1 00:00:00,012 --> 00:00:03,864 So lets get started. Any course that is concerned with the 2 00:00:03,864 --> 00:00:09,097 fundamentals of electric engineering has to be concerned with information and 3 00:00:09,097 --> 00:00:12,850 that's what we're going to talk about today to get started. 4 00:00:12,850 --> 00:00:18,072 So terms that are really going to be important to us are Signals and Systems. 5 00:00:18,072 --> 00:00:22,267 So the first thing I'm going to do is to define a signal, turns out this 6 00:00:22,267 --> 00:00:26,274 definition is very simple. You already know what a signal is, it 7 00:00:26,274 --> 00:00:29,748 turns out and we'll get, get through that very quickly. 8 00:00:29,748 --> 00:00:33,937 What's going to be more important are the various kinds of signals. 9 00:00:33,937 --> 00:00:39,048 Now when electrical engineers think about signals, the different ways in which we 10 00:00:39,048 --> 00:00:43,904 think about and categorize them. And then I'm finally going to link 11 00:00:43,904 --> 00:00:50,634 information to signals, and it turns out this link may be a bit tighter than you 12 00:00:50,634 --> 00:00:54,570 think. I would say some provocative things, I 13 00:00:54,570 --> 00:00:58,578 hope. Finally we'll talk about systems, which 14 00:00:58,578 --> 00:01:01,081 are. The way you operate on signals. 15 00:01:01,081 --> 00:01:05,364 And we're going to put systems together to create what is known as the 16 00:01:05,364 --> 00:01:09,967 fundamental model of communication. This model is very, very important. 17 00:01:09,967 --> 00:01:13,184 We're going to return to it throughout this course. 18 00:01:13,184 --> 00:01:18,032 Think of all this, not only will. In the process of understanding it, when 19 00:01:18,032 --> 00:01:23,207 we understand how real communication systems work, we will also, when we put 20 00:01:23,207 --> 00:01:28,757 the various components together, we'll be able to apply the things that we learned 21 00:01:28,757 --> 00:01:32,557 in this course. So, what's a signal? So, the definition 22 00:01:32,557 --> 00:01:35,632 of a signal is quite easy. It's a function. 23 00:01:35,632 --> 00:01:41,264 So, anything you've learned about functions in calculus, you've already 24 00:01:41,264 --> 00:01:46,183 learned about signals. They're exactly the same thing, there's 25 00:01:46,183 --> 00:01:49,099 no difference. So I can plot a signal. 26 00:01:49,099 --> 00:01:54,662 So lets say we have a signal as a function of t, which I, take to be time. 27 00:01:54,662 --> 00:01:58,548 And I'm going to call my signal s of t, and, there it is. 28 00:01:58,548 --> 00:02:01,728 That's a signal. That's all there is to it. 29 00:02:01,728 --> 00:02:07,938 I don't, there's nothing more complicated about a signal than it's just a function. 30 00:02:07,938 --> 00:02:13,092 And, before we get too far, I want to talk about electrical signals. 31 00:02:13,092 --> 00:02:18,375 And there's some interesting aspects of electric signals that have proven to be 32 00:02:18,375 --> 00:02:23,387 very important in the information age. As you know, electrical signals are 33 00:02:23,387 --> 00:02:26,843 voltages and currents, and electromagnetic waves. 34 00:02:26,843 --> 00:02:31,929 but what's very important to appreciate is that they carry two different 35 00:02:31,929 --> 00:02:35,528 quantities. First of all, they carry power You would 36 00:02:35,528 --> 00:02:40,985 plug into the socket in the wall, that's an electrical signal, that's carrying 37 00:02:40,985 --> 00:02:46,288 power, which powers your computer, your refrigerator in the home, the laser 38 00:02:46,288 --> 00:02:49,310 printer in the office, all kinds of things. 39 00:02:49,310 --> 00:02:52,744 Very important. There's also signals that convey 40 00:02:52,744 --> 00:02:55,872 information. For example a wireless signal. 