 What we finished with last week, we're talking about the very basic communication signals which are sent across transmission lines. So a transmitter, like my laptop, wants to send a signal to a receiving computer, wants to send data to that receiving computer, well we transmit some signal between the computers where that signal represents the data. One example is that we use some signal where we transmit at a high level to represent say bit one and transmit at a low level to represent a bit zero and that way we can send a signal, say a sine wave is a mathematical representation, send a signal to carry the information, the bits in this case. And we're looking at the design of different communication signals from a mathematical perspective. And we went through cases and we saw that any communication signal can be thought of as a combination of different sinusoid, sine waves combined together. We've gone through some simple examples, in practice real communication signals are much more complex than the examples we've looked at but the same principles apply. So if we take a signal is made up of different sinusoid components combined together, if we look at those individual components with our general sine equation, it's on one of our slides, S of t equals the peak amplitude sine 2 pi f t plus a phase, our general sinusoid equation where there are three variables, peak amplitude a, frequency f and the phase 5, then if we look at a signal and break it down into these components, the set of frequencies of the individual components is the spectrum of a signal. So if a signal is made up of three components and that the components of those frequencies are 1 hertz, 5 hertz and 9 hertz, then we say the spectrum of that resulting signal is 1, 5 and 9 hertz, the combination of those three frequencies. Absolute bandwidth is the width of the spectrum ranging from the minimum frequency component up to the maximum, so the difference between the two. And that's an important characteristic of our communication signals. There are some other properties that we're not going to focus on about if there's a zero frequency component, we call it the DC component, but not of interest for this topic. One thing that will be of interest is that the theory we're looking at, when we look at the signals from the perspective of different sinusoid components, we can talk about the absolute bandwidth. In practice, a real communication system, even though we design a signal with some absolute bandwidth, the medium may only support the transmission of frequencies of a reduced bandwidth. So in practice, some signals may even have an infinite absolute bandwidth. So we get to design a square wave which has an infinite absolute bandwidth, an infinite range of frequencies. But when we try and transmit such a signal across the cable, that cable can only transmit frequencies within some range. So there's a practical limit and that range that our system can transmit is referred to as the effective bandwidth or commonly just the bandwidth. So think of the absolute bandwidth as something we can calculate in theory. In practice, there are real limitations and we often refer to just the bandwidth of a system. We'll see some examples of that as we look at different transmission media because a transmission system can only carry a limited band, a limited range of frequencies. And another thing and we'll see through our examples in the handout is that the bandwidth and the data rate are related. Generally, the larger bandwidth of our signals or our transmission system, the larger data rate we can achieve. Everyone has a copy of the handout? Anyone not have a copy? Hand out just for today? Got one? Just some extra pictures for some examples. OK, there's a few at the back here. Just some things I forgot to include in the lecture notes. Maybe we can go through that example. And it's on the website if you need the electronic copy. So let's look at some examples. Again, very simple signal equations and look at them from the time and frequency domain. Here's our first example. So think of as the designer of the signal, we choose a signal that we want to transmit. I've chosen this simple signal represented by the summation of two sinusoids, two components. As the designer chose this signal, and I've chosen it in a particular pattern that the shape will look nice. It doesn't have to be so simple. So here's our signal that we want to transmit. There are two components, sine 4 pi t plus 1 third sine 12 pi t. And all of that is multiplied by some factor 4 over pi. The significance of this multiplier 4 over pi will come up as we go through all of these examples. At the moment, it's just some factor we multiply the peak amplitude by. A multiplier at the front means we change the height of the signal. We'll see the significance of y 4 over pi shortly. But focus on the two components. First one is 1 times sine 4 pi t. The second one is 1 third sine 12 pi t. Look at them separately. What's the frequency of the first component? Can someone tell me? The frequency of the left component, the first component. F1, let's say. Anyone? 2 to what? 2 hertz. Where do you get that from? Look at the general equation. Peak amplitude A sine 2 pi f t plus the phase. There's no phase component, or the phase component is 0 in these equations. So that's simple. The amplitude is the multiplier. And look at this 2 pi f t, the frequency f. We have 4 pi t. Therefore, f must be 2, because 2 times pi times 2 times t. The frequency of our first component is 2 hertz. And the second component, f2, anyone? 