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.  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 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.  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.  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?


Well, good morning artists and friends at least it's morning where I am now here in Tampa, Florida. Welcome to Monet cafe today I'm in my home studio, and I thought it was a great opportunity for me to go over Some of the questions that you guys have about different surfaces for painting on pastels I do have another video where I talked about surfaces and different pastels But I'm gonna give a little more time to this one and focus just on the papers and the surfaces And I've got my Monet cafe coffee cup here having a nice cup of coffee this morning and hang on while I take a sip Mmm, I love days like this. All right, so we're gonna get into first of all Why can't we just use regular paper or watercolor paper or whatever with when using pastels? This happens to be my Set of iridescent pastels I got from the Mount vision pastel company that actually is located here in Tampa, Florida It was great that I got to tour the company and get these beautiful iridescent pastels. They're real sparkly And they have one of the largest selections of iridescence as most companies they even have a set of darks Which I got but anyway, I'm using these as an example pastels are dusty Okay, and if you were to use these just on a regular piece of drawing paper or even if you go to craft stores They sell a paper that's called pastel. I can't do was both my fingers and quotes pastel paper It's actually not really good for pastels I mean you might can get a little bit of layering done on there But the point is that with a flat paper that does not have a sanded surface Your pastels are just going to you can get one layer down maybe but then as you start adding pastels They start getting muddy colored. They're not as brilliant and they kind of fall off So it's hard to work on a smoother type of surface. So we literally use products For papers that have a sanded surface kind of like sandpaper in a hardware store. I wish I had a sample of that I've actually bought some cheap Hardware store sandpaper and done pastels on them just as an example I would go with a finer grit not a real coarse grit though. It'll eat up all your pastels So let's talk about some of these papers here and hopefully you'll learn something When I get ready to do a painting I have choices to make as to what kind of surface them am I going to use now if you're just starting out as a beginner This might be overwhelming. Oh my goodness. I can't afford to get all of that stuff So just start with something simple try one and then go from there Okay, a good good paper to use is you art paper. Okay, this is they come in different grits This is for grades. This is 400. It's pretty fine. I think it actually goes up to a 600 800. I can't remember but it's great because it's got a fine grit But it allows for a lot of layering and I like the nice neutral color. It's not white. It's just kind of a creamy Off-white color. Okay, so that's you art paper I get them in big sheets and cut them down, but you can get them in smaller sections in a little Packet of papers that they will send you. Okay, so you art paper is great I'll see if I can give some examples of paintings on each of these all right, so there's a nice piece of you art paper and Let me go to the ones that I didn't make first. Okay, these are the ones These are homemade surfaces here, and I'll show you how you do that But now this is another one that I love it is Lecartte pastel paper and it's made by Sennelier me with my southern accent I usually get all these names wrong, but I think I finally got this one Sennelier Lecartte pastel paper. I think I used to say Sennelier Anyway, you don't have to be able to say it to be able to paint on it. Praise the Lord So here is a pad of paper that I get that has various colors in it. Okay? It's got the browns. I've used a lot of them out of here. So you can't see all the colors They don't show it on here show it on the back No, but anyway, I like they have kind of like a a tealish gray one that I've used all of them Anyway, so these are really nice. I actually like working on dark surfaces, too But the Lecartte paper is really coarse the grit on this one is 360. It feels more coarse than that to me But I like it. I think it lends more towards an impressionistic feel It keeps me very focused on my strokes and making sure I'm having efficiency of stroke and not overdoing things And I love the loose feel that I achieve with the Lecartte pastel card Some people like it. Some people don't