hello and welcome to lecture 10 where we'll be talking about digital baseband communication now this lecture used to be called pulse modulation but i renamed it digital baseband communication to make it explicitly clear what we're talking about so pulse modulation is a form of digital or mostly digital communication and we use the term baseband to distinguish it from band pass or wireless communication so this is our lecture today pulse modulation or digital baseband communication so last week we spoke about the process of digitization and that will allow us to talk about the remaining three lectures about digital communications base band band pass and multiplexing so when we say digital modulation that's code for band pass digital modulation or digital communication so we should now be familiar with the terms sampling and quantization this is old news to you we spoke about anti-aliasing filters and we spoke about quantization quantization error we also spoke about non-linear quantization and the idea of compounding today we're going to talk or we're going to start the journey of digital communications so we can have digital base band digital band pass and multiplexing so we've almost finished we've got three lectures to go today's lecture and two more now today's lecture isn't particularly long you can see it's 31 slides but it's really important we're going to be talking about pulse modulation as a form of baseband modulation so now we have our data it's been sampled and quantized it's encoded it's in digital form now that's assuming that it was originally in analog form it needed to be sampled quantized and encoded if it was originally in digital form then all all that's necessary is for it to be prepared for transmission now this transmission can either take place via cables so all these different types of cables that we've seen before or it could happen wirelessly okay so this is what we call baseband communication because generally there's no carrier and this is band pass communication it's wireless and there's generally a high frequency carrier so these are two very distinct types of communication you might think this is modern communication and this is old communication but that isn't the case each of these has their distinct areas of application their advantages their disadvantages their limitations and we're going to be looking at some of those today so we'll be talking about pulse modulation pulse code modulation line coding and we'll introduce the idea of channel capacity so a few questions for you have you ever wondered what we mean by the backbone of the internet what's the internet actually made of how do all the computers around the world communicate why are there so many cables in an internet data center so you've seen you must have seen images and videos of the microsoft and google data centers around the world why are there so many cables why isn't everything wireless by now why are there cables under the sea why isn't everything wireless via satellite plus what limits the speed of an internet connection how fast can a connection be and what in what what limits it is it the frequency is it the bandwidth is it the wavelength is it something else i have a couple of videos that i've um put together into one that i'll present for you the links to the original videos are available on the actual powerpoint but i invite you to watch this little video it's only a few minutes long but it's really useful there was a question about this in the um 2020 final exam okay i think it was worth 10 marks so it is something that i do take seriously and it's a short little video so i invite you to watch that we never stop hearing about how the internet's in the cloud but really it's in the ocean about 300 undersea fiber optic cables are responsible for 99 of international data traffic it's basically the same way we connect to each other in a single country except under water instead of underground they transmit pewdiepie from europe to america and they connect stock traders in new york and london and these cables placed by private companies are backbone of the internet but if you held one in your hand it'd be no bigger than a soda can there are just a few layers of protection from the water including petroleum jelly yes your internet is covered in vaseline they're vulnerable to earthquakes at least a few times confused sharks have bitten them but many cables are beneath sea life because in some places they go as deep underwater as mount everest is high ships lower a plow that digs a tiny groove in the ocean floor laying the cable and it's naturally buried by sand thanks to the ocean's current and that process it's both stunningly simple and mind-blowingly complex is responsible for making the internet a truly global network it's an idea that's audacious and crazy and you think it has to be cutting edge and it is today over 99 of all international internet traffic is routed through a network of over 420 submarine cables in service stretching over 700 000 miles around the world this is equivalent to wrapping a single cable over 28 times around the earth's equator this vast network of cables provides the underlying infrastructure to the internet's high bandwidth highways these cables use optical fiber to provide average data transmission rates of 35 terabits per second which is crazy because just over five years ago the average data rate was only nine terabits per second which equates to nearly a four times increase some of the newer and most cutting edge cables such as the maria cable which in spanish stands for high tide are even faster this cable which is owned and funded by microsoft and facebook connects virginia beach virginia in the united states to bilbao spain and is capable of data transmission rates of up to 160 terabits per second