6 hertz, easy. So this signal is made up of adding 2 sinusoid together of frequency 2 hertz and 6 hertz. What's the bandwidth of this resulting signal? The absolute bandwidth. Bandwidth, the width of the spectrum. Louder. Louder. 4, OK? The difference between the maximum frequency component and the minimum. In this case, there's just 2 components. Bandwidth is 4 hertz. We'll look at some other properties in a moment. Let's look at, so here's our signal from written as an equation. The top left is a plot of that signal over time. So it's in the time domain. Here's the signal strength. If we plug in different values of time, t, t equals 0, and calculate the value, we get 0. t equal 0.1, 0.2, and so on. And we plot it, we get this. So I've plotted it from time equals 0 up to 1 second. From the plot, what's the frequency of the signal? Looking at the time domain plot. What's the frequency of the resulting signal? What's the frequency of that plot? How many cycles occur in 1 second? Two. You can see it goes up, down, and then we get to here, and then we repeat. So one cycle, two cycles in one second. The frequency of the resulting signal is 2 hertz. There are two repetitions per second. Remember, hertz just means cycles per second or repetitions per second. So the resulting signal is 2 hertz. In fact, we could have determined that from the two components, because if we have a signal which is made up of components whose frequencies are integer multiples of one of them, then that resulting one, or that one, is the fundamental frequency. So f1 is, in fact, 2 hertz. f2 is 3 times 2 hertz. So an integer multiple of the first component. Therefore, the frequency of the signal when we add them together is simply 2 hertz, and called the fundamental frequency. I've put a subscript f here to mean the fundamental frequency in this case. So we can determine that either from the two components, because this is 2 hertz, and 3 times that one. If it was 5 times that one, or an integer multiple times by one of them, then that's the resulting signal frequency. But we can also determine it from the plot, because within one second, we see two cycles or two repetitions. Signal frequency, bandwidth of the signal, frequencies of the two components. We could look at the peak amplitude of the components, just the multiplier in front of the sign. In the bottom corner is a plot of the same signal, but in the frequency domain. And in the frequency domain, we look at the individual components, their frequencies, 2 and 6 hertz, 2 and 6 hertz. And we plot an impulse or a spike, whose height is the peak amplitude of that component. So at 2 hertz, the peak amplitude is 1 times 4 over pi, which is about 1.3. That's why this goes up to about 1.3 here. And the second component is 1 third the peak amplitude of the first component. So you see this is 1 third of this height. So the height is the peak amplitude of that component. The mathematical representation, the time domain, the frequency domain plot, all of the same signal, just in different perspectives. A lot of analysis of signals is done in the frequency domain because it's easier from a mathematical and from a visual perspective. Look at this plot. Bandwidth is easy to see. Difference between 2 and 6 is 4 hertz. The bandwidth, looking at this plot, it's not easy to see the bandwidth of that signal. So we can see some useful properties from the frequency domain plot. OK, so bandwidth, frequency of our signal. Let's look at one more factor, which we're really interested in. This is the signal to transmit information from A to B. Let's say the scheme that we're using to send information is that we're transmitting bits, 0s and 1s. And the simple scheme will be, for this example, when I want to transmit a bit 1, I transmit the signal that is high for some period of time, say for a quarter of a second. That is, this portion of the signal, when we're up near plus 1, represents a bit 1. And the opposite direction, when we're down near minus 1, let's say, if we transmit this signal, it means we're transmitting bit 0. So that's an example scheme. It doesn't have to be like that. There are others. But one example scheme of how do we convert bits, 0s and 1s, and transmit them as signals? Transmit high for some period of time, for bit 1. Transmit low for a period of time to represent 0. If we take this scheme in this example, over a period of 1 second, how many bits does this signal represent? How many bits do you think are there? All right, let's imagine we had a sine wave. Start simple. This is just the addition of two sine waves, but say just one component sine wave. And we're saying that if I want to transmit a bit 1, we take the sine wave in this positive portion. And a bit 0 is the sine wave at the lower half. So if I wanted to transmit a sequence of bits, which was 1, 1, 0, 1, with a simple sine wave, I would transmit a signal like this. Positive, positive, negative for 0, positive for 1. And the receiver, when they receive the signal, they measure, is it positive? Yes, that means I receive bit 1. Positive, bit 1, negative, bit 0, so on. So that's the basic approach here. Same as in the one on the screen, except now we don't just have a single sine wave, we have the addition of two sine waves, but the same principle applies. So we could say, OK, this portion represents one bit, we're positive for most of the