 So what we got to last week when we're talking about the basic communication signals that are created, when people design the transmitters and receivers, grab one of the handouts as you go by. And when we send data across a link, we transmit that data as some communication signal. And if we think in the simplest signal, a sinusoid, a sine wave, we can construct that signal to have certain properties. And we arrived at some definitions of some of those properties last week, some of them listed here. When we looked at the signal made up of sine waves, when we combined the sine waves together to get different shaped signals, then any communication signal can be considered in the same way, that it's just made up of a combination of sinusoids. They're much more complex than the ones that we've gone through in the examples that we'll touch upon in this course. But a spectrum of a signal is the range or the set of frequencies it contains. So if we have a signal made up of two sine components, the spectrum of that signal is the frequencies of those two sine components. Real communication signals are made up of many more than just two components. In fact, sometimes we have a continuous range, but the same concept applies. Spectrum is the set of signals, the set of frequencies. The absolute bandwidth is the width of that spectrum, from the minimum frequency component up to the maximum frequency component. So if we think of the individual sine waves as components of that signal, each one with a frequency, look at the minimum, the maximum, and the difference is the absolute bandwidth. There are some special cases, sometimes a signal, if it has a component with zero frequency, we say that's a DC component, but we will not cover that in this course. I call it here absolute bandwidth. What we're going to see is that in theory, signals may have an infinite absolute bandwidth. In practice, we have constraints on the range of frequencies that we can transmit. Even if a signal, in theory, has an infinite absolute bandwidth, usually most of the energy is contained within a certain area, that is within a certain range of frequencies. Also, our transmission systems in practice, whether it's an optical fiber, a copper wire, a wireless transmission system, only transmit signals containing certain frequencies. In practice, we get what's called the effective bandwidth of a signal. We just call that sometimes bandwidth. When we talk about real signals, and in practice, people refer to the bandwidth of a signal, then they're talking about the practical or effective bandwidth. In theory, though, we can have much larger range, say an infinite range of, an infinite bandwidth. That theoretical bandwidth we've referred to as the absolute bandwidth. We'll show some examples of how we determine the absolute bandwidth. There's no, we're not going to define any relationship direct between them, absolute and the effective bandwidth, but just realize in practice that when people talk about bandwidth in terms of signals, they are talking about mostly the effective bandwidth. We'll see some further examples as we go through a different media. We'll see the bandwidth available limits or determines our data rate, which is one of the key things we care about. How many bits per second can we send across a communication system? Well, there's a relationship between the bandwidth of our signal and how many bits per second we can send. The handout in front of you will go through a very simple example of several signals and look at the relationship between frequency, bandwidth, data rate and accuracy. So that's an extra handout. You can find it on the website, this handout about signals, but it's got four or five example signals. Here's the first one. Here's the equation for the signal. The signal is a function of time. So I've chosen this signal, chosen it because it's very simple. It just contains two components. I've chosen very simple values here or small numbers so we can deal with them easily. It's not realistic, but it's okay for the example. This signal, s of t has two sine components. So it's an addition of two sine waves and the first one is sine times four pi t and then the second one, one third, sine 12 pi t and everything is multiplied by a factor of four on pi, this magic number out the front. We'll explain where that comes from in a moment. First look at this equation for the signal. Two components. What's the frequency of the first component? Focus on the first sine function. What is the frequency again? It's not four. What is the frequency of this first component? One four pi t, four one, no, no, two. Remember the basic equation for our sine waves and that will give you the answer. Pink amplitude sine two pi t, well, two pi f t plus the phase. That's our general equation for our sine wave. The peak amplitude a, the frequency f, the phase five. There are the variable components in here. So we have sine four pi t, therefore f must be two, two hertz, two times two four pi t. The frequency of the first component is two hertz. Second component, frequency six hertz, okay, not so hard. Peak amplitude of the first component, one and one third for the second. In fact, they both multiply by four on pi. This four on pi out the front is a factor applied to both of these components. So in fact, the peak amplitude of the first component is four over pi. The