a bonus to think about while you compute: your eyes watch a lamp powered at 50 hertz — why don't you see it flicker? 00:14:34.193 --> 00:14:38.293 Pause now. 00:14:38.343 --> 00:14:47.293 Fifty hertz: T equals one over fifty, which is 0.02 seconds — one cycle every twentieth of a second, 20 milliseconds. 00:14:50.083 --> 00:14:53.203 This is Forouzan Example 3.3. 00:14:53.253 --> 00:15:00.093 Sixty hertz: one over sixty is about 0.0166 seconds — 16.6 milliseconds, six repeating. 00:15:00.143 --> 00:15:09.093 Faster cycles, shorter period; the two always move in opposite directions, which is a quick sanity check on any answer you ever produce here. 00:15:12.053 --> 00:15:13.703 And the bonus. 00:15:13.753 --> 00:15:22.703 That lamp actually peaks in brightness with every half-cycle — a hundred times a second — and you see steady light anyway, because your eyes are too slow to catch a change every ten milliseconds. 00:15:27.063 --> 00:15:29.413 Your senses have a frequency limit. 00:15:29.463 --> 00:15:38.413 Engineering exploits that limit constantly: your screen redraws at 60 hertz, the refresh rate of most displays, and you see a steady image. 00:15:43.053 --> 00:15:46.443 You have just done that exercise on paper. 00:15:46.493 --> 00:15:51.543 Here is the same wave with the three knobs exposed, so you can check yourself. 00:15:51.593 --> 00:16:00.543 Blue is your signal; grey never moves — two volts, five hertz, zero degrees — and everything you do is measured against it. 00:16:01.933 --> 00:16:05.013 Right now they sit on top of each other. 00:16:05.063 --> 00:16:07.153 Amplitude, two volts. 00:16:07.203 --> 00:16:09.253 Frequency, five hertz. 00:16:09.303 --> 00:16:12.283 Period, one over five, two hundred milliseconds. 00:16:12.333 --> 00:16:16.263 Two and a half cycles fit in the half-second window. 00:16:16.313 --> 00:16:20.143 Now double the frequency and watch the period. 00:16:20.193 --> 00:16:27.993 Ten hertz, and the period halves to a hundred milliseconds — because T equals one over f is not two facts. 00:16:28.043 --> 00:16:33.443 It is one fact, written two ways, and the tool will not let you break it. 00:16:33.493 --> 00:16:37.423 Now the knob that changes nothing except when. 00:16:37.473 --> 00:16:41.583 Phase, ninety degrees — one point five seven radians, a quarter of a period. 00:16:41.633 --> 00:16:46.723 Look at the two waves: same height, same rate, shifted sideways. 00:16:46.773 --> 00:16:52.363 Amplitude did not move. Frequency did not move. Period did not move. 00:16:52.413 --> 00:16:55.543 Phase is a head start, and nothing else. 00:16:55.593 --> 00:17:01.713 And here is the case worth sitting with: frequency zero. 00:17:01.763 --> 00:17:06.763 The wave stops being a wave and becomes a flat line, which we call DC. 00:17:06.813 --> 00:17:15.763 It has an amplitude, it has no period worth the name, and — as the first question of this session hinted — it carries nothing. 00:17:15.953 --> 00:17:22.643 Finally, the socket in the wall: fifty hertz, and a period of twenty milliseconds. 00:17:22.693 --> 00:17:26.163 That is the number I asked you to work out ninety seconds ago. 00:17:26.213 --> 00:17:35.163 Open this after the lecture and give yourself the other one — the sixty-hertz continent — before you look it up. 00:17:35.683 --> 00:17:38.133 So far the wave has lived in time. 00:17:38.183 --> 00:17:47.133 It also occupies space: while one cycle happens, the signal front physically travels down the medium, and the distance it covers during one cycle is the wavelength. 00:17:49.503 --> 00:17:58.043 Lambda equals c over f — or, since T is one over f, lambda equals c times T. Same thing. 00:17:58.093 --> 00:18:07.043 Here c is the propagation speed in THIS medium: three times ten to the eight meters per second in vacuum, and about two times ten to the eight in glass and copper. 00:18:09.583 --> 00:18:16.273 The formula is the same shape as distance equals speed times time, because that is exactly what it is. 00:18:16.323 --> 00:18:17.653 Work one. 00:18:17.703 --> 00:18:23.333 Red light has a frequency around four times ten to the fourteen hertz. 00:18:23.383 --> 00:18:32.333 In vacuum: three times ten to the eight, over four times ten to the fourteen — 0.75 times ten to the minus six meters. 00:18:33.303 --> 00:18:35.743 Three quarters of a micrometer. 00:18:35.793 --> 00:18:43.803 Now the same light in optical fiber, where light travels at about two times ten to the eight meters per second. 00:18:43.853 --> 00:18:46.403 Two over four is 0.5 — half a micrometer. 00:18:46.453 --> 00:18:55.403 Look at what just happened: the frequency did not change at all; the medium did, and the wavelength shrank with the speed. 00:18:55.893 --> 00:19:04.843 Which gives us the dictation sentence of the day — write it down exactly: frequency belongs to the source; speed belongs to the medium; wavelength is their quotient. 00:19:07.673 --> 00:19:14.663 The source decides how often; the medium decides how fast; nobody owns the wavelength alone. 00:19:14.713 --> 00:19:23.663 And this sentence returns on slide 29 in digital form, where the same idea is called bit length. 00:19:24.610 --> 00:19:26.170 Second checkpoint. 00:19:26.220 --> 00:19:30.400 Same rule — pause, paper, no scrolling back. 00:19:30.450 --> 00:19:31.650 One. 00:19:31.700 --> 00:19:35.340 A signal has a period of 1 millisecond. 00:19:35.390 --> 00:19:38.000 What is its frequency, in kilohertz? 00:19:38.050 --> 00:19:39.210 Two. 00:19:39.260 --> 00:19:41.090 US mains is 60 hertz. 00:19:41.140 --> 00:19:45.000 What is its period, in milliseconds? 