so that's kind of a personal preference now we also have the Canson a lot of people Canson is kind of like the one I was saying in the Craft stores you can get you can get a Canson paper. It's not really a pastel paper I see some people do great work on it, but this Canson paper is a little bit more for pastel. Okay? It's called the me taunts. Is that right? So people are correcting me I was saying it like Spanish like meaty and taste, but it's French. Okay me me taunts or something like that Touch, okay? So this one is not as Doesn't allow as much layering. It's kind of fine, but it doesn't have the same grit that the other two do So I like this paper, but I don't feel you can get quite the layering as the other papers But I do think this one is less expensive. Okay, I'm not going to go over all the cost of these But they can get kind of pricey, which is why sometimes I make my own But you can get these and you can the pad and you can cut them up That's a good way if you're just beginning don't take a whole piece like this and do a big painting cut them up into some smaller sections And just have some studies that you do, you know to practice with and get better. Okay? So this is another nice Canson product. Okay? Here is another one of the Already prepared surfaces you can buy I like this product a lot and I find myself forgetting to use it It's actually a board now the advantage of this is you don't have to mount it or anything when you're done And sometimes these other papers you are paper can actually kind of curl and warp in humid climates I do have a video on how to fix that problem if you ever have that problem. So um, but this one you don't have to worry about That it's a hard pastel board. It's really nice. It's ready to frame. This is an 11 by 14 gray I like working on a surface that has a color versus white. It has different colors that you can work on Let me see if it has the I don't see the grit of this one, but it it also Will receive quite a few layers of this and I just like the way it feels I have it in the plastic now, so this is good and you can buy different sizes in this as well okay, so now for your homemade surfaces lay that down and We have a few different options here. This is a technique that I learned I got this one a little splotchy, but from artist Rita Kirkman. She does beautiful work If you want to check out a good artist, I love her work But she did this technique and I emulated what she did because I love the glow behind this What she does is she uses this product Golden gel mediums fine pumice gel. Okay, it's this is probably stuck on. No, it's not okay So I have my ratio taped right to the top so I don't forget it Okay, so it's just a gel and it's sanded. It's got a grit to it Okay, so you can take matte board gator board You could even do this with watercolor paper, but it might warp but you take another type of surface That's not that expensive and I like doing it This one happens to be on matte board here You can go a lot of times to framers and ask for their scraps of matte board like the matte in a frame that you have in Your frames for your paintings and sometimes you can get it free or inexpensive So this one's just matte board. I have a way that I cut it But we can talk about that in another video But we're just gonna apply the sanded surface to the matte board and what I do is I mix up this ratio one-to-one ratio of fluid acrylic to The pumice gel this is the fluid acrylic now the reason you can use any color you want any Acrylic color you want which is one that I did here. Okay. I like sometimes just I like these bright bold colors And ones that should still show they're kind of transparent. They show the white still through it. It's not really opaque and dark Okay, so this was a really pretty Surly in blue or something that I I used for that board So you can pick any color you want, but I happen to really love this one read a Kirkman does Quinacridone. I think I got that word right nickel azo gold and This little and with the golden fluid acrylics. I love how they they always have these three little black bars on it They make a little stripe across it so you can see how transparent it is You see how you can see through to see those black bars? That's why the white of the paper shows through so well with this and keeps it bright with that nice glow Okay, and this color is also a great complementary color to a lot of landscape paintings So if you like landscapes the greens and the blues This is going to be a great background color for you to use for those. Okay, so when I mix this up one-to-one. Okay, so if you do The four tablespoons of this four tablespoons of that if it's real easy and then you I keep it in a little container If I have