second component is four over pi times by one third. Zero phase or zero phase in both of them, a simple example. The two plots are plots of that same signal. The top one is in the time domain and the bottom one is in the frequency domain. Recall that we can view signals from two different perspectives. Time domain, which is the signal strength, the signal magnitude versus time. And the frequency domain is the signal peak amplitude of each of the components versus frequency. To plot the time domain, okay, I've used a computer, I gave some demonstrations last week and we get this shape of these two humps at the top and the bottom and repeating. This is plotted for one second. What's the fundamental frequency of s of t? Two hertz. The fundamental frequency is two hertz. Where does that come from? You can record the frequency of the first component, let's say f1, we said was two hertz. The frequency of the second component was six hertz, which is three times two. This frequency two is an integer multiple of the first one. And if that's the case, then we say that the frequency of the resulting signal or the fundamental frequency is two hertz. This component is one times two hertz. This second component is three times two hertz, they're both integer multiples of two hertz and therefore the fundamental frequency, which is the frequency of s of t is two hertz. Then we cannot easily determine in that case. So if it's the integer multiple, then we can determine. If we had some different range of frequencies, three and five for example, then we can still determine the frequency. For example, if you look at the plot of it, you'll see the frequency out repeats over time. Fundamental frequency is two hertz, which means the frequency of the signal, the addition of the two components is two hertz, and we see that in our top plot. We see over a period of one second, there are two repetitions of our signal. The first cycle, the second cycle, two repetitions per second, two hertz. What's the period of our signal? Period of s of t, period of s of t, the frequency is two hertz, therefore the period is one over two, a second. The frequency of our signal and the period uppercase t is the inverse of the frequency, one half, 0.5 seconds. And again that's visible in the plot, the top plot. There's one repetition, or how long does one repetition take? If we get to here, half a second, so half a second, half a second and so on, if we keep plotting. So the period of that signal. What about our frequency domain plot? How do we arrive at that? If we take the two components at two hertz and six hertz and take the peak amplitude of those two components, the first component, peak amplitude, one times four over pi, which is simply four over pi, which is about 1.3 something, four over pi. Of the second component, it's one third times four over pi, so it's one third of the first component, which is what is it, 0.3, 0.4 something. With the frequencies of the component and the peak amplitudes of the components, we can determine the frequency domain plot. At two hertz, an impulse of 1.3 and at six hertz, an impulse of around 0.4, one third of the first impulse. So be sure you can determine the plot, the frequency domain plot. Given the signal, you should be able to create that plot. Any questions at the back? No. It's getting easier this course. So you can take your notes on this handout as we go, just looking at some basic properties of this signal, this example signal. Spectrum of the signal, it's easy to look at the frequency domain plot to determine the spectrum and bandwidth. Spectrum is just the two components, two and six hertz. Bandwidth is the difference between them, four hertz. The bandwidth of this signal is four hertz, from two hertz up to six hertz. Back to the time domain plot. We set a very simple scheme for transmitting bits using such a signal would be to say, when our signal is high for some period of time, take that as meaning bit one. And when it's low, take that as meaning bit zero. So depending upon the sequence I want to transmit, I can vary the phase of that signal. So I have it high if I want a bit one to be sent and low to be a bit zero. Using that simple scheme, we could say over in this period of one second, this is a bit one, it's high for some period of time, this is a bit zero, bit one, bit zero. That's our example scheme for mapping bits to the signal. If that was our scheme being used, we can determine the data rate. Because if this is the transmission of one bit, and then the second bit, third bit, fourth bit, within a period of one second, we've transmitted four bits. Hence we get our data rate, and it's written up here, four bits per second in this example. So first we looked at properties of that signal, and now we're relating the signal to the transmission of bits, and using a particular encoding scheme, we can say that if we're using this signal to transmit bits, we could transmit four bits per second. The first bit, the second bit, and so on. And we could keep transmitting at that data rate. Any questions before we look at the next example? So given, for example, the equation, you should be able to produce the frequency domain plot. You should be able to determine the frequencies of the components, the fundamental frequency, the period, the bandwidth, and given some assumptions, here we've made assumptions about