this is the equivalent of streaming 71 million hd videos at the same time and it is 16 million times faster than the average home internet connection the makeup and production of these cables is also extremely important submarine cables are typically thick in size with most being three to four inches in diameter while the actual wire the internet runs across is typically no thicker than a human hair this is because the majority of the cable's purpose is strictly for protection the process of laying the cable is equally as important as the production of the cable the laying of the cable is performed by a special trawlership that is capable of carrying giant spools of internet cables and unrealing them as it passes from shore to shore the first step to laying the cable requires an extensive survey to be performed at the sea floor to map the route for which the cable will be laid after being loaded onto a ship's hole in large spools the reels will be unwound as the ship travels along the mapped route a sea plow is towed along the back of the ship as well to aid in bearing the cable a few inches below the surface for added protection at the end of the installation process extensive testing and inspection of the cables performed before the cable is put into service now you may be wondering when this fast network of undersea cables began surprisingly enough the first undersea cable was laid over 177 years ago all the way back in 1842 when samuel morse the developer of morse code and commercial telegraphy decided to submerge a cable insulated with hemp and india rubber in the waters of new york harbor to run a telegraph through it after a successful experiment it wasn't long after this in 1858 when the first transatlantic telegraph cable was laid between the united states and great britain this connection with endpoints in newfoundland and ireland allowed communication between the transatlantic shipping companies to go from a matter of weeks to just a matter of minutes the demand for internet capacity is only set to increase as new consumers and industrial devices turn online over the next few decades most projections place half of the world's population as internet users by next year in 2020. historically bandwidth capacity connectivity and low latency have all been the drivers behind the construction of undersea cables by the year 2022 there are 35 new cables slated to be turned online in order to handle the increased traffic demands from some of the largest companies such as alphabet microsoft amazon facebook and apple all of which combined are responsible for nearly 70 percent of all internet traffic although there are opportunities for satellites to serve more disadvantaged areas of the world where physical links are not practical or possible undersea cables will continue to remain the backbone of the internet for decades to come so you might remember this slide from the previous lecture and i said we'll we'll be looking at it in more detail uh in today's lecture so you're familiar with this block here sampling where we have analog signal we have some analog message and it's sampled so you're familiar with that bit and then we quantize it the output of the quantizer will be digital information but we'll need to encode that into a series of ones and zeros but we still need to do something to that before it's ready to actually transmit as a waveform a baseband signal on the actual medium on the actual cable that is the process of pulse modulation so we call it baseband excuse me communication because there's no high frequency carrier so even though we call it modulation it's modulation between inverted commas because it isn't real modulation in the true sense of the word where we have a high frequency carrier so there's no carrier involved excuse me so once we have our analog signal and it's been digitized into a series of digital symbols and it's been encoded into ones and zeros getting these ones and zeros into a series of pulses that's what we call pulse modulation and there are different ways of doing this so we have the simplest way pulse amplitude modulation where the amplitude of the pulse is proportional to the amplitude of the data now i was going to say the digital data but it's possible to have and it's actually rather common for pulse amplitude modulation and indeed all of these modulation schemes well pulse amplitude and pulse width and pulse position these can all be analog okay they can be digital and they can be analog in today's lecture we're assuming everything is analog is digital because we're doing digital band pass community based band communication but it's possible that um the amplitude of your pulse is actually analog so it could happen after sampling but before quantization so if the amplitude of the pulse is proportional to your message or to your sample that's called pulse amplitude modulation pam and if the width of the pulse here is proportional to the amplitude of your sample then we call that pulse width modulation or the position of your pulse compared to the start of your period could be proportional to the amplitude so we have pulse width modulation and pulse position pulse position modulation but most common and most important for today's lecture is what we call pulse code modulation pcm this is what most digital communication consists of and this is what we're interested in where each sample each sample is broken down into n bits each sample is represented using n bits so that sample is that n bits this sample is the next set of n bits okay this is called pulse code modulation and it's what forms most data communication traffic on fiber optic cables so a simple sine wave as our analog example that's then sampled using a sampler and then quantized so together that's adc sampling and quantization that's