00:19:45.050 --> 00:19:46.210 Three. 00:19:46.260 --> 00:19:53.720 An FM radio wave at 100 megahertz travels through air at three times ten to the eight meters per second. 00:19:53.770 --> 00:19:56.200 What is its wavelength? 00:19:56.250 --> 00:20:00.300 Pause now. 00:20:00.350 --> 00:20:01.780 Answers. 00:20:01.830 --> 00:20:05.970 The first: route through seconds and hertz. 00:20:06.020 --> 00:20:14.970 T is ten to the minus three seconds, so f is one over ten to the minus three — one thousand hertz, which is 1 kilohertz. 00:20:16.190 --> 00:20:21.000 The second: one over sixty of a second — about 16.6 milliseconds. 00:20:21.050 --> 00:20:28.030 You just did it two slides ago; the point of asking again is that it should now take five seconds. 00:20:28.080 --> 00:20:35.190 The third: lambda equals c over f — three times ten to the eight over ten to the eight, which is 3 meters. 00:20:35.240 --> 00:20:38.870 One cycle of FM radio is about the height of a room. 00:20:38.920 --> 00:20:45.880 If you wrote 3 and the units meters, take full marks. 00:20:45.930 --> 00:20:47.400 Section three. 00:20:47.450 --> 00:20:49.300 Two ways to look at a signal. 00:20:49.350 --> 00:20:52.810 So far every signal has been a single sine wave. 00:20:52.860 --> 00:20:54.830 Real signals are mixtures. 00:20:54.880 --> 00:21:03.830 This section is about describing mixtures: Fourier's recipe card, the frequency domain, and the one subtraction the whole chapter stands on. 00:21:06.954 --> 00:21:14.244 The load-bearing idea of the whole physical layer comes from Fourier (Jean-Baptiste Joseph Fourier). 00:21:14.294 --> 00:21:23.244 The claim: any composite signal, however messy — your voice, a song, this sentence as it leaves my mouth — is a combination of simple sine waves. 00:21:26.604 --> 00:21:28.094 Not approximately. 00:21:28.144 --> 00:21:29.264 Exactly. 00:21:29.314 --> 00:21:36.124 However tangled the wiggle, it is sines underneath, added together, and nothing else is needed. 00:21:36.174 --> 00:21:38.854 Think of it as a recipe card. 00:21:38.904 --> 00:21:46.604 Each ingredient sine has three properties — and you now own all three: its own frequency, its own amplitude, its own phase. 00:21:46.654 --> 00:21:54.834 Write down the list of ingredients and you have described the signal completely, without drawing a single wiggle. 00:21:54.884 --> 00:22:00.124 That list is the frequency domain, named properly on slide 19. 00:22:00.174 --> 00:22:02.364 And two flavors. 00:22:02.414 --> 00:22:09.874 A periodic composite signal is made from a series of DISCRETE frequencies — separate, countable ingredients. 00:22:09.924 --> 00:22:16.524 A nonperiodic composite contains a CONTINUOUS range of frequencies — an unbroken smear of them. 00:22:16.574 --> 00:22:22.070 You will draw both before the section ends. 00:22:22.600 --> 00:22:25.130 Now watch the claim happen. 00:22:25.180 --> 00:22:29.920 Thirty-four seconds, silent — I am the narration. 00:22:29.970 --> 00:22:37.890 On the left: three honest sine waves — one at some frequency f, one at three times f, one at five times f. 00:22:37.940 --> 00:22:41.020 Watch them add, point by point. 00:22:41.070 --> 00:22:45.400 The composite looks complicated — but nothing complicated happened. 00:22:45.450 --> 00:22:47.760 Three sines and a plus sign. 00:22:47.810 --> 00:22:50.580 That is all a composite signal is. 00:22:50.630 --> 00:22:53.310 Now pause on the right side. 00:22:53.360 --> 00:22:56.260 Each component sine has become one bar. 00:22:56.310 --> 00:23:02.880 Its position along the axis is its frequency; its height is its peak amplitude. 00:23:02.930 --> 00:23:09.980 Three sines in the time view; three bars in the frequency view. 00:23:10.030 --> 00:23:16.780 Same signal, photographed from two angles — the oscilloscope view, and the recipe view. 00:23:16.830 --> 00:23:23.982 Keep both photographs in mind; the next slide names them properly. 00:23:24.032 --> 00:23:25.462 Two plots, one reality. 00:23:25.512 --> 00:23:29.442 Let us name the two photographs you just took. 00:23:29.492 --> 00:23:33.322 The time domain: amplitude against time. 00:23:33.372 --> 00:23:42.072 This is the oscilloscope view, the plot you have seen all your life — every wiggle recorded, moment by moment. 00:23:42.122 --> 00:23:49.522 Complete, honest, and almost unreadable for a mixture: three ingredient sines look like one tangled wave. 00:23:49.572 --> 00:23:54.432 The frequency domain: peak amplitude against frequency. 00:23:54.482 --> 00:24:03.432 This is the recipe view — one spike per ingredient sine, where the spike's position is its frequency and its height is its peak amplitude. 00:24:03.852 --> 00:24:08.972 The same three tangled waves become three clean spikes standing in a row. 00:24:09.022 --> 00:24:16.682 This is the idea behind Forouzan's Figure 3.9, and it is the view this course lives in from now on. 00:24:16.732 --> 00:24:24.672 Now notice what the frequency domain throws away, because a summary is only trustworthy when you know what it forgot. 00:24:24.722 --> 00:24:32.542 It drops the moment-to-moment changes, and it drops the phase — it shows peak amplitude per frequency and nothing else. 00:24:32.592 --> 00:24:36.192 It is a summary, and summaries are allowed to forget. 00:24:36.242 --> 00:24:42.052 What it keeps is exactly what this course needs: which frequencies are present, and how strong. 