time. This portion represents a second bit, a third bit, and a fourth bit. So in this case, over a period of one second, we've transmitted four bits of information. And that's our data rate. We achieve a data rate of four bits per second in this example. So we're trying to relate our signals to some properties that we're interested in about our data transfer, in particular data rate. So a very simple example. Now, let's see what happens when we change the characteristics of our signal. In the first case, I had a signal with two sine components. The frequency of the signal was 2 hertz, bandwidth 4 hertz. We achieved a data rate of four bits per second. Using the same approach, the second one, the second example, we use a different signal. It has three sine components. What's the bandwidth? Calculate the bandwidth. The answer's on the sheet. Calculate it. Yes, you're right. So you look at the three components, determine their frequencies, and look at the minimum and the maximum. The first two components are, in fact, the same as the previous example. 4 pi t means the frequency is 2 hertz. The second component would have a frequency of 6 hertz. And the third component has a frequency of 10 hertz. 20 pi t. f must be 10. So 2, 6, and 10 gives us a bandwidth from 2 up to 10, a bandwidth of 8 hertz. And that's absolute bandwidth of 8 hertz is given at the top of the plot. So using a different shape signal with everything else the same, we occupy a larger bandwidth in this case. We transmit a signal with a larger range of frequencies. We can plot that in the frequency domain. Now we have 2, 6, and 10 bandwidth of 8 hertz there, the three components, and in the time domain. Compare the two plots. The first one in the time domain, the blue plots, and the second one. Similar, just that in the second plot with three components, we see it's closer to plus 1 and minus 1 during this period of time. You see, in the first plot, it takes some time to rise up to plus 1. In the second plot, it's a bit faster. The slope is larger. It's getting closer or shorter time to rise to plus 1. And it's closer to plus 1 for a longer period of time. And that's the result of adding this third component in to give us this shape. Using the same scheme of mapping bits to signal, one bit, two bits, three bits, four bits transmitted over one second. Data rate is still four bits per second. Using a different signal, we get a different shape, but we achieve the same data rate. Which one's better? First one or second one? Which signal is better? You need to choose one. You're a designer of a communication system. You need to choose one of these two. Which one are you going to choose? Maybe the second one, because it has a larger bandwidth. Let's say something about the bandwidth. The bandwidth impacts upon other factors. But in practice, we want to use a signal which occupies a small bandwidth. We want to minimize the bandwidth. And we'll say more later. But the main reason is that the more bandwidth we use, the higher the cost of this transmission system. But we'll see that there's some other trade-offs. So we'd like to use less bandwidth, in which case signal one is better. It occupies four hertz, signal two occupies eight hertz. Any other differences? So there's one difference. Signal one, absolute bandwidth, four hertz. Signal two, absolute bandwidth, eight hertz. Generally, we want to choose a signal which or we want to use a smaller bandwidth as possible in practice. It will result in a lower cost. Any other differences? Well, data rate. Sorry, wrong way. Data rate, four bits per second. Data rate, four bits per second. Same data rate. So there's no difference there. Signal one is better because it's lower bandwidth. Let's come back to signal two after we look at signals three and four. One, signal two has three components. Signal three here, the third example has four components. I just added one component at the end. You can check and you'll see the bandwidth is 12 hertz. And you see the shape. It's closer to plus one and minus one. And signal four, or example four, I added up to however many, there is 10 components or so there. So I've got plus one third or seventh and so on up to 119th. And I plotted it and we see that the resulting signal is almost always plus one and minus one. Much higher bandwidth, 36 hertz. That's the negative here. But the positive of using this signal compared to the first one is this generated signal is closer to our ideal case of a high level representing bit one and a low level representing bit zero. We'd say it's more accurate representation of say an ideal square wave. Plus one, minus one, plus one, minus one. This is more accurate than the previous signals, which are approximating this plus one, minus one. It's getting closer to just purely a square wave. What does accuracy matter? It matters in terms of it gives less chance of errors. An error is when the receiver receives a signal and interprets the data wrongly. I receive a signal, I think it means a bit zero, but it's in fact a bit one that was transmitted. So the general trade-offs we see by choosing different signals, we impact upon the bandwidth. We want to generally reduce the bandwidth. But with a larger bandwidth, we can get a more accurate signal which reduces the errors, which is a good thing. What about data rate? All of them have the same data rate if you look quickly. Four bits per second, four bits per second, and four bits per second. Last example, two