41 00:02:55,872 --> 00:02:58,967 What you use with your cell phone to call one person. 42 00:02:58,967 --> 00:03:02,662 It's carrying information. It's carrying what you're saying. 43 00:03:02,662 --> 00:03:06,742 Now it turns out we're not going to talk much about power in this course. 44 00:03:06,742 --> 00:03:10,677 it's not our major concern. What is our concern, of course, is 45 00:03:10,677 --> 00:03:13,839 information. But you cannot design an information 46 00:03:13,839 --> 00:03:17,414 system without having some consideration about the power. 47 00:03:17,414 --> 00:03:22,068 How much power am I using, does it use, to send, to call somebody over my cell 48 00:03:22,068 --> 00:03:26,664 phone? How efficiently am I expending that power? These are going to be issues 49 00:03:26,664 --> 00:03:31,369 that are very important to the design of modern information systems, so we've 50 00:03:31,369 --> 00:03:36,558 gotta talk about power a little bit. But we won't certainly focus on it. 51 00:03:36,558 --> 00:03:41,420 it will come up. So, the various categories of signals 52 00:03:41,420 --> 00:03:46,915 that we think about. Well, there's two broad categories, 53 00:03:46,915 --> 00:03:51,351 Analog and Digital. A analog signal is a function of a 54 00:03:51,351 --> 00:03:56,192 continuous variable. So here's my good old s of t again. 55 00:03:56,192 --> 00:04:04,091 And it's a function of time and certain times continuous variable, and we can 56 00:04:04,091 --> 00:04:11,926 plot it, looks soemthing like that, very crudely The sinusoid, the sine wave is 57 00:04:11,926 --> 00:04:16,721 governed by 3 parameters versus the amplitude. 58 00:04:16,721 --> 00:04:22,881 Which determines how big the signal is. The frequency at zero, determines how 59 00:04:22,881 --> 00:04:27,973 often the peaks occur. If I were to whistle, [SOUND], that turns 60 00:04:27,973 --> 00:04:32,570 out to be an acoustic sine wave, at least, approximately. 61 00:04:32,570 --> 00:04:36,922 The frequency of my whistle, the pitch of my whistle. 62 00:04:36,922 --> 00:04:43,262 Corresponds with the frequency f 0. Phase has to do with how the sine wave 63 00:04:43,262 --> 00:04:48,661 begins at the origin. So here we have a very good analog signal 64 00:04:48,661 --> 00:04:55,732 as a sine wave as an explicit formula controlled by three different parameters. 65 00:04:55,732 --> 00:05:01,810 Now the next analog signal I want to talk about though, is a little different, and 66 00:05:01,810 --> 00:05:07,888 it's different in a very interesting way. So here's a plot of a segment of speech. 67 00:05:07,888 --> 00:05:13,462 That's me saying the vowel e, and what I want to point out is that there's no 68 00:05:13,462 --> 00:05:16,473 format. The sine wave has a formula. 69 00:05:16,473 --> 00:05:20,562 There is no explicit analytic formula for speech. 70 00:05:20,562 --> 00:05:27,218 However, we are going to want to operate on signals to understand the structure of 71 00:05:27,218 --> 00:05:30,782 signals, whether there is a formula or not. 72 00:05:30,782 --> 00:05:35,499 The structure of the signal with a formula, like I said, is covered by 3 73 00:05:35,499 --> 00:05:39,129 parameters. Here, we're going to have to think about, 74 00:05:39,129 --> 00:05:43,204 what, and for the speech signal, what the structure of it is. 75 00:05:43,204 --> 00:05:47,477 It kind of looks like a sine wave. But I think you can see that the 76 00:05:47,477 --> 00:05:50,415 succeedant peak values don't look the same. 77 00:05:50,415 --> 00:05:53,802 The peaks of these wave forms don't look the same. 78 00:05:53,802 --> 00:05:59,267 And wherever the peaks of every other, thing, tend to look the same. 79 00:05:59,267 --> 00:06:05,557 This is even more apparent at the bottom, where there's the big guys, very negative 80 00:06:05,557 --> 00:06:10,132 peaks, and then the ones that are smaller, that's negative. 