00:24:42.102 --> 00:24:46.172 And a small question before you advance — answer it in your head. 00:24:46.222 --> 00:24:51.612 A composite made of ONE sine wave: what does its frequency-domain plot look like? 00:24:51.662 --> 00:24:57.078 One spike, alone on the axis. 00:24:57.128 --> 00:25:01.538 The definition the chapter is named for is one subtraction. 00:25:01.588 --> 00:25:09.798 The bandwidth of a composite signal is the range of frequencies it contains: B equals f-high minus f-low. 00:25:09.848 --> 00:25:13.028 Highest ingredient minus lowest ingredient. 00:25:13.078 --> 00:25:18.958 That is the entire definition — a difference between two numbers, nothing deeper. 00:25:19.008 --> 00:25:22.608 Worked once, so the trap is visible. 00:25:22.658 --> 00:25:26.208 A signal contains frequencies from 1,000 hertz up to 5,000 hertz. 00:25:26.258 --> 00:25:31.508 Its bandwidth is five thousand minus one thousand: 4,000 hertz. 00:25:31.558 --> 00:25:34.408 Not five thousand — four thousand. 00:25:34.458 --> 00:25:42.498 Bandwidth is the width of the band, not the height of its ceiling, and the exam will check exactly this. 00:25:42.548 --> 00:25:49.738 And here is why this number becomes the spine of the course: bandwidth belongs to signals AND to media. 00:25:49.788 --> 00:25:54.838 A signal occupies a band — the range of frequencies its recipe uses. 00:25:54.888 --> 00:25:59.528 A medium passes a band — the range of frequencies it can carry well. 00:25:59.578 --> 00:26:05.378 Two uses of the same word, and the interesting engineering happens when the two bands meet. 00:26:05.428 --> 00:26:12.148 Specifically: when the signal's band is wider than the medium's band, the medium edits your signal. 00:26:12.198 --> 00:26:17.609 Slide 23 shows that happening. 00:26:17.859 --> 00:26:24.229 Forouzan Example 3.10, and it reappears with the five numbers changed. 00:26:24.279 --> 00:26:31.819 A periodic signal is decomposed into five sine waves with frequencies 100, 300, 500, 700 and 900 hertz. 00:26:31.869 --> 00:26:35.159 What is its bandwidth? 00:26:35.209 --> 00:26:42.019 And draw the spectrum, if all components have a maximum amplitude of 10 volts. 00:26:42.069 --> 00:26:45.449 Step one — find the edges of the recipe. 00:26:45.499 --> 00:26:51.579 The lowest ingredient is 100 hertz; the highest is 900 hertz. 00:26:51.629 --> 00:26:54.059 Step two — subtract. 00:26:54.109 --> 00:26:56.059 B equals 900 minus 100: 800 hertz. 00:26:56.109 --> 00:26:59.589 Two marks for those two steps. 00:26:59.639 --> 00:27:06.719 The remaining marks are for the drawing, and this is where they are lost. 00:27:06.769 --> 00:27:14.629 Five spikes — at 100, 300, 500, 700 and 900 — each one 10 volts tall, and NOTHING between them. 00:27:14.679 --> 00:27:17.549 I draw lollipops, not a curve. 00:27:17.599 --> 00:27:22.569 The gaps are not laziness; the gaps are the physics. 00:27:22.619 --> 00:27:26.159 This signal simply does not contain 200 hertz. 00:27:26.209 --> 00:27:29.979 There is no ingredient there, so there is no ink there. 00:27:30.029 --> 00:27:32.169 Why spikes at all? 00:27:32.219 --> 00:27:34.679 Because the signal is PERIODIC. 00:27:34.729 --> 00:27:42.369 A periodic composite contains only discrete frequencies, so its spectrum is a row of separated spikes. 00:27:42.419 --> 00:27:49.478 Write that sentence next to your drawing — it is worth marks on its own. 00:27:49.528 --> 00:27:53.988 Let us seal that rule so it cannot come loose under exam pressure. 00:27:54.038 --> 00:27:57.968 A periodic composite has a discrete spectrum. 00:27:58.018 --> 00:28:03.938 Only specific frequencies exist, so the spectrum is a row of separated spikes. 00:28:03.988 --> 00:28:12.938 And note the aside: periodic composites are rare in data communications — because a signal that repeats forever, identically, is a signal with nothing new to say. 00:28:15.418 --> 00:28:20.178 That is the same reason the pure sine wave from minute one says nothing. 00:28:20.228 --> 00:28:24.468 A nonperiodic composite has a continuous spectrum. 00:28:24.518 --> 00:28:29.858 An unbroken range of frequencies, drawn as a filled curve over a band. 00:28:29.908 --> 00:28:36.608 And this is nearly everything you care about: speech, music, video — and your data. 00:28:36.658 --> 00:28:44.618 Either way — and this is the point of the slide — bandwidth is the same subtraction: f-high minus f-low. 00:28:44.668 --> 00:28:49.478 The shape of the spectrum changes with the flavor; the arithmetic never does. 00:28:49.528 --> 00:28:56.400 Spikes or curve, you find the edges and you subtract. 00:28:56.450 --> 00:29:04.280 Now the promised meeting between the two owners of the word bandwidth — and the reason any of this matters for a real link. 00:29:04.330 --> 00:29:10.410 A signal occupies a band: the range of frequencies it actually contains. 00:29:10.460 --> 00:29:18.630 Speech occupies roughly 300 hertz to 3,300 hertz — that is where almost all of its energy lives. 00:29:18.680 --> 00:29:24.190 Music occupies up to about 20 kilohertz, the upper limit of human hearing. 00:29:24.240 --> 00:29:29.630 A medium passes a band: the range of frequencies it carries well. 00:29:29.680 --> 00:29:37.060 Every real medium — copper, glass, air — is like this; none of them carries everything. 00:29:37.110 --> 00:29:42.410 A telephone voice channel, for instance, is allocated about 4 kilohertz. 00:29:42.460 --> 00:29:51.410 That number was chosen using exactly the speech figure you just heard: wide enough for voice, and not a hertz more than the economics required. 00:29:51.750 --> 00:29:57.110 And here is what happens when the signal's band is wider than the medium's band. 00:29:57.160 --> 00:30:00.180 The components outside the band are deleted. 