the bits, the signal. How do we get the bandwidth? The difference between the minimum frequency component and the maximum frequency component. So ours is simple, between two and four, a bandwidth, look here, four bits. Next example, different shaped signal, so I've used a different equation in this example. Let's go through quickly and find the values of those different properties. Find them quickly, find the signal frequency, the bandwidth, and the data rate. So look at the equation and to determine the frequency of the three components in this case. There are three sine waves, or three sine functions. Find the frequency of each of them. Everything okay? Fine. You've forgotten your book? Let's wait. Maybe a handout we can give you. Even if you forget your book, there's no excuse because we've got some handouts today. So we're on the second example. Try and find the frequencies of each of the three components. Like we've done here, we found the frequency of the first two components. Try and find the bandwidth of this signal and think about the data rate. Yeah, uppercase A here is the peak amplitude, the maximum. So use our general equation to find the frequency of the three components. The frequency of this component is, no, look, here's the general equation, A sine 2 pi Ft. Therefore F must be 2 hertz, okay? Now do that for the other two components, okay? First component and easy for the first two components are the same frequencies as the previous question. Two hertz, six hertz. Next one, 10 hertz. Bandwidth, 8 hertz because it ranges from 2 hertz up to 10 hertz. The width of the frequency band is 8 hertz. So this is an 8 hertz signal. The answers are up here, so just know how to work them out. We can determine the peak amplitudes of 4 on pi or 1 times 4 on pi, 1 third of that and 1 fifth of that. So this is 1 third of the first component. This is 1 fifth of the first component. Bandwidth, we can see visually from 2 to 10, 8 hertz. Data rate. Well again, we're using this assumption that when our signal is high for some period, that's a bit 1 and low, bit 0. So it's in fact the same as the previous case. So this 1 second, 1 bit, 2 bits, 3 bits, 4 bits, 4 bits per second. So we can say with this signal we can transmit at a rate of 4 bits per second. And the fundamental frequency is still 2 hertz in this case. Let's write them down so people got the right answer. So for this second signal, component 1, 2 hertz, component 2, what do we get? 6 hertz and component 3, 10 hertz, bandwidth, 8 hertz. Fundamental frequency, the frequency of the signal is still 2 hertz, 5 times 2, 6 times 2, 1 times 2. And the data rate, and it's up on the top of the plot here, data rate 4 bits per second. So compare these 2 signals. This one, 2 components. This one, 3 components. Same data rate, both are 4 bits per second. So which one's better? They both offer the same data rate. We both arrived at 4 bits per second. So from the perspective of data rate, they're the same. Does one have an advantage over the other? Which one? This one, and I think you're correct, let's explain it in simpler terms. At least we can visualize. Compare the shape of the 2 in the time domain. This one versus this one. And we'll see it in the subsequent examples. What our scheme we said was, is when the signal is high, we mean bit 1. When it's low, it's bit 0 for some period of time. But in fact, it's not always up at plus 1. For this first bit, it's actually quite low, and it takes some time to go up, and then it reaches 1, and in fact, it oscillates about 1. And then it comes down. Whereas in the second one, it goes up to 1 a little bit faster. If we looked at the slope here, it goes up to 1 and oscillates closer to 1 for a longer period of time, and then goes back down. What we'd like for this signal is that it's always at plus 1. Because that's what we're trying to represent, that it's a high signal for some period of time, 1 bit, a low signal for some period of time, another bit. So, we would say that this second signal is better than the first one in terms of it more accurately represents the data we're trying to send. In general, we say it's more accurate. The second one is more accurate than the first one, and it will be important in the presence of errors and noise in the system. There's a lot of noise in this room, and what happens when we've got too much noise? The receivers cannot understand, so feel free to discuss and about the topic, but don't talk about other things during the lecture. So, just comparing the two signals, both the same data rate, same in terms of data rate. In terms of accuracy, the second signal is better than the first. The other main factor is the bandwidth. The second signal occupies 8 hertz of bandwidth, the first signal 4 hertz of bandwidth. Generally the larger the bandwidth we use, the higher the cost. So the first signal is better than the second one in terms of bandwidth. We want to use a small bandwidth, but we want a high data rate and a high accuracy. So the higher the bandwidth we consume, the worse that is in terms of our design. Signal 3. I've added one more component, so it's the same as signal 2 plus 1 7th sine 28 pi t. What's the bandwidth of this signal? Well, it ranges from 2 hertz for the first component up to 14 hertz for the last component. 