digitization you sample at a rate of fs samples per second and you quantize into l levels or n bits and we can say l is 2 to the power n the number of levels is 2 to the power of the number of bits we then encode that and this digital data that's what we use for our pulse code modulation so how many bits are we generating per second well we mentioned this last week it's the product of the number of bits per sample and the number of samples per second so both the sample rate and the bit depth determine the data rate so let's call this the data rate this is how many bits we're generating per second so question if we had 16 levels so l is 16. the question is how many bits per sample are needed so how much is n so we know l is 2 to the power n that means n is log l to the base 2. so in this case it will be log 16 to the base two which is just four so we need four bits per sample every sample requires four bits so if we knew the sample rate we could just multiply that to find the data rate so we looked at this bit a second ago now putting this into the entire pcm system flowchart what we have before the sampler is your analog message we have a low pass filter why do we have a low pass filter this is to make sure that we have a band limited signal to band limit your original signal you can think of this as an anti-aliasing filter because it by band limiting our analog signal we're preventing the sampler from under sampling okay so we band limit our signal using a low-pass filter which is a form of anti-aliasing filter now after encoding we then launch our pulses onto the channel remember this is where the signal is most vulnerable to the effects of channel degradation so this is where noise distortion and interference happen there's also attenuation now all of this happens on the channel so what do we do to to avoid these effects there's something called a regenerative repeater and you might have seen pictures of these in the video i played so i'll show you in a second what that looks like but the regenerative repeater sort of recreates these pulses after they've been corrupted by noise they're recreated and transmitted on to our regeneration circuit ready for decoding reconstruction remember a sampler always has to have a reconstruction filter to recover the original message so you've got analog message at the input analog message at the output the sampler requires a reconstruction filter so we've got the transmitter at one end the receiver at the other end and the channel in between just like the block diagram we looked at in lecture one so this is the repeater i spoke about and it's a screenshot from the youtube video so this is your under c cable there and this thing here is a repeater so what does that do it takes your signal that's been attenuated and affected by interference noise and distortion and by setting a threshold and by sampling it can determine whether a point is below or above the threshold and then it can reconstruct a fresh signal so it's as if the noise has been removed but the noise hasn't actually been removed it's effectively been removed because we've recreated the signal so it's as if the signal is brand new and we did that just by um sampling and applying a threshold it's a good process but it's not perfect okay so these repeaters every 50 miles or maybe 80 kilometers along a cable they'll have one of these and the process of that or the purpose of that is to recreate or regenerate the signals so if you have the several of these along a cable you can minimize the effect of distortion noise degradation attenuation so we've spoken about pcm we've spoken about [Music] the data rate and sample rate but what we haven't spoken about yet is the bandwidth so if we're sampling at a particular sample rate and we have a particular bit depth if we multiply the two that gives us the bit rate okay or the data rate now if it's possible to squeeze two bits per second into every cycle per second so that's your bandwidth efficiency if we can get two bits per second into every hertz then the bandwidth of your pcm signal is half that data rate so your data rate divided by 2 is the minimum bandwidth for the pcm so if you've got a data rate of a hundred thousand bits per second you'll need at least half of that so 50 kilohertz of bandwidth okay that that's that's important and you'll see you'll see that in a minute so an example if we sample at 10 kilohertz so that's your sample rate and we have 16 levels in our quantizer so that's l the question is how many bits per second are needed so what's the data rate what's the bit rate so remember we said the data rate is simply fs times n so it's fs times log 2 l so here n is simply log 2 of 16 which is 4. so we simply multiply 10 times 4 40 kilohertz or 40 kilobits per second so the unit is bits per second so this is a true or false question we're given a signal with 16 levels and a signal with 32 levels and we're saying will the first require half the bandwidth of the second now remember we said the bandwidth or the minimum bandwidth is fs times n divided by 2. so they say assuming the same sample rate it means that the bandwidth is proportional to the bit depth so if you double the bit depth you'll double the bandwidth if you're half the bit depth you'll half the bandwidth so are we halving the bit rate here or the bit depth so if l equals 16 and is log 16 which is 4. but for 32 n is log 32 which is 5. now even though 16 is half 32 4 is not half of 5. so the bandwidth which is proportional to n will be a factor of four over five or five over four but not um half okay so this is false so the bandwidth for the 16 will probably be four-fifths of the bandwidth for 32 but not half almost the same question again this time we have 16 levels and 17 levels and it's asking will it be twice the