00:30:00.230 --> 00:30:01.370 Not delayed. 00:30:01.420 --> 00:30:02.560 Not shrunk. 00:30:02.610 --> 00:30:07.600 Deleted — the medium simply cannot carry them, so they do not arrive. 00:30:07.650 --> 00:30:12.300 What arrives is a different signal: the recipe with ingredients missing. 00:30:12.350 --> 00:30:21.300 You have heard this effect your whole life — music down a telephone line loses everything above the band, which is exactly why music on hold sounds flat and dull. 00:30:22.660 --> 00:30:26.760 Nobody turned the quality down; the channel edited the signal. 00:30:26.810 --> 00:30:30.100 A medium is a filter with a band of its own. 00:30:30.150 --> 00:30:39.100 Whether a medium's band is wide enough for the signal you want to send — and what that costs — is the engineering question of the next few sessions. 00:30:41.750 --> 00:30:43.240 Third checkpoint. 00:30:43.290 --> 00:30:46.360 Pause and answer on paper. 00:30:46.410 --> 00:30:46.660 One. 00:30:46.710 --> 00:30:52.030 A composite signal contains frequencies from 2,000 hertz to 9,000 hertz. 00:30:52.080 --> 00:30:54.470 What is its bandwidth? 00:30:54.520 --> 00:30:55.680 Two. 00:30:55.730 --> 00:31:01.770 One spectrum is a row of separated spikes; another is a filled curve. 00:31:01.820 --> 00:31:03.790 Which signal is periodic? 00:31:03.840 --> 00:31:05.010 Three. 00:31:05.060 --> 00:31:11.610 What does the frequency-domain plot of a single pure sine wave look like? 00:31:11.660 --> 00:31:16.090 Pause now. 00:31:16.140 --> 00:31:17.000 Answers. 00:31:17.050 --> 00:31:21.930 The first: nine thousand minus two thousand — 7,000 hertz. 00:31:21.980 --> 00:31:25.700 The range, never the highest number alone. 00:31:25.750 --> 00:31:29.860 The second: the spikes belong to the periodic signal. 00:31:29.910 --> 00:31:37.300 Periodic composites contain only discrete frequencies; nonperiodic composites fill a continuous band. 00:31:37.350 --> 00:31:44.870 The third: a single spike at the wave's frequency — one ingredient, one line, nothing anywhere else on the axis. 00:31:44.920 --> 00:31:53.870 That spike is the answer to the question from minute one: one ingredient means f-high equals f-low, so the bandwidth is zero. Slide 37 does the subtraction. 00:31:59.390 --> 00:32:00.780 Section four. 00:32:00.830 --> 00:32:03.930 Digital signals — bit rate and levels. 00:32:03.980 --> 00:32:11.790 Now we cross to the other half of the pairing from section one: the nonperiodic digital signals that actually carry data. 00:32:11.840 --> 00:32:13.900 Two questions run the section. 00:32:13.950 --> 00:32:16.120 How fast is a digital signal? 00:32:16.170 --> 00:32:18.500 And how much can one level of it carry? 00:32:18.550 --> 00:32:27.500 The second question sounds like free money; slide 34 names the catch, and the catch is noise. 00:32:28.016 --> 00:32:35.396 Start with a picture in your head — Forouzan's Figure 3.17 draws it, and this slide says it. 00:32:35.446 --> 00:32:41.976 On the left, a two-level digital signal — the digital signal of your imagination. 00:32:42.026 --> 00:32:45.936 High means 1, low means 0, one bit per level. 00:32:45.986 --> 00:32:50.926 If the signal changes eight times, eight changes carry eight bits. 00:32:50.976 --> 00:32:57.056 On the right, the same wire, the same eight changes — but now four levels. 00:32:57.106 --> 00:33:06.056 And a level now says two bits: the top level might mean one-one, the bottom might mean zero-zero, and the two in between carry zero-one and one-zero. 00:33:07.456 --> 00:33:10.616 Same eight changes — sixteen bits. 00:33:10.666 --> 00:33:16.176 Notice what did NOT change: the wire, and the number of changes per second. 00:33:16.226 --> 00:33:18.086 Nothing physical improved. 00:33:18.136 --> 00:33:26.796 The wire has no idea how many bits a level is worth — we decide, by defining more levels and agreeing what each one means. 00:33:26.846 --> 00:33:34.886 That should feel familiar: it is Session 1's lesson about agreements, now operating one level below the bits themselves. 00:33:34.936 --> 00:33:41.316 The obvious question is how far this trick stretches — eight levels, sixteen, a thousand? 00:33:41.366 --> 00:33:50.316 Slide 34 answers it: the limit is the voltage gap between levels, and the enemy is noise. 00:33:51.369 --> 00:33:54.509 So how many bits does a level carry, in general? 00:33:54.559 --> 00:33:59.009 There is an exchange rate, and it is a logarithm. 00:33:59.059 --> 00:34:02.319 Two levels: log base two of 2 is 1. 00:34:02.369 --> 00:34:06.199 One bit per level — the case you knew. 00:34:06.249 --> 00:34:09.239 Four levels: log base two of 4 is 2. 00:34:09.289 --> 00:34:14.399 Two bits per level — the right-hand picture from the last slide. 00:34:14.449 --> 00:34:17.639 Eight levels: log base two of 8 is 3. 00:34:17.689 --> 00:34:19.169 Three bits per level. 00:34:19.219 --> 00:34:28.169 This is Forouzan Example 3.16, and it is clean — eight is a power of two, so the logarithm comes out whole. 00:34:28.509 --> 00:34:31.969 Sixteen levels: four bits per level. 00:34:32.019 --> 00:34:39.709 You can see the pattern — every doubling of the level count buys exactly one more bit per level. 00:34:39.759 --> 00:34:46.419 And now the trap, which is Forouzan Example 3.17 and a permanent resident of exam papers. 00:34:46.469 --> 00:34:47.689 Nine levels. 00:34:47.739 --> 00:34:55.239 Log base two of nine is 3.17 bits — write that as your final answer and you have just claimed to send seventeen hundredths of a bit. 00:34:55.289 --> 00:34:56.819 Bits come whole. 