extra left over so that I can use it again when I do this I like to kind of just make a day of it not a whole day But take a period of time and go ahead and make quite a few of these boards I cut them up in different sizes because I happen to love this color again. This is another one You can do I've done it in green I had a painting that I did recently if you want to see another color it was a painting I have on my YouTube channel called joy in the morning. It was a field of flowers and I did it on this Pinkish magenta red background color again kind of a transparent parent color But if I do this with my fingers you can kind of hear that sanded surface and on this one too I play guitar so I have an advantage of having rough fingertips, but this one's even more sanded I must have put more pumice gel in that one. Okay, so you get the idea make your own pastel surfaces Okay, so now there's a couple of other ways you can do this too These I don't have physical examples of them, but I happen to love this product and I forget about this one too It's a color fix primer. You can get in different colors made by art spectrum fine tooth Again, it's similar to the pumice gel in that it already has the the grit in it You're making your own sandpaper So the same thing with this one you can get you matte board gator board whatever kind of surface you want And I always use a foam brush With this one these and with this I use a foam brush to apply it. Okay, you could use a paintbrush too You could swirl it around if you like that impressionistic Feel on your board which kind of again makes more of an impressionistic style so this is just a great product that you can use to make your own papers and Again different colors. I happen to like this color too. Okay, so I've got a few of those This is another one. It's called a dry medium pumice. I'll have to get the the recipe for this one But it's like literally dry like sands to make your own gritty surface So this is another product that you can use to mix with acrylics So again lots of different Techniques and things that we can use to make our own surfaces Here's one that I talk about a lot in my on my YouTube channel And I I like this technique because kind of quick and easy when I'm traveling too. I Happened to like watercolor as well as pastel so often I will do a watercolor painting on watercolor paper. Okay, watercolor paper is kind of cheap You know unless you buy, you know, if you're really good watercolor artist and you buy the expensive ones But this is just I mean you get these at Walmart, you know, and they're not that much So I basically just will do a watercolor under painting. Keep it really loose. It doesn't even have to be anything Detailed it's more just to get the mood and get some colors down and Then if you want to apply pastel to your watercolor all you do is get this product it's called clear gesso and It's a gesso product that has and clear is a good one because if you want your watercolor painting to show through So that you can do the pastel on top the clear allows you to do that So this has some grit to it again I would take my foam brush and apply this I wait for the watercolor painting to dry and then you just apply the Liquid I mean the clear gesso on top of it wait for it to dry one of my last videos I show how I attach the watercolor paper To my board when doing it so it doesn't warp watercolor paper will bend and warp when you apply the water So there's a neat little way you can tape it down to keep it from doing that so that's another very inexpensive way to Do watercolor and create your own pastel surface now I want to recommend something here that is a wealth of information beyond what I just described, okay? Dakota art pastels WWW dot Dakota pastels comm has an amazing catalog. Okay, this catalog is going to give you More information overload than you probably need right now. Okay, but it is just so detailed in all of its information It has all of the different pastels that you can buy it gives their names and it tells Whether they're soft medium or hard they have them range from soft to medium to hard down here I talk about a lot of these different ones in my videos I don't have all of them, but you know you will come to find which ones are your favorite again I just went to the mountain vision Manufacturing company and they have a great starter set Okay, if you want to go back and look at my video on when I toured the mountain vision company Okay, so Basically in here. I'm not going to go through all of the again Look at all they have all the pastels that you can get you can get this catalog for free if you just contact them They will mail it to you for free. Isn't that nice because they want you to buy their