81 00:06:10,132 --> 00:06:13,552 And they kind of interlace with each other. 82 00:06:13,552 --> 00:06:18,475 Well, that's a very tedious way to try to get at the structure of this signal. 83 00:06:18,475 --> 00:06:22,822 We're going to have to develop much more interesting ways and much more 84 00:06:22,822 --> 00:06:27,027 informative ways to under, appreciate the structure of a signal. 85 00:06:27,027 --> 00:06:30,973 But we will have signals that don't have any signal, formula. 86 00:06:30,973 --> 00:06:37,104 We'll have Signals that do have formulas. And we had to develop methods by which we 87 00:06:37,104 --> 00:06:41,147 can appreciate the structuring process, the signals. 88 00:06:41,147 --> 00:06:46,527 Whether or not there is a formula. It's going to be very interesting for us. 89 00:06:46,527 --> 00:06:50,092 So, the next kind of signal is a digital signal. 90 00:06:50,092 --> 00:06:53,868 An additional signal is a function of the integers. 91 00:06:53,868 --> 00:06:59,605 It's a function of the discrete valued independent variable, which we're just 92 00:06:59,605 --> 00:07:05,032 going to take to be the integers. So here's an example of a digital signal, 93 00:07:05,032 --> 00:07:10,716 and it's a sequence of numbers. So I intend for these numbers to be read 94 00:07:10,716 --> 00:07:13,949 from left to right and here's a plot of it. 95 00:07:13,949 --> 00:07:19,544 Just for fun, so this goes across like that and that corresponds to these 96 00:07:19,544 --> 00:07:22,901 sequence of values that we see across here. 97 00:07:22,901 --> 00:07:29,210 So from left to right to top to bottom you see the values of my Digital signal, 98 00:07:29,210 --> 00:07:34,327 So, I don't know about you, but I don't see much structure there. 99 00:07:34,327 --> 00:07:38,963 I don't quite see what's so interesting about this signal. 100 00:07:38,963 --> 00:07:45,120 I do want to point out, before we get too far along, about how I plotted it. 101 00:07:45,120 --> 00:07:51,606 This is what's known as a stem plot And every value is drawn by, with a little 102 00:07:51,606 --> 00:07:57,258 line, with a little bubble at the top to indicate the value. 103 00:07:57,258 --> 00:08:02,684 So this indicates this function only exists at the integers. 104 00:08:02,684 --> 00:08:07,756 The value at 29 1/2 doesn't exist. It's not even defined. 105 00:08:07,756 --> 00:08:14,242 This is a function only advantage. That's what a digital signal is. 106 00:08:14,242 --> 00:08:21,847 So, what is this thing? Well, it turns out, this is another digital signal. 107 00:08:21,847 --> 00:08:26,772 This is text and, and you may say that's a signal. 108 00:08:26,772 --> 00:08:34,272 Well, it turns out, if you take position of the character along the line. 109 00:08:34,272 --> 00:08:38,714 The value, of the signal, is a member of the alphabet. 110 00:08:38,714 --> 00:08:43,721 So, s of 1, is capital T. Well that's a digital signal, it's a 111 00:08:43,721 --> 00:08:49,204 function of the integers. What's even more interesting about this 112 00:08:49,204 --> 00:08:52,982 example, is that these 2 are the same thing. 113 00:08:52,982 --> 00:09:01,368 So I typed this text into my computer, inside the computer what the computer did 114 00:09:01,368 --> 00:09:07,572 was turn those symbols, the type characters into numbers. 115 00:09:07,572 --> 00:09:12,449 So a capital T is 84, a lower case h is a 104 etc. 116 00:09:12,449 --> 00:09:14,663 So. They're exactly the same. 117 00:09:14,663 --> 00:09:19,174 So I think you'll agree that the text version, you can understand the 118 00:09:19,174 --> 00:09:24,465 structure, you know it's English text. For example, it's not something random. 