00:34:56.869 --> 00:35:01.099 There is no such thing as most of a bit arriving. 00:35:01.149 --> 00:35:04.559 The realistic answer is 4 bits per level. 00:35:04.609 --> 00:35:12.899 Which gives the rule: the level count should be a power of two — then the logarithm comes out whole and nothing is wasted. 00:35:12.949 --> 00:35:21.819 A nine-level design pays for four bits' worth of receiver — sixteen levels' worth of complexity — and wastes seven of the sixteen. 00:35:21.869 --> 00:35:30.819 So when you meet a level count in the wild, it will almost always be 2, 4, 8, 16, and so on — and when an exam hands you a 9, it is testing whether you will round a bit. 00:35:37.631 --> 00:35:40.981 Now watch levels turn into speed. 00:35:41.031 --> 00:35:47.311 Forty-one seconds, silent. Watch the counter, not the waveform. 00:35:47.361 --> 00:35:56.311 Three runs, and every run has exactly the same speed of change — the same changes per second, sixteen changes in all. 00:35:56.671 --> 00:36:01.771 First run, two levels: the counter crawls to sixteen bits. 00:36:01.821 --> 00:36:10.771 Second run, four levels — same changes, nothing faster: thirty-two bits. 00:36:13.121 --> 00:36:22.071 Third run, eight levels: forty-eight. 00:36:24.421 --> 00:36:33.181 Read the freeze frame out loud: same speed of change, more meaning per change. 00:36:33.231 --> 00:36:35.361 The wave never sped up. 00:36:35.411 --> 00:36:44.361 The meaning per change did — one bit, then two, then three, exactly log base two of L. And this cannot be free forever. Slide 34 says why. 00:36:46.380 --> 00:36:50.840 Two definitions to own, and then we price real payloads. 00:36:50.890 --> 00:36:59.840 Bit rate, written N. Most digital signals are nonperiodic — they carry data, so they never repeat — which means period and frequency stop being the right tools. 00:37:02.510 --> 00:37:07.980 The replacement is bit rate: the number of bits per second, written bps. 00:37:08.030 --> 00:37:15.440 When you read a spec sheet — a hundred megabits, a gigabit — this is the number you are reading. 00:37:15.490 --> 00:37:20.360 For digital signals, bit rate is what frequency was for analog ones. 00:37:20.410 --> 00:37:27.460 Bit length — the digital cousin of wavelength, and the return of the dictation sentence from section two. 00:37:27.510 --> 00:37:36.180 Bit length equals propagation speed times bit duration, where bit duration is the time one bit occupies: one over N seconds. 00:37:36.230 --> 00:37:45.180 Same shape as lambda equals c times T. The medium owns the speed; the sender owns the rate; bit length is their quotient. 00:37:45.780 --> 00:37:50.030 Sanity check, so the definition becomes a picture. 00:37:50.080 --> 00:37:58.080 Send one gigabit per second into copper, where signals propagate at about two times ten to the eight meters per second. 00:37:58.130 --> 00:38:07.080 One bit lasts one billionth of a second, so its length is two times ten to the eight divided by ten to the nine — 0.2 meters. 00:38:07.330 --> 00:38:09.670 Twenty centimeters of cable per bit. 00:38:09.720 --> 00:38:13.340 A thousand bits physically fit in an ordinary room. 00:38:13.390 --> 00:38:22.340 Networking becomes easier the moment bits become objects with sizes — and in Session 6, when we ask how many bits are in flight on a link, this is the picture to reach for. 00:38:27.747 --> 00:38:34.757 Now we price payloads, and there are three: text, voice, and television. 00:38:34.807 --> 00:38:37.377 Forouzan Example 3.18 first. 00:38:37.427 --> 00:38:42.777 We need to download text documents at the rate of 100 pages per second. 00:38:42.827 --> 00:38:49.107 A page averages 24 lines of 80 characters, and one character costs 8 bits. 00:38:49.157 --> 00:38:52.347 What bit rate does the channel need? 00:38:52.397 --> 00:38:55.937 Step one — the cost of one page. 00:38:55.987 --> 00:39:04.617 Twenty-four lines, times eighty characters, times eight bits: 24 times 80 is 1,920 characters, times 8 is 15,360 bits per page. 00:39:04.667 --> 00:39:08.927 Step two — a hundred of those every second. 00:39:08.977 --> 00:39:13.027 One hundred times 15,360 is 1,536,000 bits per second. 00:39:13.077 --> 00:39:15.797 Call it 1.536 megabits per second. 00:39:15.847 --> 00:39:24.797 And now look past the numbers at the structure, because the structure is the whole genre: things per second, times bits per thing. 00:39:28.887 --> 00:39:31.527 Pages per second times bits per page. 00:39:31.577 --> 00:39:40.527 Every bit-rate question you will ever see — in this course, on the exam, in your job — is that multiplication wearing different clothes. 00:39:44.597 --> 00:39:53.547 The next two slides wear two different sets of clothes, and the template does not move. 00:39:56.141 --> 00:39:58.711 Payload two — and this one you do. 00:39:58.761 --> 00:40:01.311 Two minutes, calculator out. 00:40:01.361 --> 00:40:10.311 A digitized voice channel samples a 4-kilohertz analog voice signal at twice its highest frequency — two samples per hertz of that 4 kilohertz. 00:40:12.131 --> 00:40:14.441 Each sample costs 8 bits. 00:40:14.491 --> 00:40:16.541 What bit rate does the call need? 00:40:16.591 --> 00:40:20.641 Pause now. 00:40:20.691 --> 00:40:26.211 The most common error here is multiplying four thousand by eight and forgetting the two. 00:40:26.261 --> 00:40:29.101 Step one — samples per second. 00:40:29.151 --> 00:40:34.431 Twice the highest frequency: two times 4,000 is 8,000 samples every second. 00:40:34.481 --> 00:40:41.581 Step two — the template: things per second times bits per thing. 