products, right? Oh my gosh, I just get dreamy eyed when I look at all these beautiful colors going through here But on page I think it's 31 and marked it Yes, they have a great great chart here to compare all of these different pastel surfaces, okay? We talked about pastel board ampersand. I just showed you that one. I had that color. I believe and Then color fix I didn't show you this. I like color fix paper a lot, too You can get in a pad with all these different colors. It's a great product. I actually haven't done Let's see. What do they call it pastel matte? I know a lot of people on our Facebook Monet cafe art group on Facebook use pastel matte very beautifully and Again art. There's a you art paper right here. It only comes well It actually now comes in another color comes in a you art dark, okay? So wow like I said it can get overwhelming if you're just starting but trust me This will all you'll start to get it and figure out which ones you like but just try something or even making your own surface and just have fun with it it's more about just learning the medium and getting used to it and There's definitely time to grow and get better. Don't get frustrated at first. Just have fun I always say that sometimes we feel like we're supposed to create a masterpiece and it's like no You're gonna make a lot of bad paintings before you get good It's like gosh, maybe a thousand paintings before you're really really a good artist So I don't want to scare somebody like what I gotta paint a thousand paintings. It may not take you that long Anyway, so this is just a great great resource for more pastel products and things I wanted to just give that to you guys and as always I focus on beginner intermediate and advanced artists But my heart is really tender towards beginner artists So this is a good way to maybe learn a little bit more at one time about what you might use and try So now I have the wonderful opportunity to pick one of these surfaces and start a painting Oh, I'm so excited. Oh, and if you guys want a Monet cafe coffee cup or a Monet cafe apron on my website It's Susan Jenkins fine art calm It's in the about section and usually a little link at the end of the videos You can actually go to that page and pick as seen on Monet cafe and in there You'll have the links to find these so as always guys happy painting and I'll see you real soon


We're playing Vikings first. We got Vikings Viking CFM boys work one and two We got to get a double I we cannot afford to slip up on any but on any players. We can't afford to it Bro, I can't lie. I mean he stomped the hell out of him And it's one of those things we're like now this is it's a player that has that reputation too. All right Here we go. Here we go. Here we go.  My bets got pop curry was three for thirteen from three. Yeah curry wasn't that good Yeah, pull was definitely not that tough, but I think that I think they definitely can win both games at home and turn back around It's like cover-three or cover-three cloud or something Glad I paid you a lot of money here Fire Our sixes I'm playing my bad draw that draw that draw. I mean low key these games have been tight though Like these games have not been blowouts, you know, it's not like the Kings can't win or the Warriors can't win on the road mixin Mixin I don't know who got a wire suit. I like DK. I should have checked on boys Mayor Jackson, let's go man. Oh, God. Have you fake one see if I'm my swear to God. I'm gonna just go cry Stevo's a lawyer with four gifted Jacobs, I got with down Jacobs. I'm sure. Oh the arm of the Packers lost. That's good for the boys Max with 33 is crazy. How is that crazy though?  Oh my God.  How did that guy just shed me that fast? What planet are we on right now? Nice, bro. That's exactly what I need.  I honestly don't like it one of six was one that game easily What are we talking about right now? They played the worst half of their hope in the whole season and they play That's easily like what are we doing? What are we talking about right now? Oh Let's go to Patrick. No, there'd be the sixes.   How you put a neck roll on Calvin Ridley?  He's like a rookie. I feel like it's different Jones, okay Why is nobody honest? It's just no way. Thank you. He's the most hated player him and westbrook are just like most That's cliff sky mcdaniels. Oh mcdaniels needs to play over Tobias Harris mcdaniels. He's better than Tobias Harold should get minutes What is that what we said? All right. All right, rod. You're banned. You are banned from talking basketball What are you watching? I would say b-ball pause one of the best six was the first two games What Yeah, you're banned you're banned you're banned rod. No, no, don't even say Talk about the weather or something, dude. How's the weather in minnesota right now, dude Harold can get but dude. I literally at rod if you type about basketball again You're every time every chat that you put in about basketball you owe a sub.  