components. If you look at the calculations and determine the data rate, we see that over a period of one second in this case, we have one, two, three, four, five, six bits sent. A higher data rate. How do we get that? Compare this one to the very first one. What's the difference? Compare the values of data rate and bandwidth to the first signal. Frequency is what? Frequency has gone up. So in this one, our data rate's gone up to six bits per second. Why? Well, our frequency is up to three hertz, and in fact, our bandwidth is up to six hertz. An increase in the frequency and bandwidth here has led to a higher data rate compared to the first one. Frequency of two hertz, bandwidth of four hertz. So here's another trade-off. We can use the same type of signal, two components, same accuracy, but generally, increasing the bandwidth also increases the data rate. So we've got really three trade-offs to consider when we choose a signal. And let's go to the last slide, which summarizes some of them. With all things the same, if we increase the bandwidth, we can get a more accurate signal, which means less errors, less chance of things going wrong at the receiver, which is a good thing. That's an advantage. We see between the first and the last plot an increased frequency, and you should write it here. I left it off, or I should have wrote it in. Increased frequency and bandwidth increases data rate in these examples. In fact, the more important part is the bandwidth. An increased bandwidth in general increases the data rate, which is a good thing. We want a high data rate. But increasing both of those leads to higher costs. Why high costs? Because the fact is, when we transmit signals with a particular bandwidth, we're usually limited because other people want to use those frequencies as well. And there's a demand for using those frequencies. So there's some cost involved of using a set of frequencies. So we cannot just transmit over any range of frequencies. In a wireless system, for example, we may have to pay a license to use some frequencies. And therefore, the larger bandwidth, the larger range of frequencies, the larger the cost of our communication system. And also, another factor is, when we use very high frequencies, the hardware for the transmitter and receiver become more complex, and therefore also more costly. So increasing bandwidth is good for accuracy and data rate, but bad for cost. So when people design signals, they need to consider those trade-offs. Someone who designs a communication system needs to consider maximizing the data rate, minimizing the errors, and minimizing the cost. And that's why it's not easy to select the best signal. I think we'll not go into any more details of this. I think the main thing to take away is the different trade-offs that need to be considered when designing communication signals. And the mathematics part of it really is the very basics of the sine wave and how we can combine them to get different properties and signals. We will see a more general relationship between bandwidth and data rate in the lecture tomorrow, some equations that relate them together. Maybe there's one slide that... This example, I'm not going through it. You cannot answer this example without me giving you extra information, and it's the example, essentially, that we went through, that you have in the handouts. Except in the handouts, I use four hertz and eight hertz. The example I was going to go through, where I have in the past used four megahertz and eight megahertz, but exactly the same concepts, just one million times larger, some of the values. So you have the example in front of you. You don't need to go through that one. This is just one different view of how bandwidth and accuracy of a signal relate together. This is a different communication signal than the ones we've shown, but it shows the principle that we have a sequence of bits to send. So a random set of bits, is it one, zero, one, one, one? Ideally, this is the signal that we want to transmit. Now, the mapping is the opposite from what I said in our example, in this picture, which came from the textbook, the mapping is if we want to send bit one, we send a low signal, bit zero, high signal. It's just the reverse or the inverse. So if this is what we want to transmit, two pulses representing two different bits there, but we generate a signal to transmit through a system and the lower ones are the signal transmitted when different bandwidths are used from 500 hertz up to 4,000 hertz. And the plots are of what we would see if we use different bandwidths. And the main point is that as we increase the bandwidth available in our communication system, the signal transmitted gets more accurate to the ideal one, gets closer. You can see this one at 4,000 hertz bandwidth is a close representation of this original square wave, whereas the first one at 500 hertz bandwidth still has the high and the high here, but it's not an accurate representation of the desired signal. Increasing bandwidth increases the accuracy of the signal. And as a result, a more accurate signal produces less errors at the receiver. And I think this is just another summary of those trade-offs. Greater bandwidth, greater the cost. That's a bad thing. But greater the bandwidth, greater the data rate. That's a good thing. We want high data rate. And the other thing is the accuracy. We want to be an accurate signal and generally a greater bandwidth, although it's not