00:40:41.631 --> 00:40:48.271 Eight thousand samples times eight bits: 64,000 bits per second. 00:40:48.321 --> 00:40:50.851 Sixty-four kilobits. 00:40:50.901 --> 00:40:53.241 You have met this number before. 00:40:53.291 --> 00:41:02.191 In Session 1 we computed telephone-quality audio as eight thousand samples a second times eight bits — 64 kbps, and I told you to remember it. 00:41:02.241 --> 00:41:08.661 Here it is again, earned honestly from the other direction. 00:41:08.711 --> 00:41:17.661 Sixty-four kilobits per second is the most famous constant in telephony: one voice channel, the brick the entire global telephone network is plumbed in multiples of. 00:41:19.721 --> 00:41:23.631 Every landline call on Earth is a 64k stream. 00:41:23.681 --> 00:41:30.471 Now, why sample at TWICE the highest frequency — where did the two come from? 00:41:30.521 --> 00:41:39.471 Take the two as given. The sampling theorem proves it, and that theorem is not in this course — Session 5's Nyquist result is a different one, the bit-rate limit of a channel. 00:41:42.031 --> 00:41:47.462 Forouzan Example 3.19, banked. 00:41:47.512 --> 00:41:54.372 Payload three, Forouzan Example 3.20 — and the template gets stress-tested. 00:41:54.422 --> 00:42:01.222 High-definition TV: a 1920 by 1080 screen, refreshed 30 times per second, 24 bits per color pixel. 00:42:01.272 --> 00:42:04.412 What is the raw bit rate? 00:42:04.462 --> 00:42:11.022 Step one — bits per thing, where the thing is one screen. 00:42:11.072 --> 00:42:15.052 Nineteen-twenty by ten-eighty is 2,073,600 pixels per screen. 00:42:15.102 --> 00:42:18.392 Step two — things per second. 00:42:18.442 --> 00:42:27.392 Thirty screens a second, so the whole product is 1920 times 1080 times 30 times 24: 1,492,992,000 bits per second. 00:42:28.292 --> 00:42:36.982 One and a half billion bits, every second — about 1.5 gigabits per second, raw. 00:42:37.032 --> 00:42:45.982 Put the three payloads side by side: 64 kilobits for a call, one and a half megabits for a hundred pages of text, one and a half gigabits for raw television. 00:42:49.442 --> 00:42:58.392 One template — things per second times bits per thing — spanning five orders of magnitude. 00:42:59.242 --> 00:43:02.982 That range is why engineers respect bit rate. 00:43:03.032 --> 00:43:11.982 And yet your actual TV feed arrives at 20 to 40 megabits against 1.49 gigabits raw — a reduction of about 97 to 99 percent, thrown away where your eye does not notice it. 00:43:17.092 --> 00:43:26.042 This course prices everything raw, exactly so you can see what compression is saving you. 00:43:28.881 --> 00:43:33.771 Three worked examples in a row is a lot of arithmetic to watch. 00:43:33.821 --> 00:43:41.991 Here is the same arithmetic with the numbers under your hand, and a second panel that asks whether what you built is actually enough. 00:43:42.041 --> 00:43:45.861 Two levels, eight thousand changes per second. 00:43:45.911 --> 00:43:53.901 Each change carries log base two of two, which is one bit, so the bit rate is eight thousand bits per second. 00:43:53.951 --> 00:44:02.161 Four levels — two bits per change — and the same eight thousand changes now carry sixteen thousand bits. 00:44:02.211 --> 00:44:07.171 Sixteen levels, four bits per change, thirty-two thousand. 00:44:07.221 --> 00:44:11.531 The wire is changing at exactly the same speed in all three. 00:44:11.581 --> 00:44:17.361 Only the size of the alphabet changed, and that is the entire idea of this section. 00:44:17.411 --> 00:44:20.551 Now price it against real traffic. 00:44:20.601 --> 00:44:29.551 Text, a hundred pages a second: a hundred pages, twenty-four lines, eighty characters, eight bits — one million five hundred and thirty-six thousand bits per second. 00:44:32.241 --> 00:44:36.141 That is Example 3.18, and it fits exactly, with zero headroom. 00:44:36.191 --> 00:44:45.141 One digitized voice call: four kilohertz, two samples per hertz, eight bits — sixty-four thousand bits per second. 00:44:47.371 --> 00:44:55.091 That is the two-minute exercise you did a moment ago, and the number you will meet in every remaining session of this course. 00:44:55.141 --> 00:44:58.541 And then television, uncompressed. 00:44:58.591 --> 00:45:06.991 Nineteen twenty by ten eighty, thirty frames a second, twenty-four bits a pixel — one point four nine gigabits per second. 00:45:07.041 --> 00:45:11.861 Sixteen levels at half a million changes a second gives you two megabits. 00:45:11.911 --> 00:45:17.651 The tool states the gap plainly: short by a factor of seven hundred and forty-six. 00:45:17.701 --> 00:45:26.651 Push the slider to its maximum and it is still hopeless — which is why nothing you have ever watched was sent to you raw. 00:45:27.374 --> 00:45:29.684 So — the obvious exploit. 00:45:29.734 --> 00:45:38.684 If eight levels carry three bits per change and sixteen carry four, why not define a thousand and twenty-four levels and carry ten bits per change? 00:45:39.584 --> 00:45:42.054 Nothing in today's formula forbids it. 00:45:42.104 --> 00:45:44.204 Here is why nobody does. 00:45:44.254 --> 00:45:49.064 Your wire has a fixed voltage window — say three volts. 00:45:49.114 --> 00:45:58.064 With two levels you can put them at zero volts and three volts: the gap between neighbors is the whole window, three full volts, and a receiver cannot miss. 00:45:59.784 --> 00:46:04.054 Now pack eight levels into the same three volts. 00:46:04.104 --> 00:46:13.054 Eight levels means seven gaps, and three volts across seven gaps is about 0.43 volts between neighbors — under half a volt. 00:46:13.454 --> 00:46:16.624 Every level you add squeezes the gaps thinner. 