119 00:09:24,465 --> 00:09:28,269 It actually makes sense. Whereas you look at a sequence of 120 00:09:28,269 --> 00:09:33,122 numbers, It's not quite apparent. And certainly if you plot it, it's even 121 00:09:33,122 --> 00:09:36,456 less apparent. What the structure is. 122 00:09:36,456 --> 00:09:43,876 The structure's signal may depend on how it's presented, kind of interesting thing 123 00:09:43,876 --> 00:09:48,847 to think about. So, let's talk about some other kinds of 124 00:09:48,847 --> 00:09:53,566 signals. another way of categorizing and I want to 125 00:09:53,566 --> 00:09:59,127 talk first about images. So the speech signal we already talked 126 00:09:59,127 --> 00:10:04,107 about is a function of time. Images are functions of space. 127 00:10:04,107 --> 00:10:10,142 So, they're a function of X and Y. So, I can give you an example of a black 128 00:10:10,142 --> 00:10:13,932 and white image. Here's a picture of a woman. 129 00:10:13,932 --> 00:10:17,972 And you say, why are you showing a picture of a. 130 00:10:17,972 --> 00:10:22,458 A beautiful woman. Well it turns out this image has been 131 00:10:22,458 --> 00:10:27,515 used in the image processing field for decades as a test image. 132 00:10:27,515 --> 00:10:32,183 And here's why. This one image contains a curve, contains 133 00:10:32,183 --> 00:10:38,448 some straight lines, contains a border, contains a highly complicated area. 134 00:10:38,448 --> 00:10:44,432 Something we call texture. Contains a smooth surface with a gradient 135 00:10:44,432 --> 00:10:50,425 of shading and it certainly contains a face, a very important thing. 136 00:10:50,425 --> 00:10:57,662 So, if you're trying to develop an image algorithm or image processing procedure. 137 00:10:57,662 --> 00:11:00,622 You want an image to test out how well it works. 138 00:11:00,622 --> 00:11:05,077 Well, you may discover that your procedure works very well on straight 139 00:11:05,077 --> 00:11:08,597 lines and curves, but doesn't work too well on texture. 140 00:11:08,597 --> 00:11:13,692 And so you want an image to test it with. Rather than having a textured image and a 141 00:11:13,692 --> 00:11:18,502 straight line image, etc., it's a bit more convenient to just have one image 142 00:11:18,502 --> 00:11:21,837 you can run through and see how well it works on that. 143 00:11:21,837 --> 00:11:28,620 That's why electrical engineers develop such test images so this one has been 144 00:11:28,620 --> 00:11:35,253 used for decades because it has all the right things in it that you need to test 145 00:11:35,253 --> 00:11:38,291 out images. But this is a function. 146 00:11:38,291 --> 00:11:42,802 Well I'm going to plot it. So here it is as a function. 147 00:11:42,802 --> 00:11:49,316 And so, here is the x and y. And, this is what's known as a heat map. 148 00:11:49,316 --> 00:11:57,086 This is a way of applying what's called 2, what we call dimensional signals, so 149 00:11:57,086 --> 00:12:02,082 you can readily see what's, big and what's small. 150 00:12:02,082 --> 00:12:08,777 So big values are indicated in red, and big in the image turns out corresponds to 151 00:12:08,777 --> 00:12:14,757 white, so in terms of that corresponds to that little area right there. 152 00:12:14,757 --> 00:12:19,187 Blue values are small and that corresponds to black. 153 00:12:19,187 --> 00:12:24,547 So the gray scale values in between are somewhere In between. 154 00:12:24,547 --> 00:12:30,830 This is called a heat map, because the big values are hot, they're red. 155 00:12:30,830 --> 00:12:38,425 The small values are cold, they're black. So, this is just a very convenient way, 156 00:12:38,425 --> 00:12:45,538 of looking, at a plot, of such a signal. However, here we have the same situation 157 00:12:45,538 --> 00:12:52,229 we just had and with the digital signal. Looking at the image, the plot of the 158 00:12:52,229 --> 00:12:57,004 function, I have a hard time appreciating what it really is. 159 00:12:57,004 --> 00:13:02,933 It's a lot easier for me as a human to look at the image as opposed to a plot of 160 00:13:02,933 --> 00:13:06,247 it. Again this is how the computer sees it. 161 00:13:06,247 --> 00:13:12,182 There's absolutely no difference between the 2 and we're going to develop more 162 00:13:12,182 --> 00:13:17,777 insight into the presentation of information as we go through the course. 