written here. I thought I had it. Maybe it's at the bottom. Greater the bandwidth, greater the accuracy of the signal. We're gonna cover a few other topics to finish today. Any questions about our basic signals before we move on? What does it say? You can't read it. It's deleted from the bottom of the slide, but it says greater the bandwidth, greater the accuracy. You can see some dots. My slide was too small. In the quiz, quiz four, which is available tomorrow, there's a couple of very, very simple questions about the sign equations. In an exam, they may be harder, but in the quiz, you'll see that find the bandwidth of this signal, find the period of this signal, simple questions like that. So I'll give you some quick practice on those equations. In this topic, we've got three things left. And two we want to cover today. The last one we'll cover tomorrow, channel capacity. Analog and digital data transmission and data signals, and analog and digital signals. The difference between analog and digital. In fact, I think most of you know this from other courses, the concepts of analog and digital. We'll give a couple of quick examples of the difference, but in two, not next topic, but the topic after, we return to analog and digital signals and transmission. So we'll skip through a lot of this today and return to it in depth in another topic. And then we'll look at transmission impairments. When we talk about analog versus digital, in fact, we need to be more precise in communication systems. Are we talking about the data that we want to get from A to B, analog data or digital data? Or the signals that are going to be transmitted from A to B? Are they analog signals or digital signals? And in fact, when we combine, we can talk about either an analog transmission system or a digital transmission system. So it gets a bit more complex than simply analog versus digital. Again, the signals and transmission we'll cover in a later topic. Let's just give two examples, quick examples of analog and digital data. Analog data. That is, information we want to communicate from A to B. One example, audio. When I'm talking to you in this lecture, the data that I'm sending you is audio. Speech. So that's an example of analog data. Another example, you listen to the radio. Well, the analog data in that case is music. This diagram shows in the green lines, the frequency or the spectrum of typical speech and music. The dashed one is music, the solid one is speech. What that means is that when someone talks, the frequencies of the audio, of the speech, range from hundreds of hertz, so here's 100 hertz, up to about here, getting close to 10 kilohertz. And as we go up, this is the magnitude. Ignore the units here, but the higher it is, the stronger the signal. In fact, because it's a logarithmic scale, really, if we just look at the high part of this solid green line, we see the main portion of speech, the loudest signals, the loudest part of speech, are around 300 or 400 hertz here, up to around 3,000 hertz, approximately. This is a logarithmic scale here, so I cannot tell you the exact numbers. When someone talks, they're generating audio signal with frequencies ranging from 3 or 400 hertz up to about 3,000 hertz, 4,000 hertz. That's an example of analog audio, analog data, audio. When someone plays music, we have singing, we have instruments also, there's a wider range of frequencies. So there's some lower frequencies and higher frequencies, so ranging from the tens of hertz up to about the same, maybe even a bit further, 10, 11, 12 kilohertz. So music has a larger spectrum than speech. That's analog data. Think of a system that transmits analog data. Your radio, think of the radio in your car. What are the two different types of radio that you know about? You can tune into two different types of radio in your car. What are they? AM and FM. In another topic, we'll describe what AM and FM are. But which one is better in terms of quality of the audio? FM. I think most people will recognise generally FM gives better quality audio. It may not be better content, but better quality audio. Why? Well, the radio transmission from the tower to your antenna on your car signals are being transmitted over a particular bandwidth. And it turns out that the bandwidth of those different systems differ. And AM is about, and it differs in different regions, but the bandwidth of one channel, so you tune into one AM radio channel, that channels transmitting signals across a particular bandwidth. It's about 5 kHz, 5 to 10 kHz. Whereas with FM, it's about 15 kHz. With FM, the bandwidth available is larger with AM. And in effect, we can transmit more data, more information with FM. With larger bandwidth, more data can be sent at the same time. Relating it to the types of data here, audio or speech requires a bandwidth of about 4 kHz. If we look closely here, we're ranging from about 100 Hz up to 3,000, maybe 4,000 Hz, 4 kHz. When someone's talking, the bandwidth needed to transmit that voice is about 4 kHz, which fits nicely into an AM radio channel. But if you want to play music across the radio, there's a larger bandwidth required to capture all of those frequencies of the music, the low frequencies up to the very high frequencies, say with classical music, so up to say 10 kHz, even larger. If we try and transmit our music, which requires a bandwidth of 10 kHz, our AM radio channel only transmits a bandwidth of 5 kHz. It cannot transmit all the frequencies