28 pi t means the frequency would be 14 hertz, 28 divided by 2. And of course we have the intermediate frequencies. So the bandwidth from 2 hertz up to 14 hertz, a bandwidth of 12 hertz for this signal. It's given on the top of the slide. If you do the calculations or if you look at the shape here, we still have 4 bits in the one second, same data rate, increased bandwidth, same data rate, but higher accuracy. That is, it's getting closer to this square wave. You see the shape here, it's oscillating closer, about one more, a larger fraction of the time than the previous two signals. So this third signal, same data rate, worse in terms of bandwidth, but better in terms of accuracy. Fourth signal. I added many components. I haven't written them all in the equation. Up to 1 over 19, there's some pattern here. And we can find the bandwidth of this fourth one to range from 2 hertz up to 38 hertz. It's a bandwidth of 36 hertz, 76 divided by 238, so 2 up to 38 bandwidth of 36 hertz, larger bandwidth, still 4 bits in one second, 4 bits per second, same data rate, but getting much closer to this plus one, minus one, plus one, minus one, getting much more accurate. So we can start to see these trade-offs here. Increasing the bandwidth going from, what, initially changing the design of the signal impacts upon the different parameters of bandwidth, potentially data rate, and accuracy. And we're seeing some relationship between these factors. We're seeing increasing the number of components increases the bandwidth when everything else is fixed. Increased bandwidth gives us better accuracy. So go back again. bandwidth of 4 hertz, 8 hertz, 12 hertz, 36 hertz. Increased bandwidth, better accuracy in this case, but the same data rate in all those cases. Last example, going back to just two components. What's the difference between this and the first signal? Determine the bandwidth for this signal and the frequency of the signal. So two components, so compared to this to the first plot that we had, similar shape, but you see the fundamental frequency differs now. We'll set it to 3 hertz instead of 2 hertz, 6 pi t, 18 pi t. So 2 times pi times 3, and this is 6 times 3. So frequency of the first component is 3 hertz and the second component is 6 hertz. We see this in this frequency domain plot. What's wrong here? Oh no, we're okay. 18, sorry, yes, 18 pi t, frequency of 9 hertz here, 9 hertz, 3 and 9 bandwidth of 6 hertz. Difference between 3 and 9. Now it's similar to the very first plot, similar in shape here, similar accuracy. If we compare, I'm going to flick back to the first one, looks the same, just the frequency is different. Here we have two oscillations in the one second. Here we have three oscillations in the one second. And if we use this same scheme of 1 bit, 2 bits, 3, 4, 5, 6 bits in one second, data rate of 6 bits per second in this simple example. So the main point to catch from this and from these examples and what we've covered so far is that the design of the signal and the transmission system impacts upon the data rate, how fast we can send bits, the bandwidth that we consume, and the accuracy of our communication system. And we need to select a signal that achieves the trade-off that we're after. This summarizes some of those points that we see in those five examples. When we increase the bandwidth, we got a signal with increased accuracy and as a result less errors. That's a good thing. And we saw by increasing our frequency in these simple examples, we increased the data rate, which is good. We want a high data rate, high data rate, high accuracy. But, and although we haven't said increasing the bandwidth increases the cost, why? In practice, the bandwidth that you have available to use is limited. And that means that you often need to pay to use a particular set of frequencies, a particular bandwidth. So the example is the licences for mobile phones, 3G, the 3G auction in Thailand, that they are licensing bandwidth to transmit between mobile phones and cell phone towers. And those licences were selling for what, billion baht or whatever. And that's because the range of frequencies available is limited and therefore a high demand and a higher cost if you want to use a higher bandwidth. So we'd like to have an increased bandwidth for better accuracy, but if we increase the bandwidth, the cost goes up. That's a trade-off. Similar increasing the frequency to manufacture the transmitting and receiving devices, higher frequencies require higher complexity in the hardware. Higher complexity means harder to build, means higher cost eventually. And there are other issues to deal with. That is, we'll see later different frequencies have different characteristics in transmission through different media. The main point, someone who designs a signal, needs to design a signal that maximises the data rate, minimises the errors that is high accuracy and also minimises the cost. There's no one easy solution you need to consider a trade-off between the different factors. Before we go back to the lecture notes, any questions about these examples, how we determine some of the parameter values? Most people finish the quiz, quiz three today. It's getting harder. Less people are getting full marks, but I think everyone's trying, so I think we'll keep that going. There'll be another quiz on this topic coming soon. Any questions about our signal so far? Easy? Okay. If I could, if I could, if I was