163 00:13:17,777 --> 00:13:21,822 Now another kind of signal that's interesting. 164 00:13:21,822 --> 00:13:29,237 This video, because you know video is a sequence of images occurring in time so 165 00:13:29,237 --> 00:13:33,857 that makes it a, function of three variables. 166 00:13:33,857 --> 00:13:41,092 So space and time, so the jargon is that an image is a 2D signal because it 167 00:13:41,092 --> 00:13:45,882 depends on two variables. This is a 3D signal. 168 00:13:45,882 --> 00:13:51,503 Cause it depends on three variables. and this is common terminology. 169 00:13:51,503 --> 00:13:57,568 So, again I one dimensional signal, for example was for speech, that we say 170 00:13:57,568 --> 00:13:59,094 earlier. 'kay. 171 00:13:59,094 --> 00:14:03,178 But it can be a little bit more complicated than that. 172 00:14:03,178 --> 00:14:09,828 Because, if it's color video. Actually is 3, 3 D signals rolled up into 173 00:14:09,828 --> 00:14:14,373 one. Consider it as a signal, signal so our 174 00:14:14,373 --> 00:14:23,022 color video actually consists of a red, a green, and a blue signal each of which is 175 00:14:23,022 --> 00:14:29,863 a function of space and time. So this is a multivalued signal. 176 00:14:29,863 --> 00:14:33,962 So this image up here is in color, as an image. 177 00:14:33,962 --> 00:14:39,895 Not as a plot but as an image. And it's still considered a 2D image. 178 00:14:39,895 --> 00:14:46,848 So again, the dimension of a signal has to do with the number of variables upon 179 00:14:46,848 --> 00:14:51,330 which it depends, not how many values it may have. 180 00:14:51,330 --> 00:14:58,727 So this 2D image here Is red, green and blue components, each of which is a 2D 181 00:14:58,727 --> 00:15:02,769 signal. Now let's bring in information. 182 00:15:02,769 --> 00:15:09,799 Where's the information? So obviously something controversial here. 183 00:15:09,799 --> 00:15:14,912 That information does not exist without a signal. 184 00:15:14,912 --> 00:15:19,034 To represent it. So, lets think about this for a second. 185 00:15:19,034 --> 00:15:22,425 I've already shown you that text, is a signal. 186 00:15:22,425 --> 00:15:26,062 So, all books, contain signals from 1 viewpoint. 187 00:15:26,062 --> 00:15:31,874 Certainly there's more to it than just that, it's the structure of that signal, 188 00:15:31,874 --> 00:15:36,537 that conveys Information. You may say, well information exists 189 00:15:36,537 --> 00:15:41,417 without there being a signal. For example, a memory that I have in my 190 00:15:41,417 --> 00:15:44,227 head. Well, it turns out that memory is 191 00:15:44,227 --> 00:15:49,137 mediated and brought to fore, in your brain, by electrical signals. 192 00:15:49,137 --> 00:15:54,498 And we'll talk about that a little bit. So It makes, there is no such thing 193 00:15:54,498 --> 00:15:59,535 information just existing in and of itself without there being a signal to 194 00:15:59,535 --> 00:16:03,205 represent it. So, signals and information are linked 195 00:16:03,205 --> 00:16:07,634 together in very important ways. Not all signals can be, contain 196 00:16:07,634 --> 00:16:12,922 information, but information doesn't exist without there being a signal. 