of the music. So what's heard at your car audio system is just 5 kHz of that music, say it cuts off the low frequencies and the high frequencies. So it doesn't sound so good. But if you play that music across an FM radio channel, which supports a bandwidth of 15 kHz, all of those frequencies of that music can be transmitted and received. And hence FM radio sounds better in terms of audio quality. So examples of two types of data, audio being speech and music, and AM radio and FM radio are the transmission systems that can be used to transmit that data. And the bandwidth of them is important to determine the quality that the user receives. So it talks about the bandwidth supported by AM and FM radio here. Another communication system that you've used or you use is the home telephone system. Not your mobile phone, but the old style home fixed landline telephone. The telephone network is designed to support a bandwidth of around 4 kHz as well. It's shown in this grey box here, from about 400 Hz up to about 4000 Hz. So again, when you're talking on the telephone, the home telephone, speech uses frequencies of about 4 kHz. The telephone supports transmitting about 4 kHz. It works fine. Another person can hear and understand what you're saying and it sounds good quality. But if you try and transmit music across that home telephone system, the person at the other end of the telephone will not hear the good quality music in terms of not hear the low frequencies of the music and the high frequencies of the music. Because your telephone system only supports a limited bandwidth. So we need to design the communication system to support the types of data that we want to communicate. So example of analog data. There are others, of course, but just examples. Example of digital data. Digital data, bits, 0s and 1s. Well, here's an example. Here's a ASCII table. See if you can make sense of it. We want to transmit a message from A to B. So the data is that message. Why is it digital data? Because usually if that message we convert into 0s and 1s. See if you can read what I'm writing. What did I just say? Well, what have I done? I've taken some, in this case, English characters. Some letters from the alphabet. And the ASCII encoding here, this example, tells us how to map those characters into bits into 0s and 1s. So what I wrote on the board, the sequence of bits actually represents a sequence of English letters. That is our message. Hello is the message. And this table was just one example that shows that, okay, the letter H, the first three bits are 1, 0, 0, and the last four bits 1, 0, 0, 0, which is these seven bits. And you can check and see the other encodings. Seven bits at a time. So an example of digital data, okay? It's an English message, but represented as bits in binary. I'm not asking you to perform ASCII encodings and so on, or remember this, it's just one example. Effectively today we can convert any information we want into binary using some encoding scheme. And again, when we talk about the different types of analog and digital signals, up until now we've talked about just these sine waves as the signals we're sending, where we can now distinguish between analog and digital signals as well. So we can have analog and digital data, and the signals that we send can be either analog or digital. And we can map between them. But we'll return to that in another topic, I think, to try and finish this one as early as possible. And we'll talk about telephones, modems, codecs and transceivers in another topic. What we want to finish with today in the last 30 minutes is just an introduction to transmission impairments and a couple of examples on that. Transmission impairments, the impairments are when things go wrong. We have our source transmitter, has some data to send to the destination B. We take that data, convert it into a signal, transmit the signal to B. Unfortunately, in real life, the signal that was transmitted may degrade. There may be some impairments in the communication system such that the signal received is not the same as the signal transmitted. What causes these impairments? And what's the impact? Well, the impact is that what's received may not be correct. So if I transmit some signal and the signal received differs from what was transmitted, then what can go wrong is that the receiver makes some... if we're using digital data, what we get is bit errors. I transmit a signal representing bit one. But the receiver receives a signal which is different and I think it was bit zero. There's a bit error, because one was transmitted, zero was received. So that's the consequence of what will seize the different transmission impairments. Or if we're looking at analog, then the signal quality goes down. That if we transmit some signal, then if we think of an audio signal, the receiver cannot hear or understand what the other person is saying because the quality is very poor. It's very weak or there's a lot of noise on the signal. And therefore makes the transfer of the data ineffective. What causes impairments? Well, there are different causes. In this topic, we're going to go through two. Attenuation and noise. There are a couple of related ones. Distortion is related to attenuation and also delay distortion. But we'll not try and go into the details of them in this topic. Attenuation and noise may be the most significant ones in many systems and the easiest ones to understand. Attenuation. It simply means that when