bandwidth well remember we said the bandwidth is proportional to the bit depth now 17 levels n is log 2 of 17 but that's not going to give you an integer so what you need is the next highest integer which is going to be 5. and for the 16 you've got log 2 of 16 which is 4. so again it's not twice it's a factor of 5 over 4. so it's false so we've spoken about sampling quantization digital encoding pulse modulation pulse code modulation and we always spoke about pulses as if we knew what they looked like but now we're going to talk about something called line coding which is actually what the pulses actually look like how do we design the pulses what kind of pulses do we use for a one and for a zero now we could have a whole lecture about this i've chosen to summarize it into one slide and not to go into too much detail about that just so that we can focus on other things such as bandwidth and channel capacity and there are many many different line coding formats okay i will introduce you to a few and you can read up on many others in your own time so the simplest way of thinking of a one and a zero zero is going to have no voltage and one is going to have a high voltage whatever that high might be now notice we have something called unipolar and something called bipolar in a unipolar signal we have either a zero at zero volts or a one at some high level so there's only two levels whereas in a bipolar signal we have a high level positive and a low level negative and we have a zero level we also have something called return to zero and non-return to zero so we have rz return to zero and we have nrz non-return to zero and what that refers to is within the one bit period does the signal return to zero so here it's zero for a whole bit period and here it's one for a whole bit period one for a whole bit period and then zero for a whole bit period whereas in a return to zero scenario if it's unipolar you'll have zero for the duration of the bit period but for a one it's one for some fraction of the bit period let's say half the bit period and then it returns to zero for the remainder of the bit period again for the next one it's one and then it returns to zero for the next bit period or the next half of the bid period here we have a zero for the entire bid period and again we have a one then it returns to zero then we have a zero followed by a zero and then a one that returns to zero so that's what we mean by a return to zero and you can think of some of the advantages and disadvantages of these different line coding formats you can think which ones contain synchronization data within them which of these data formats is most wasteful of power okay you can think about where we would use return to zero and where we would use non-return to zero so these are some things for you to think about for you to read about but i won't go into too much detail about them what i will speak about is something called the bandwidth requirements something called bandwidth efficiency so a few minutes ago when we spoke about pulse code modulation we said i'll remind you i said if it's possible to squeeze two bits per second into every hertz or every cycle per second where is it here we said if it's possible to to fit two bits per second into every cycle per second that'll give us a minimum bandwidth for our pcm and i said this was something called bandwidth efficiency but now we understand what this means that in a non-return to zero scenario we can transmit two bits per level change that means two bits per second per hertz as opposed to a return to zero scenario where we can only transmit one bit per level change that means one bit per second per hertz so imagine a non-return to zero scenario where you have a one followed by a zero imagine you can imagine that one sine wave would be enough to encode that information whereas if we needed to return to zero within the one bit period the frequency of the sine wave you would need to represent that would be twice that so within every hertz within every one unit of bandwidth for non-return to zero we can represent two bits whereas for return to zero we can only encode one bit this is probably one of the hardest slides to actually understand and visualize so i encourage you to take some time to try to understand what that means so the number of bits per second per hertz is what we refer to as the bandwidth efficiency all you need to know is the difference between non-return to zero and return to zero for this module so we've almost finished a quick recap of the mathematical expressions so remember we said if we're quantizing using l levels then the number of bits is simply log l why do we use these brackets here this is called the ceiling function it means the next highest integer so if i were to if we had something like 3.1 that would give us 4. okay the next highest integer means so if n is 3.1 that means 3 isn't enough you would need the next highest integer which would be 4. so it's called the ceiling function so sample rate inversely proportional to the sample period the number of bits per second that's just another way of saying n fs okay but i've written it like this because sometimes this is what you'll have this is what what will be given to you and therefore the bandwidth of using a bandwidth efficiency of two for non-return to 0 we can find the minimum bandwidth for pcm is simply the product of this this divided by two so it's simply n fs over two and that's what we've already um looked at a few slides before and strictly speaking this bracket should look like that so it's the ceiling function rather than just square brackets okay we've almost finished final few things we need to talk about is how fast can we send data down a channel so when you have your cable your baseband communication channel how fast can you