00:46:16.674 --> 00:46:25.284 One whisper of interference and level five reads as level six — and your three clever bits arrive as three wrong ones. 00:46:25.334 --> 00:46:30.284 The enemy that lives in that gap has a name: NOISE. 00:46:30.334 --> 00:46:39.284 More levels per volt means less room between levels, and less room means less tolerance for the interference that every real wire suffers. 00:46:39.434 --> 00:46:42.324 Today the catch gets its name — that is all. 00:46:42.374 --> 00:46:46.294 Session 5 measures noise properly, in decibels. 00:46:46.344 --> 00:46:55.294 And in the same session, two theorems — Nyquist's and Shannon's — put an exact ceiling on how many levels a real channel tolerates. 00:46:55.854 --> 00:47:03.973 The free money is real; it has a credit limit, and Session 5 computes it. 00:47:04.023 --> 00:47:05.443 Fourth checkpoint. 00:47:05.493 --> 00:47:08.513 Pause, paper, no scrolling back. 00:47:08.563 --> 00:47:09.763 One. 00:47:09.813 --> 00:47:13.843 A digital signal uses 16 levels. 00:47:13.893 --> 00:47:16.323 How many bits does each level carry? 00:47:16.373 --> 00:47:17.523 Two. 00:47:17.573 --> 00:47:20.953 A designer insists on 9 levels. 00:47:21.003 --> 00:47:23.633 How many bits must the system budget per level — and why? 00:47:23.683 --> 00:47:24.673 Three. 00:47:24.723 --> 00:47:29.003 A page is 30 lines of 100 characters, 8 bits each. 00:47:29.053 --> 00:47:31.763 You need 50 pages per second. 00:47:31.813 --> 00:47:33.733 What bit rate? 00:47:33.783 --> 00:47:38.003 Pause now. 00:47:38.053 --> 00:47:39.093 Answers. 00:47:39.143 --> 00:47:46.033 The first: log base two of sixteen — 4 bits per level. 00:47:46.083 --> 00:47:48.173 The second: 4 bits. 00:47:48.223 --> 00:47:57.173 Log base two of nine is 3.17, but bits come whole — the system pays for sixteen levels' worth and wastes seven of them. 00:47:58.043 --> 00:48:03.093 If you wrote 3.17, circle it in red and remember why. 00:48:03.143 --> 00:48:08.413 The third: one page is 30 times 100 times 8 — 24,000 bits. 00:48:08.463 --> 00:48:13.033 Fifty of those a second is 1,200,000 bits per second: 1.2 megabits. 00:48:13.083 --> 00:48:20.773 Things per second, times bits per thing. 00:48:20.823 --> 00:48:22.333 Section five. 00:48:22.383 --> 00:48:31.270 Back to the question from minute one — and this time you own every word needed to answer it. 00:48:31.860 --> 00:48:37.050 Here is your answer, in language you did not own at the start of this session. 00:48:37.100 --> 00:48:40.950 Draw a single pure sine wave in the frequency domain. 00:48:41.000 --> 00:48:45.600 One spike, alone on the axis, at its one frequency f. 00:48:45.650 --> 00:48:54.600 Now do the subtraction the whole chapter runs on: bandwidth equals f-high minus f-low — and both of them are the same f. 00:48:55.360 --> 00:48:57.450 B equals f minus f. 00:48:57.500 --> 00:48:58.590 Zero. 00:48:58.640 --> 00:49:00.490 Zero bandwidth. 00:49:00.540 --> 00:49:07.040 The 'range of frequencies' is a single point; the recipe has exactly one ingredient. 00:49:07.090 --> 00:49:10.110 You drew this spike yourself at checkpoint three. 00:49:10.160 --> 00:49:15.240 And in plain terms, zero bandwidth means the wave is perfectly predictable. 00:49:15.290 --> 00:49:22.490 Give me the three knobs — A, f and phi — and I will tell you the wave's value at any moment you like. 00:49:22.540 --> 00:49:25.540 Nothing it ever does can surprise you. 00:49:25.590 --> 00:49:33.770 It is the DC flat line's slightly livelier cousin: both perfectly known, and both, therefore, silent. 00:49:33.820 --> 00:49:36.700 Because information IS surprise. 00:49:36.750 --> 00:49:45.700 A signal that tells you something must be able to change in ways you could not predict — and unpredictable change, Fourier says, is built from many frequencies. 00:49:47.980 --> 00:49:50.270 No bandwidth, no surprise. 00:49:50.320 --> 00:49:52.800 No surprise, no information. 00:49:52.850 --> 00:49:59.530 So: a signal with no bandwidth carries no information — and bandwidth is not a technicality. 00:49:59.580 --> 00:50:03.070 It is the room a signal needs to say anything at all. 00:50:03.120 --> 00:50:06.540 If your minute-one guess was 'because it never changes' — you were right. 00:50:06.590 --> 00:50:09.960 You were just missing the word bandwidth. 00:50:10.010 --> 00:50:18.960 And notice that the held question from section one answers itself the same way: a periodic digital signal repeats identically forever, so it too has nothing new to say. 00:50:20.960 --> 00:50:29.910 Signals that carry data must be able to surprise you, which is exactly why the data-carrying half of the pairing is nonperiodic. 00:50:32.287 --> 00:50:37.207 Before the exam does it to you — the five mistakes of this session. 00:50:37.257 --> 00:50:40.447 Predict each one before I reveal it. 00:50:40.497 --> 00:50:46.927 One: converting milliseconds to kilohertz in one jump, and dropping a power of ten on the way. 00:50:46.977 --> 00:50:55.927 Route through seconds and hertz, always: 100 milliseconds, to ten to the minus one seconds, to 10 hertz, to ten to the minus two kilohertz. 00:50:57.727 --> 00:50:59.577 Two safe hops. 00:50:59.627 --> 00:51:08.577 Two: 'higher frequency means a bigger, stronger signal.' No. A, f and phi are independent knobs — frequency says how often, amplitude says how tall. 00:51:12.417 --> 00:51:16.787 You watched them move independently in the playground. 