It costs you five dollars. Okay, and I swear to god Try me. We gotta start putting some goddamn accountability on the we say Yo, my trust heros, bro. Do you understand that that man played all year? and was Oof stiff armor. Oh, he missed his three threes today. He did. Sorry My bad pj. Tucker didn't turn into Steph Curry overnight. I don't know what player you've been watching all year booth I can't you know, I pj.  That's how I feel. That's literally how I feel Hardin was beyond Tonight like he was like you could have put me out there And it would be the same as hard in the first half who hates on a button up This is why you can't this is you guys just want me to be a slob forever I can't I can't throw a little a little summer button up on in april That's why we can't make it as a people Gamers bro, I mean come on Michael. Oh, I don't expect the sixes to get past the second round I really don't is that sad to say but I just honestly really don't Hardin can't win in the world. He really can't William Jackson, can we crib this can we crib this? There's just no way that guy beat both of you. Who the f*** that superhero Let's go Dodson, bro. I swear to god controls Did we break it miss that tackle though? Sixes don't match up well against baltham. Sixes don't match up well again. Why not vex? Why not? Let me tell them. Why don't they match up well against boston? Why why? Well, they don't have nobody that can cover that tatum. Who the f*** does dude?  Now. Why do I play? Why do I say I'm playing as chief chiva?  Why are you up so late playing it? Thank you a little cloud zone right there for that Nothing good comes out of this this switch And you're left tap. Oh, is he not at left tap bro. No wonder I'm getting screamed at That's how I can tell the chat really don't get You're not really human beings want what they can't have it's never worth it.  Oh, oh, trust me Man, I don't really get down with the leaks anymore, but you know, I was a heavy leak boy This dude's schino. He had like the the drive for me. What was it called?  You cannot play on a hornets and then be good That's just not how mba works.  What are we doing man? I And chris paul low key the most overrated player ever y'all love some overrated mother I'll tell you that What's chris paul top 20 or what? He's just no way you caught that pass Why am I just still blocking it's just crazy to see how much y'all y'all What are we doing right now? Like what are we doing in my chat? Good blocking boys. I swear to god that play I should just never run that play It is just instant shed every time. I don't know why people run that But I mean now and I was in shot 30 times a game. He made 12 of them Played and he would get like he like he played no defense. He wasn't a defensive player Wasn't a passer wasn't a facilitator made nobody better didn't give a f*** like No, now see I go too far Now people put alan arson like overweight and hardened and saying no But have you talking dearen fox and Kyrie No, and all right. Y'all's definitely smoking now. Hold on. All right the rose. All right. No, no All right now i'm done. I'm done. Wade is the third best shooting guard ever This is joren coby wade then who's fourth right boys?  Clay thompson is not over james harten in any f***ing universe. Okay, wade. Yeah, where's wade? Did I not just say w-


I can't say I've seen that before. Hi everyone, Shawn with jaspyscasebreaks.com. Here doing a 2020-2021 Panini Obsidian basketball six box, half case break, pick your team number four, where we're also giving away $400 in break credit. So on release day here, this is the second half of case we started with pick your team number three, all card ship, and how to be entered into the $400 break credit giveaway by two or more teams get entered to win. No max entries, two teams, one entry, four teams, two entries, six teams, three entries, et cetera. If you only buy one team, good luck with that team, but you will not be entered for the break credit giveaway and top four names each win $100 in break credit. So there you go. Here is our list of customers and respective teams from Alfonso Mendoza and the Hawks down to the wizard, which are in a random number block. There are two different random number blocks. You'll see the Lakers, Washington wizards, and the Timberwolves and Warriors are both in separate random number blocks. Here is the result of those random number block randomizers here. Zero gets any and all redemptions, even known one-on-one redemptions, while the one spot gets any live and