Superman and I could see the signals being sent by my Wi-Fi transmitter up to the access point, and if I could look at the individual frequencies and the signal and the time domain, it wouldn't look like this. It would be much more complex than this. We're focusing on very simplistic examples here, but the principles still apply. If I looked at that signal, I would be able to, in theory, break it into the different components and find the bandwidth, frequency, examine the data rate, and so on. So in practice, it's much more complex, but the principles apply. What's the general formula? Can we come up with a formula to determine the data rate from the other factors? We'll see at the end of this lecture slides a general formula, okay, or several general formulas. Here, just follow the simple principles that we've used in this example of, okay, if we represent the signal high as one bit, then we can count the bits per second. We'll arrive at a more general and one that covers all scenarios shortly. This question is what we just went through, except I went through an example we saw we had a bandwidth, I think, of four hertz and four and eight hertz, some variations on that. But the same if you multiply everything by a million and go up to megahertz and four and eight megahertz. So I'm not going to go through this. This is essentially what we went through in those other handouts you have in front of you. This is a different view, and it's from the textbook, of how the bandwidth impacts upon accuracy. And maybe it's best to look here visually that these are, at the top is what we'd like to send. The sequence of bits. Imagine that as, okay, pulses to represent the different bits. The next set of plots are what's transmitted through a system which has a particular bandwidth. And what you can see is as we increase the bandwidth from 500 hertz, 900 hertz up to 4,000 hertz, the signal transmitted gets more accurate. It gets closer to what we desire. So it's just a different view of this relationship between larger bandwidth, more accuracy in our signal. The closer it is to what we want to represent. Let's finish on signals, at least the mathematics of them for a moment. The trade-offs that we've arrived at in practice, even if we have infinite bandwidth signals in theory, a transmission system, a practical system has some limit on the bandwidth of signals that it can send. Bandwidth is a limited resource. What that means is the more we want to use, the higher the cost. Because it's limited and there's demand for this resource, the more people want it, the higher the cost goes up. So in general for communication systems, the greater the bandwidth we use, the greater the cost of our system. Data rate, and we saw in our examples frequency related, and in general, and we'll see some more specific equations later, the greater the bandwidth, we'll see the greater the data rate we can achieve. And there's another thing that we care about is the accuracy of the signals, and we'll see there's a relationship again between bandwidth and accuracy, and that's shown in this plot. The greater the bandwidth, the more accurate we can be. So we want high bandwidth for good performance, but we want low bandwidth for cheap, for low cost. I know people are excited about bandwidth signals, frequencies, that's why everyone is talking to their friends about it. But let's move on to something a little bit different. Let's talk about data, and analogue and give some quick examples of analogue and digital data. An example, we want to send analogue data across a communication system. An example of analogue data, audio. You talking, music, someone talking on a phone. Audio is an example of analogue data. So we can distinguish between the types of data between analogue and digital. This plot shows us, for some example, audio applications, what range of frequencies are the signals? When I talk, I'm producing an audio signal which covers a range of frequencies. What's a typical range for human speech? Well, this is a frequency domain plot, and the solid green line shows that speech for most humans range from around 100 hertz up to, what's this, about 7 or 800 hertz. If we look at when the signal strength is highest, so this axis shows us the signal strength, the higher it is, the higher the signal strength, the magnitude, usually in this area. Around several hundred hertz, up to three or four kilohertz. So when you talk, you're generating signal with frequencies of around 300, 400 hertz up to 3,000, 4,000 hertz. That's an example of analogue data. Music usually has a larger range of frequencies. Music, not just singing but instruments, usually in the tens of hertz up to 10, 12 kilohertz. So if you consider the frequencies of different musical instruments and combine them together, it's wider range, a higher bandwidth than speech, and therefore if we want to transmit music across a communication system, our communication system needs to support this higher bandwidth. So if I want to transmit someone talking across a communication system, I need a system that carries this range of frequencies. If I want to transmit someone playing music, then I need a larger range of frequencies transmitted, a larger bandwidth. Think of radio. What are the two different types of radio that you listen to in your car? AM and FM. We'll look at what they mean in another topic, AM