00:51:16.837 --> 00:51:24.147 Three: 'bandwidth is the highest frequency of the signal.' It is the RANGE — f-high minus f-low. 00:51:24.197 --> 00:51:29.097 A band from 1,000 to 5,000 hertz has a bandwidth of 4,000, not 5,000. 00:51:29.147 --> 00:51:36.197 This one and the powers of ten are the two most common errors in this session. 00:51:36.247 --> 00:51:41.977 Four: drawing a periodic signal's spectrum as a smooth filled curve. 00:51:42.027 --> 00:51:46.717 Periodic means discrete spikes — lollipops with nothing between them. 00:51:46.767 --> 00:51:50.397 Filled curves belong to nonperiodic signals. 00:51:50.447 --> 00:51:59.397 Five: 'nine levels, log base two of nine, 3.17 — so three bits will do.' Bits come whole and levels come in powers of two: nine levels needs 4 bits, and you are paying for sixteen. 00:52:03.237 --> 00:52:12.187 Round bits up, always — and better, choose level counts where there is nothing to round. 00:52:14.854 --> 00:52:19.834 Let me close the content by naming exactly what you should now be able to do. 00:52:19.884 --> 00:52:28.834 Classify any signal on both axes — analog or digital, periodic or nonperiodic — and name the pairing data communications uses, and why. 00:52:29.324 --> 00:52:38.274 Describe a sine wave completely with three knobs, and convert between period, frequency and wavelength — routing through seconds and hertz, never jumping. 00:52:42.534 --> 00:52:51.484 Read a frequency-domain plot, and compute bandwidth as f-high minus f-low for any composite — drawing spikes if it is periodic, a curve if it is not. 00:52:53.904 --> 00:53:02.854 Price a digital payload with things per second times bits per thing — a page of text, a voice call, raw television, or anything an exam invents. 00:53:05.564 --> 00:53:14.514 And exchange L levels for log base two of L bits per level — remembering that bits come whole, so nine levels still costs four bits. 00:53:15.374 --> 00:53:19.624 If any of those feels shaky, the section that covers it is still there. 00:53:19.674 --> 00:53:25.004 This is a video — use it as one. 00:53:25.254 --> 00:53:28.314 Five last questions, across the whole session. 00:53:28.364 --> 00:53:30.324 Pause and answer them on paper. 00:53:30.374 --> 00:53:31.584 One. 00:53:31.634 --> 00:53:34.134 A signal completes 25 cycles every second. 00:53:34.184 --> 00:53:38.834 What is its period, in milliseconds? 00:53:38.884 --> 00:53:40.034 Two. 00:53:40.084 --> 00:53:46.034 A composite signal contains frequencies from 500 hertz to 4,500 hertz. 00:53:46.084 --> 00:53:48.734 What is its bandwidth? 00:53:48.784 --> 00:53:49.954 Three. 00:53:50.004 --> 00:53:55.414 Draw the frequency-domain plot of a pure 8-kilohertz sine wave. 00:53:55.464 --> 00:53:56.674 Four. 00:53:56.724 --> 00:53:59.694 A digital signal uses 64 levels. 00:53:59.744 --> 00:54:02.624 How many bits per level? 00:54:02.674 --> 00:54:03.964 Five. 00:54:04.014 --> 00:54:09.094 Digitized voice: 8,000 samples per second, 8 bits per sample. 00:54:09.144 --> 00:54:11.514 What is the bit rate? 00:54:11.564 --> 00:54:15.614 Pause now. 00:54:15.664 --> 00:54:18.364 Take your time on these. 00:54:18.414 --> 00:54:24.404 One — T equals one over twenty-five of a second: 40 milliseconds. 00:54:24.454 --> 00:54:29.194 Two — 4,500 minus 500: 4,000 hertz, the range and nothing else. 00:54:29.244 --> 00:54:38.194 Three — a single spike at 8 kilohertz, nothing anywhere else on the axis; and if it were the only ingredient, that signal would be saying nothing at all. 00:54:41.764 --> 00:54:46.554 Four — log base two of sixty-four: 6 bits per level. 00:54:46.604 --> 00:54:52.524 Five — 8,000 times 8: 64,000 bits per second — 64 kilobits, the famous one. 00:54:52.574 --> 00:55:01.524 If you got all five, you are ready for the next session — and for this week's online quiz. 00:55:02.085 --> 00:55:03.585 So take this with you. 00:55:03.635 --> 00:55:06.235 No bandwidth, no information. 00:55:06.285 --> 00:55:15.235 Three knobs describe a sine wave; a recipe of sines describes any signal; bandwidth is the width of the recipe — and a signal with no width has nothing to say. 00:55:17.115 --> 00:55:24.315 On the digital side, one multiplication: bit rate equals changes per second times bits per change. 00:55:24.365 --> 00:55:26.395 The first factor is physics. 00:55:26.445 --> 00:55:34.515 The second factor is cleverness — and today you learned that cleverness has a catch with a name: noise. 00:55:34.565 --> 00:55:43.515 Before the next session, read Forouzan section 3.4 — attenuation, distortion, noise, and the decibel. 00:55:44.245 --> 00:55:52.665 Redo Examples 3.4, 3.5 and 3.10, and 3.16 through 3.20, cold — if the powers of ten slip, do them again. 00:55:52.715 --> 00:56:01.665 And the homework with the calculator demo: find TWO different combinations of levels and changes per second that carry one 64-kilobit voice call, and bring both. 00:56:04.965 --> 00:56:06.685 Two dates for your diary. 00:56:06.735 --> 00:56:14.725 Weekly Online Quiz A1 closes on Saturday at midnight — twenty minutes, one attempt, and it covers this week. 00:56:14.775 --> 00:56:23.725 And Classroom Quiz 1 is in Week 5, in the first thirty minutes of Session 9 — thirty minutes, twenty marks, in class and on paper, covering everything up to that point. 00:56:26.495 --> 00:56:33.445 Several versions of the paper circulate in the room, so the only strategy that works is doing the examples. 00:56:33.495 --> 00:56:38.865 Next session measures the noise in the gap between your levels, in decibels. 00:56:38.915 --> 00:56:42.505 Bring the calculator; logarithms do not do themselves. 00:56:42.555 --> 00:56:46.860 See you there.