197 00:16:12,922 --> 00:16:18,792 So, we talk about information being encoded in a signal by modifying its 198 00:16:18,792 --> 00:16:22,881 structure. That's why I was talking earlier about 199 00:16:22,881 --> 00:16:28,266 the structure of a signal, cause that's where the information is. 200 00:16:28,266 --> 00:16:33,885 It varies the structure of the signal, that's how you think about it. 201 00:16:33,885 --> 00:16:36,898 So. What we're going to do is look at this 202 00:16:36,898 --> 00:16:42,543 sine wave, so if I take this signal, which we've already talked about as 3 203 00:16:42,543 --> 00:16:48,859 parameters, highlighted in blue here, if I change the amplitude of that signal in 204 00:16:48,859 --> 00:16:54,690 such a way that the amplitude varies according to the speech signal that I'm 205 00:16:54,690 --> 00:17:01,107 producing now, that turns out to be What's called amplitude modulation, and 206 00:17:01,107 --> 00:17:06,778 that underlies AM radio. If I change the frequency, according to 207 00:17:06,778 --> 00:17:12,292 what I say, that gives you frequency modulation, or FM radio. 208 00:17:12,292 --> 00:17:16,747 There is something called phased modulation, but it turns out it's not 209 00:17:16,747 --> 00:17:21,692 used very often, because it's been shown that frequency modulation has better 210 00:17:21,692 --> 00:17:26,777 technical characteristics than phase modulation, but anyway, this, that's why 211 00:17:26,777 --> 00:17:31,777 I wanted to find out what the structure of the components of a sine wave were, so 212 00:17:31,777 --> 00:17:37,400 that I can change those. Components according to the information I 213 00:17:37,400 --> 00:17:42,513 want to encode in. So, what does the system do? What does 214 00:17:42,513 --> 00:17:49,558 the system that operates on signals to produce a modified signal so the system 215 00:17:49,558 --> 00:17:54,672 might do the encoding of the information, and it also. 216 00:17:54,672 --> 00:18:00,275 It can do the extraction. It can also use a thing that extracts 217 00:18:00,275 --> 00:18:07,498 information and the way we indicate, systems is with a what's called a block 218 00:18:07,498 --> 00:18:11,378 diagram kind of thing. So here is the idea. 219 00:18:11,378 --> 00:18:15,842 The input of my system is x. It's always in most. 220 00:18:15,842 --> 00:18:21,811 Drawings comes in from the left side of this block, box that denotes the system. 221 00:18:21,811 --> 00:18:25,832 And the output is y, usually comes out from the right. 222 00:18:25,832 --> 00:18:31,692 And so the arrow indicates the inputs, and the arrow coming out, indicates the 223 00:18:31,692 --> 00:18:35,653 output. So what this system does, is it Operates 224 00:18:35,653 --> 00:18:42,630 on the signal x, does something, who knows what, and produced an output y. 225 00:18:42,630 --> 00:18:49,507 So we could go down the mathematical path to talk about functions that are 226 00:18:49,507 --> 00:18:56,066 functions of functions So, that, that turns out to be overly com-, complicated. 227 00:18:56,066 --> 00:19:01,821 We won't need to go down that path. We'll just appre-, just learn and talk 228 00:19:01,821 --> 00:19:07,494 about systems as things that take, as an input, a signal, and produce another 229 00:19:07,494 --> 00:19:12,082 signal. So here's that Fundamental Model of 230 00:19:12,082 --> 00:19:19,113 Communication that I keep, was saying earlier is so important. 231 00:19:19,113 --> 00:19:25,865 It's a sequence of systems. I've labeled important signals. 232 00:19:25,865 --> 00:19:31,437 The source The idea is there is a source that has a message signal. 233 00:19:31,437 --> 00:19:36,803 And the goal of communication system is to get that signal over to its 234 00:19:36,803 --> 00:19:40,932 destination, which technically is called the sink. 235 00:19:40,932 --> 00:19:43,871 I do not know where the term sine comes from. 236 00:19:43,871 --> 00:19:48,439 Its just the terminologies used. We'll just go withe flow and use the 237 00:19:48,439 --> 00:19:51,970 terminology. The, the idea of three occasions to get 238 00:19:51,970 --> 00:19:56,216 something that contains information from one place to another. 