in-person one-on-ones and any non-numbered cards for those random number block teams will be randomized separately to each random number block at the end of the break to one person in the random number block. And so here is that Lakers, Washington random number block and same rules apply there. Here are those lists in person. So here's the full list. Thanks to everybody for getting in on this. Took a little bit, the city is flying out the door now. And here is the Timberwolves, Warriors random number block. I'll put that up top. Here is the Lakers and wizards random number block. We'll put that down here on the bottom. So here is the boxes. You can see I put a little four on there to show for pick your team four. Since this is the second half of a case, we started with pick your team three. So thanks to everybody for getting in. Good luck. Only six left in that next random number block then. Nice. Yeah, I think pick your team five is in the random number block with only six spots left. Guys, two team random number block and that's from a fresh case and pick your team six. I think it's down to two teams as well. So looks like we've got two more half case breaks to do a whole another case of obsidian after this. And that all that's gonna leave because that'll take out all of our obsidian guys. Last obsidian we'll have available will be that random team last four boxes from a case that we've been doing four box random team breaks from first two, nothing crazy. So hopefully it's all been waiting for us in the last four boxes there. And that is halfway gone as well. So it looks like we got a whole bunch of obsidian coming up. You got two patch autos in here, maybe? I've seen one thick card, but why two? And we got two patch autos or two relic autos.  Pretty raw, but lots of potential. Oklahoma City Thunder, Austin Crawford, that is 16 out of 25. And for the Kings, you got De'Aron Fox, Swipe up. For the Kings and Oliver Soria, that is 60 out of 75. Could be real good. Oh, Evan agrees with you. You got Buddy Healed for the Kings as well, Oliver Soria. Non-numbered. And Cassius Stanley for the Pacers. I forget that there's two Cassius's in this. Cassius Stanley, Cassius Winston. Indiana Pacers, Oliver Soria as well. You got Zach Levine for the Bulls, Matt Daniels.  And we got Larry Nance Jr., Cavs edition. Adrian Tolentino. That is 16 out of 49 for the Cleveland Cavaliers. And Aaron Nakesmith, two dual relic auto Celtics. Adrian Tolentino as well. That one is 10 out of 35. Very nice. Aaron Nestsmith. First up, die cut for the Lakers. It's Anthony Davis. Lakers, random number block. Lakers random number block is down here next to me. 171 out of 75, spot one, Orlando Luna. There you go, Orlando. And you got Onyeka Akangu for the Hawks and Alfonso Mendoza. That is 34 out of 50. We got Devin Vossel for the Spurs, Icapola, non-numbered. And Montrez-Harel for the Lakers. Also part of the random number block, but that's a non-numbered card. So that'll be part of the non-numbered card randomizer at the end, where all non-numbered cards for each separate random number block will be randomized as one to the random number block. And Cavaliers, Jared Allen. Adrian Tolentino. We've got Jersey and Otto, Poku. Lexi Pokozewski. Thunder, Austin Crawford, very nice. That is 48 out of 49. Nice Poku rookie Otto. You got for the Nuggets, Monty Morris. Denver Nuggets, Jess Bukheim. 70 out of 149. Right? With the little design in the background. It makes it look really nice. There's Austin. He's happy. He likes Poku. So do we. You got Colin Sexton for the Cavs. Adrian Tolentino. That is 21 out of 50. And Jared Allen again for the Cavs. Adrian Tolentino. This one is a number, Jared Allen. 51 out of 99. Very happy, he says. Kyle Kuzma. Lakers. That's part of the random number block. That is also non-numbered. So that'll be randomized with the Montrez-Harrell. And Bradley Beal for the Wizards. Also same random number block, also non-numbered. So now you got a third card in there for the random number block randomizer. And Nathan Knight for the Hawks. Have not seen a rookie card of him so far this year. Alfonso Mendoza. First Otto is Troy Brown Jr. for the Bulls Aurora autograph. Matt Daniels in the Bulls. That is 143 out of 149. And we've got Christian Leitner. Timberwolves edition lightning strike Otto. Timberwolves is random number block. That is 13 out of 99. Spot three is Anthony Liske. For a while he was the most hated man in basketball, right? Christian Leitner. Yeah, right, Ben? That was the most interesting press conference. He was just like, do you think somebody sat him down afterwards and tried to explain it to him? Or do you think they were just like, whatever. Devante Graham, Hornets, Sean Maddock. He's pretty