we transmit a signal, as that signal traverses or propagates across our transmission system, the signal's strength gets weaker over some distance such that the received signal is weaker than the transmitted signal. That's attenuation. The signal attenuates. It gets weaker over distance. That's the property of physics that causes that for all signals. So if I turned off my microphone and I was talking to you, then I transmit a signal at some strength but as it travels through the air to you, it gets weaker, which means that the person at the front will hear me better than the person at the back. Why? Because my signal attenuates. It gets weaker over distance. Therefore, it's easier for the person at the front to understand the information on communicating than the person at the back. So that's an example of attenuation. The signal strength reduces as a function of distance. So that's a given. We cannot avoid that. When we design a communication system, we need to take that into account. Maybe we'll try and draw what that looks like. We have our transmitter. Transmit some signal of some strength as some sine wave of some magnitude, representing the strength. And it propagates across some distance, getting weaker the further it goes. So the receiver receives some signal, which is much lower magnitude. That's the idea. The signal attenuates. By how much does it attenuate? Well, in the next topic, we'll see some equations that relate the signal attenuation against distance. It depends on different factors. So when we design a communication system, we need to make sure if we transmit some signal, the receiver can hear and understand what was transmitted. For example, when I want to talk to you, if I am talking using the microphone and I transmit at some signal strength, in fact, there's an amplifier in this audio system, so it increases the signal strength and it goes to the speakers and then the signal propagates to your ears. So if I'm talking and I keep talking and I turn down the output of the amplifier, you see the signal gets weaker at your ears. So at what strength can your ears receive my signal? Let's try it without the microphone. So as I transmitted a weaker and weaker signal, there was still a signal propagating, but because it reduces in strength across distance, his ears are only good enough to discern, to understand a signal of a certain strength. When I was talking too quiet, the signal he received was too weak for his ears to make sense of it. So the capability of the receiver is important. The received signal should have sufficient strength so that the electronics at the receiver, we're talking about computer systems now, the electronics at the receiver can understand or interpret that received signal. Like your ears can only understand or hear something above some magnitude. The receiver can only understand some signal received with some particular strength. And in practice, it's usually a characteristic of the product, the device that you buy. Another thing that's important is that when we design a system, we need to design a system such that the receiver can receive a signal strong enough that it can understand. So we need to consider the distance between transmitter and receiver because the signal gets weaker over distance. We need to consider how strong does it have to be for the receiver to understand and we need to consider how strong it must be at the transmitter such that we'll receive a strong enough signal at the receiver. So the transmit power, the receive power and the distance that we'll see are quite important. But there's another factor. When I'm talking to the one person, it's reasonably quiet in this room. So I'm going to talk and say something and you're going to put your hand up if you can't hear me, okay? Say it louder. You're not very good for the demo. You're supposed to make as much noise as during some lectures talking to your friends. As other transmitters started transmitting, if I was communicating at the same level, it would become harder and harder for the receiver to hear. These other transmissions are what we generally call noise. So the receive signal at the signal received should be much higher than the noise that is the other transmissions in this case. Because if the noise is very high even if I'm communicating at a normal level it will be very hard for the receiver to receive and understand what was being transmitted. So we need to consider the noise as well. Attenuation, distortion, let's not cover for now. Let's go straight to noise. What causes noise? Different factors contribute to noise. So noise is everything else that is transmitted in the system. Quickly go through the four factors. We're not going to go through the physics or the equations here, just examples. There's thermal noise, always present in real systems. Due to electrons moving there's some what we may call background noise or thermal noise that's present in every system. We cannot get rid of it. It's usually very small. There may be when some signals are transmitted because they contain multiple frequencies those frequencies of those different signals can interfere with each other. So when I send signal to the receiver and there's others transmitting those others are considered noise and there's what's called intermodulation noise from different frequencies, crosstalk again from other transmitters and another case of noise, impulse noise. For example some short spike or peak of noise. For example