squeeze data down that channel you have this channel how fast can you squeeze data through it that's really important that's basically what almost all communications comes down to the question is always how fast can i communicate and how accurately can i communicate so what limits the rate at which one can communicate now there are several things which limit it but in general it's the slowest link we call that the communicate the bottleneck of our communication system if you've got two parties and they're communicating and there are several blocks there are several different components in this communication system you might have wired communication followed by wireless communication and then more wireless communication and then wired communication and wireless communication here you might have several links you might have an infrared link a bluetooth link a wireless link a satellite link and a cable link what determines the speed of the overall connection is the weakest link the slowest link that's what we call the bottleneck that's what's going to slow everything down okay so it doesn't matter if you've got 100 megabits per second here and 500 megabits per second here and 40 megabits per second here and 70 megabits per second here if you've got a three megabit per second connection here that will slow everything down it means everything will be working at 30 at three megabit okay so the bottleneck will determine the rate at which we communicate but there's something else which also determines how fast we can we can communicate or another way of putting it is this three where did that come from who decided that three well it turns out that is sometimes beyond our control that's called the channel capacity the channel capacity capacity is the maximum speed at which a channel can transmit data and that's determined by a couple of things and we spoke about this all the way back in our second lecture probably we introduced this idea of signal-to-noise ratio and i said the signal-to-noise ratio determines how fast we can communicate so this is something called the harley shannon law so the harley shannon law says that the rate at which we can communicate the theoretical channel capacity for a channel is corrupted by white additive gaussian noise is the product of the bandwidth b and the logarithm to the base two one plus the signal to noise ratio okay so the higher the bandwidth the higher the channel capacity the greater the signal to noise ratio the higher the channel capacity and as simple as that example let's say we wanted to transmit at that rate and we had a channel that allowed a channel a signal-to-noise ratio of 70 decibels and the question is what bandwidth is needed so what value of b will allow us to communicate at this rate so you want to transmit it 2.3 megabits per second well that's your channel capacity we want to find b so we need to find the signal-to-noise ratio so if we know that the signal-to-noise ratio is 70 db then we need to actually find the ratio as a ratio ie without units so when calculating decibels it's almost always 20 log 10 except when we're dealing with power in which case it's 10 log s over n so s over n to 70 decibels is 10 to the power 7 10 million so we've got this expression here rearrange and you can find the bandwidth of 100 kilohertz so you might have initially guessed well if we needed to 2.3 megabits per second we would need a bandwidth of 2.3 megahertz but no it's not that easy it's not that straightforward it depends on the signal to noise ratio if you have a good signal to noise ratio like 70 decibels then 100 kilohertz is enough to support 2.3 megabits per second a few things to watch out for we use log to the base 10 when converting to um and from decibels but in the shannon harley law we always use log2 okay so just make sure you don't confuse those there's a couple more examples but to keep the lecture short i will not go through this example these examples are solved um in the pencast section i.e in the problem sheet okay the answer is right here but how to get from these numbers to that is really straightforward and i go through it in the pencast section there's one final example many of you won't even remember what a fax machine even looks like but it's a good example nevertheless of how using a fairly noisy telephone line with a very limited bandwidth what determines how fast these these pages actually come out of the fax machine so it all comes down to this thing called channel capacity so that's it for today's lecture we've introduced um baseband digital communications as a form of pulse modulation or should i say pulse modulation as a form of digital baseband communication we mentioned different pulse formats we focused our attention on pulse code modulation we spoke about different line coding formats and we introduced the idea of channel capacity we also spent some time talking about the internet backbone and why baseband communication and cable communication is so important and it all comes down to this idea of channel capacity and the idea of bottlenecks okay so lots of things to think about next week we will look at the other type of digital communication and that's band pass modulation by bandpass ie we're talking about carrier modulation ie we're talking about wireless modulation and really it's very similar to what we've already spoken about so it's am and fm and pm once again except this time for digital signals okay i hope you found that helpful so we've almost finished we've literally got two lectures to go the last lecture is just a mini lecture it's like half a lecture and our digital modulation really is our last substantial lecture so make sure you're ready for the class test on the 12th of may i hope you found that helpful until we meet again stay home and stay safe