special. That's 19 out of 50. And you got Russ, wizard's edition. That is 67 out of 99. Spot seven is Travis Melbourne. Dante DiVincenzo for the Bucks. That is Jess Buckheim. And Kristoff Porzingis for the Mavericks. Hugh Strother. And nice rookie Peyton Pritchard for the Celtics, Adrian Tolentino. Non-numbered. Well, very nice rookie there. And rookie Jersey Otto, another nice one. Tyrese Maxi. 76ers. Tyler Stumpf. That is 23 out of 49. Tyrese Maxi. And you've got Sam Mack. The return of the Mack. Houston Rockets. Icapola. That is 14 out of 75. Two more boxes, guys. Welcome to the city. We've got nine Chronicles draft picks we have. Sam Mack, Ben. Sam Mack. So we have a nice Jersey Otto on the back. It's got a little two colors and some yellow. So that should be out of 10. Julius Randall for the Knicks. David Bararino, 92 out of 99.  Brian Vornberg, nine out of 99. You got another rookie, Jayshon Tate. Rockets. Icapola. And Rayon Rondo. Clippers, Patrick Davis. Yeah, tunnel vision's great looking. You got Darius Garland, Cavs, Adrian Tolentino. Apparently I'm out of penny sleeves. Voice gun. Always supposed to be prepared. Troop master's gonna be disappointed with me. And Lakers. Montrez-Harrell, Lakers edition. Part of the Lakers, random number block. That is eight out of 99. Spot eight, Mark Rowell. Last spot in the movie. And it is a rookie. It's Cassius Winston for the Wizards. That's better than the two color patch. You got three colors on the bottom, two colors on top, rookie patch autos. Wizards, random number block. Out of 10, seven out of 10, Travis Melberg. There you go, Travis, congrats, man. Little dual patch auto Cassius Winston out of 10. Let's see the seven out of 10 right there. Congrats, man. And last box of the case and of the break. You got Chris Paul, Eclipse Relic for the Suns and Austin Crawford. That is 35 out of 99. CP3 there. And Victor Lodipo for the Heat. David Badarino. Five out of 25, one off the Jersey number. Devante Graham for the Hornets. Sean Maddock. And CJ McCollum for the Blazers. Brian Bornberg. And Yannis for the Bucks. Jess Buckheim. First auto for the last box is JJ Redick. Just retired, congrats JJ. Dallas Mavericks edition. Hugh Strother, that is three out of 25. J.J. Redick. And our last hit of the break is Lonnie Walker. Little Matrix, Jersey and autograph for the Spurs. I, Coppola. And that is 20 out of 49, Jersey and auto. Lonnie Walker. So there you go. We've got two randomizers to do. One is for the non-numbered cards in the Lakers and Wizards, random number block. There was no non-numbered cards in the Minnesota or Gold State Warrior random number block. So we gotta randomize that. So those are the three non-numbered cards for the Lakers, Warriors random number block and we need to do the randomizer for that over, for the break credit as well. So there's the random number block for participants for the Lakers, or sorry, Lakers Wizards. And now we gotta figure out how many people are in on the break credit randomizer as well. So we're gonna copy the list of customers over to another spreadsheet and alphabetize that for you. Remember, every two teams give you one entry. So Adrian, you've got one. Alfonzo with one. Austin, you've got one. Brian, thanks for getting in. And David, you've got two. Hugh, thanks for getting in. Icappola, you get one. Jess, you've got one. Matt, thanks for getting in. Oliver, you got one. Patrick, Patrick, thanks for getting in. And Roy, thanks for getting in. And Sean, you've got one. And Tyler, thanks for getting in. So top four out of 10 names. So we're gonna copy and paste that here. We use the same dice roll for both randomizers, guys. Good luck. So five and a three, eight times for both randomizers for you. Good luck. So first on the non-numbered cards for the Lakers Wizards. Eight and final time, there you go. So Mark on top, you've got it. Eight times on the randomizer. Eight times on the dice. Mark's gonna get all non-numbered cards for that random number lock. He actually had first and second spot. And Mark, you can see a little note on there saying you for the non-numbered spots with your last spot, mode, just spot. So pop back over here for the break credit portion of it. So eight times now on the list of people that had two or more teams. Eight and final time, top four, Sean, Patrick, Oliver, and Austin. All with $100 in break credit each. Eight times on the randomizer. Eight times on the dice. Sean, Patrick, Oliver, and Austin. Break credit $100 each. And there you go guys. That was 2020, 2021 Panini Obsidian basketball, six box, half case break, pick a team number four where we just give away $400 in break credit as well. I'm Sean, JasperCaseBricks.com. Thanks for hanging out. See you next time.