and FM. Which one's better quality, AM or FM? FM. I think if you listen to a radio channel in AM versus FM, you'll find that the audio quality is better in FM. On where do you find most talk radio stations? AM or FM? It differs, in fact. I think you'll find in most cases, if you think of just people talking, interviews and so on, versus music, mostly music, you'll find mostly music on FM and on AM talking. In fact, it's a mix. But think of all your favorite music channels, are they on AM or FM? I think most will be on FM. Why? FM supports a higher bandwidth of signals to be transmitted. It's in the order, and I never remember the exact numbers. It differs. FM, when we use FM radio, usually supports, I think, around 15 kilohertz. Whereas AM may be less, maybe around 5 kilohertz. It varies in different areas. That's the bandwidth when we use a particular radio channel. Which means FM can carry a higher bandwidth than AM. Think of the data that we want to carry. If we want to carry just speech, humans talking, we only need a narrow bandwidth, shown about here. About three or four kilohertz are needed to carry speech so that someone who hears it can understand. But for music which has a higher range of frequencies, from low frequencies up to higher frequencies, we need a higher bandwidth to carry all of those frequencies. And FM is better suited to carrying a wide range of music. So you'll generally find that the high quality in terms of the audio quality music are on FM radio. Whereas when you just need talk, you don't need music, then you find it more on AM. Because AM supports a lower bandwidth than FM. So AM radio and FM radio are our communication systems. What's the data we're sending? Speech and music. And both of them are examples of analog data. Another communication system is your home. Maybe if you have one, a land lined fixed telephone. Not your mobile phone, but the one with a cable. Just the normal telephone system. As a communication system, it transmits frequencies in this range. Again, about 400 hertz up to 4 kilohertz. Which carries most of the speech frequencies. But if you play music over your home telephone line, you'll find at the other end, the receiver will not hear the high quality music if you play it across the speaker end. Because not all of those frequencies of the music are transmitted across the telephone system. So the green ones are examples of analog data. And the telephone channel, AM radio, FM radio are examples of transmission systems that are used to transmit that data from one point to another. Just some of many examples. Examples of analog data. What about digital data? Well, best example is say our characters. Here's one example, ASCII encoding. Everyone's done some programming and had to convert letters into their decimal or binary representation. Here's the basic ASCII table. See if I can read it. See if you can read what I'm writing. From left to right, top to bottom. What did I say? Here's some digital data. An example of digital data in this case. Just a sequence of bits. I don't need to digital data. There's no spaces needed. Well, because I know that each seven bits represents one character in this case. I have one specific encoding here. I encode these characters in the table into bits. And the way that I read this table is the character lowercase a is 1 1 0 0 0 0 1. It's a mapping from these 128 characters into seven bits. So this is an example of digital data. There are other encodings. This is just one of the common ones. If you've got the first three characters, I think you'll guess the last two. And yes, the first character is uppercase s. So I'm not asking you to remember this encoding. This is just giving it one example of digital data, text, as opposed to audio analog data. Depending upon what type of data we have to send, we use different communication techniques. So you can do any mapping given that ASCII table. In fact, we can encode any data normally into binary if we want even audio. So where are we? We can distinguish between analog and digital data. Examples of analog data, audio. Examples of digital data, text, as we see up here. But the signals that we send, we can also distinguish between analog signals and digital signals. And in fact, the communication systems that we build, we can talk about analog transmission and digital transmission. So we have different types of analog versus digital. Analog and digital data, analog and digital signals, and analog and digital transmission. I'm not going to try and go through these right now because I think people, we need a lot of time to explain. In two topics time, we have what's called signal encoding techniques. And we go through a set of examples of how to encode analog data and transmit it as analog signals. And also digital data, digital signals, analog data, digital signals, and digital data, and I think digital signals as the fourth combination. We will come back to this in two topics time. For now, just be aware that when we talk about analog and digital, we now need to be more precise. Do we mean analog and digital data or analog and digital signals? And we just gave two examples of analog data and digital data. We'll cover these slides in the later topic. Let's repeat it again later. This may be the last topic for today, transmission impairments. What goes wrong in communication systems? What, when