some electrical disturbance. Or in this room if I was talking then someone shut the door. Some short impulse of a large sound that makes it harder for that short time for the receiver to receive. In electronic systems lightning couldn't cause an impulse of noise. A lightning strike causes a large discharge on the system. Errors in the communication system. We're not too concerned about the details of the individual components. Combined there's always noise in a communication system. Sometimes we cannot control how much noise. When we design a system we need to, if we know approximately how much noise or the maximum amount we need to design such that the receiver can still receive and understand. And generally noise we think is random it varies over time. Sometimes it's small sometimes there's a peak and it may change over time. In our audio system what's the noise? Well there's supposed to be noise from other people talking. What's the background noise? If no one talks air conditioner, lights. It may be hard to hear but there's noise coming from the lights from the different things in the environment cause noise which make it harder to transmit. This is our last slide for today. It gives an example of the impact of noise in this case on a digital signal or digital data more importantly. We've got A wants to send some bits to B. The bits are shown at the top the data sequence of zeros and ones just random here. We're going to send this perfect square wave signal to represent those bits. And we see the scheme is whenever we want to send a bit one for some short period we send a signal say some voltage level of low say negative one volt. Whenever it's a bit zero high low high high low low and so on. So there's a scheme that maps bits to the signal level. The receiver knows that so when the receiver receives a signal if the signal is low it assumes it receives a bit one. If the signal is high say plus or positive voltage it assumes it receives a bit zero and so on. So this is the transmitted signal. In our communication system there's some noise and here it's shown as this random varying signal. There's some small amount of background noise maybe some small increases maybe there's some disturbance in the communication system leading to a large spike of noise and another large negative spike of noise in this case. So just some random noise in this system. Let's say we measured that noise. We transmit this signal through our communication system and we think this extra noise is introduced into the signal. The received signal is the summation of the two. If we add them together we get this shape. Signal plus noise. And you can see the shape of the transmitted signal but affected by the noise. We see it's low but some variation then it goes up to high with some larger variations and so on. So it's just the addition of those two together. So think of this as what our destination received. Now what the destination does is it measures the signal at a regular points at different sampling times. And according to our scheme if the signal is negative or below this dashed line we assume a bit 1 was received if it's positive above the dashed line we assume a bit 0 was received. And that's what the receiver does. Measures the signal and maps it back to 0s and 1s. And these are the sample times that the receiver checks. Measures here, okay, it's negative 1 was received. Measures here, okay, positive 0 received. And keeps doing that. It measures at this point negative 1 was received and measures at this point it's positive, 0 received and this top line here the data received is what the receiver thinks was transmitted. At the bottom we have the original data exactly the same as the data transmitted here and we see there are two errors bit errors we call them. Everything's the same except for this bit the receiver thought it was a bit 0 but it was in fact a bit 1 transmitted and this second to last bit wrong bit received. These are our bit errors and these are bad for our communication system because our received data doesn't match the transmitted data. Why? Well you can connect in time these bits to these large increases in noise. Here we transmitted a low level but there's a large amount of positive noise which took this negative value into a positive value effectively flipped the bits. And similar here the transmitted was a positive value but there's a large negative value. When you add them together the result is negative and interpreted as a bit 1 received. So here's an example of noise in a system and in some cases depending upon the magnitude of that noise it can cause bit errors. So we need to consider that when we design communication systems. We want to minimise or reduce or keep the bit errors to 0 where possible. But sometimes we cannot know what the noise will be so we may need to deal with that. Two main impairments that we've mentioned today and all the ones we'll cover in this topic attenuation our signal gets weaker across distance the signal strength. Think of our sine wave it gets smaller and smaller the further the signal propagates. And the second one noise noise is always present in a system and it has an impact upon the received signal and as a result the quality of the received signal or the number of errors in the received signal. The last topic here is about some mathematics that relate bandwidth and some other factors to the data rate. We'll cover them tomorrow morning. Any questions in the last 10 minutes?