239 00:19:56,216 --> 00:20:02,401 Now it turns out, and the easy if it wasn't for this funky, cloud-like thing 240 00:20:02,401 --> 00:20:07,678 in the middle, the channel. That's another system, but I've drawn it 241 00:20:07,678 --> 00:20:13,618 like this because this basically refers to phenomena we have no control over. 242 00:20:13,618 --> 00:20:19,350 And let me guarantee you at the channel nothing good happens to a signal in a 243 00:20:19,350 --> 00:20:23,348 channel.What comes in, is not what comes out at all. 244 00:20:23,348 --> 00:20:29,562 An in fact the channel can do Things the signals that you may not know in great 245 00:20:29,562 --> 00:20:33,584 detail. So trying to send the message in directly 246 00:20:33,584 --> 00:20:39,713 through this channel is a big mistake, in most cases, it won't get through. 247 00:20:39,713 --> 00:20:45,516 So here's what we're going to do. We're going to take our message signal 248 00:20:45,516 --> 00:20:51,440 in, and put it into a transmitter. And what the transmitter does, is, 249 00:20:51,440 --> 00:20:57,241 creates a signal, which is better suited, to go through the channel, then the 250 00:20:57,241 --> 00:21:01,380 message m would be. This is called engineering design. 251 00:21:01,380 --> 00:21:06,682 This is what electrical engineers, and communication engineers do. 252 00:21:06,682 --> 00:21:13,179 Try to get signals through the channel. So this is termed the modulated message. 253 00:21:13,179 --> 00:21:19,353 That's where the transmitted signal is. Transmitter is a box which takes the 254 00:21:19,353 --> 00:21:25,722 message m as input and produces x as an output, that goes through the channel. 255 00:21:25,722 --> 00:21:32,554 Where nothing good happens, and produces the received signal r, which is, trust 256 00:21:32,554 --> 00:21:39,774 me, it's a corrupted modulated message. it's going to do all kinds of things, and 257 00:21:39,774 --> 00:21:46,030 nothing good happens in a channel. The receiver's job, is to try to figure 258 00:21:46,030 --> 00:21:53,060 out What that message was that was being transmitted, despite the fact that it's 259 00:21:53,060 --> 00:22:00,328 been corrected, so I put this hat on top of the, symbol here, because it means 260 00:22:00,328 --> 00:22:05,522 that it's not exactly equal to m, so it's an approximation. 261 00:22:05,522 --> 00:22:10,379 So and half basically equals the message M plus some error. 262 00:22:10,379 --> 00:22:16,799 And one of the things you wanted to do when you design communication systems is 263 00:22:16,799 --> 00:22:21,377 try to fight the channel so you can minimize that error. 264 00:22:21,377 --> 00:22:25,623 And it's this. Message in hat that goes into the sink. 265 00:22:25,623 --> 00:22:29,027 Goes to the destination. That's what you get. 266 00:22:29,027 --> 00:22:34,739 It's known as the demodulated message. So, here are all the labeled pieces of 267 00:22:34,739 --> 00:22:39,272 our fundamental model. We are going to talk about this again and 268 00:22:39,272 --> 00:22:41,854 again. We're going to worry about how 269 00:22:41,854 --> 00:22:46,063 transmitters are designed. How receivers are designed. 270 00:22:46,063 --> 00:22:50,342 Turns out. You cannot design these without designing 271 00:22:50,342 --> 00:22:54,432 them together. and we will talk about that as we go 272 00:22:54,432 --> 00:22:58,532 through the course. So this is the fundamental model. 273 00:22:58,532 --> 00:23:04,252 You now know what a signal is, you know what a system is generically, and now 274 00:23:04,252 --> 00:23:08,340 we're ready to get serious and talk about things to get.