I transmit a signal at a source, the signal comes out, think of it as a perfect signal, and then it travels across our communication system and it arrives at the receiver. Unfortunately, the received signal is different than the transmitted signal. What causes these differences? What impairs our transmission? Ideally, the received signal would be identical to the transmitted signal. And then things would be great because we'd work out what the data was sent. But in practice, there are some impairments in transmission systems that prevent the received signal being identical to the transmitted one. What are these impairments? What goes wrong? Or some simple categories of the impairments. If we transmit a signal and the received signal doesn't match the transmitted signal, what does that mean from the receiver? Depending upon the type of signal, we may get some degradation in signal quality. For example, if there's a lot of noise in this lecture, I transmit some signal, and the signal that you receive is not the same as what I transmitted, which makes it harder for you to understand the information being transmitted. So if there's some impairments, the signal quality at the receiver is lower, making it harder to understand the information. If I'm sending zeros and ones, there's a possibility that I send a bit one and I transmit a signal representing that bit, but the receiver receives a signal and they think it's actually a bit zero. We call it a bit error. That is, the received bit is different than the transmitted bit. That's, of course, bad. We need the received data to be the same as the transmitted data. What causes these impairments? What causes things to go wrong? Attenuation, distortion, and noise. For this course and for today, we're just going to talk about attenuation and noise, the main impairments. Attenuation distortion extends upon attenuation, delay distortion as well, they're related, but we'll not try and explain them in detail in this course. Attenuation and noise. Because I think most of you can connect for those two. When I talk to you, what is the loudest, what position is the signal that you receive the loudest? The front of the room or the back of the room? Even with a microphone on, depending upon the speakers. Why? Attenuation, this is the concept of attenuation. When I transmit a signal, you can think of the strength of the signal coming out of my voice, out of my mouth. And as that signal passes through, in this case, air, the signal strength, think of the height of the sine wave, gets weaker. It's part of physics that the signal strength degrades over distance. Therefore, the further the distance the receiver is from the transmitter, the weaker the signal will be. And we say the signal attenuates, it gets weaker. So that's simple, attenuation. Signal strength reduces as a function of distance. The larger the distance, the larger the signal strength reduces, or the larger the attenuation. So if you don't understand the word attenuation, think of reduction of the signal strength, decreased. So when we design a communication system, if we know the capability of the receiver in terms of how strong a signal they can understand, then we can design the system so that we have a strong enough signal at the transmitter. What's an example? So people at the back, can you hear me now? Back row, can you hear me okay? Okay, so that was a case where I reduced the transmitted signal strength, and therefore the people at the back could not receive. So the signal strength at the transmitter the amount the signal attenuates across distance, that's the second point, and the capabilities of the receiver all impact upon how well we can communicate. So across a particular distance, the signal will attenuate by some factor. When we transmit a higher power signal, there's a higher chance the receiver will successfully receive that information. If we transmit a lower power signal at the transmitter, then it's less chance that they'll receive that information. The larger the distance we transmit, again, the weaker the signal to the receiver. So we need to design a system that considers these factors, the transmit power, the distance and the attenuation between transmitter and receiver and the capabilities of the receiver. The received signal must be great enough that the receiver can make sense of it. Here's the receiver electronics, we're talking about electronic communication systems, can interpret that information. Think of that as your ears. Your ears can hear a particular sound or can make sense of audio above a particular signal strength. If it's too quiet, your ears will not hear it. So that's the received capabilities of your ears, the receiver. In communication systems, there's not just the single transmitter, there's also other effects in the system, noise. And another principle is that the receiver and the received signal strength must be usually much larger than the noise that is received. Let's try. We need a volunteer, okay. One volunteer, you're my volunteer. You can see if you can hear me, okay. You put your hand up when you can hear what I say. I'm transmitting at about the same strength. So in the first case, I transmitted a signal over this distance of four meters, he received my signal, okay, understood. In the second case, I transmitted about the same strength signal, same distance, but there was noise in the system. There were other transmitters transmitting at the same time, and that meant he could not hear me or he could not understand what I said. So from the receiver's perspective, the signal that they receive from the transmitter should be much higher than the noise around them. And that's obvious in this lecture. If there's one person talking to their friend, most of you will hear me. If everyone's talking to their friend at the same time, only few of you will hear me and understand. So we need to keep the noise low. Let's skip attenuation distortion. Attenuation, the signal gets weaker over distance. That's a problem. And skip delay distortion. What about noise then? We said, what if others are transmitting? Well, what are the contributors to noise? Different types we can classify as noise, in any communication system there's what's called background noise or thermal noise. It's due to the physics of electrons moving or agitating. It's always there. We can't avoid thermal noise. It's usually very small. There's ways to calculate it. You don't need to know how to calculate it. But in any communication system, there's what's called thermal noise. Then there are other types of noise that may or may not be present. When we transmit signals at different frequencies, those frequencies can effectively interfere with each other. We get what's called intermodulation noise. Sometimes the signals across different systems cause interference called crosstalk between one wire and another wire. Signals transmitted at the same time can interfere. And other types of noise called impulse noise like a peak or a spike in noise. Due to some electrical fault, some lightning strike on our communication system incurs a large impulse of noise on our system, some flaw or error in the communication system. The main point is that there are different contributors to noise. There's always some background or thermal noise and depending upon the environment, depending on other transmitters, what's around, the noise may vary over time. If everyone stopped talking, is there any noise in this room? What is the noise? If everyone stopped talking, there's this background hiss from the microphone. That's some interference from the audio system. What other noise? Air conditioning. Lights are creating some small amount of noise. So in this audio system, we can say there's this background noise. Then as other people start talking, there's further noise from those other transmitters. So we need to design our system that takes into account this noise. Last slide for today. This shows an impact of noise on an example digital signal. I have some data to send from A to B. Here's the sequence of bits. I generate a signal to represent those bits. This square wave or this set of pulses here. The scheme in this signal, which is opposite to what we normally think, is that if I want to send a bit one, I've got a low voltage. Bit zero, high voltage and so on. So think of this as the signal transmitted. We send it across a communication system. But in this communication system, there's some noise. What does it look like? Well, some random variations due to the thermal or background noise. Maybe there's some disturbances from other transmitters around that cause a spike or a small increase in noise. Maybe there's some disturbance here. There's a large increase in noise and it's varying and another large, in this case the magnitude is negative of noise. So think of noise as some random variations in this case. We transmit the signal. Ignoring attenuation, the receive signal, we can think of as the addition of the transmitted signal and the noise. Add these two together and you get this shape. The signal plus noise. You can see the pattern here. It's low but there's some of these random variations and it's high here plus these variations. So it's just the addition of these two to get this one. The receiver receives this signal and it knows for this period of time, if the signal is negative or low, it means bit one. If it's positive or high, it means bit zero. So what it does is take samples, records the signal level. It's below the dash line. It's negative, therefore bit one. Sometime later, record the signal level. It's positive, must be bit zero. And keep doing that for all of the signal received and we get the received data. We see that compared to the original data, the received data is the same except for two locations. Two bits are wrong. We say there are two bit errors. The receiver thinks it received a zero here but in fact what was transmitted was a one. That's a bit error. And same at this point. It thinks it receives a one because the signal here at the sample point is low but in fact what was transmitted at that time was a zero. That's a problem. Why did it occur? Because of the noise. There is a large increase in noise here, caused a bit error and a large amount of noise here, negative noise caused a bit error. So here's an example of the impact of noise on our transmission of data. The larger the noise, the more chance of errors. So when we design a communication system we need to consider or take into account the noise in that system. Let's stop for today. Tomorrow we'll do nothing with you. On Wednesday we will finish and look at some two general equations for calculating data rate from bandwidths and other factors. Channel capacity.