hello and welcome to lecture 11 where we'll talk about digital modulation or digital band pass modulation so this is essentially the equivalent of lectures two to two to six but now we're talking about digital versions so digital am and digital fm and digital pm so last lecture we spoke about digitization sampling and quantization we um spoke about the nyquist rate again we introduced different types of pulse modulation we spoke briefly about pulse modulation about line coding we introduced pulse code modulation and we spent some time talking about channel capacity and the shannon hartley theorem today we're going to be looking at digital modulation so i use the word band pass to distinguish it from um baseband so in lecture 10 we looked at pulse modulation which was baseband now we're looking at band pass modulation so this is where we actually have a carrier so this is generally going to be wireless communication okay so we're going to talk about modulation demodulation and a little bit about the frequency domain representation we'll then look a little bit at versions of amplitude modulation frequency modulation and phase modulation where we have multiple levels we refer to this as m3 and this will lead us nicely to our final lecture where we'll talk about multiplexing so where are we we are right here lecture 11. there's one lecture to go and after that we have our class test on the 12th of may a few things to say about that class test it's worth 15 percent of your module you know that it's scheduled at 10 a.m on the 12th of may if you can't make it for that time if you're unable to access the test at that time if you know that in advance let me know okay if you can't make it for this time let me know okay you may be entitled um to claim extenuating circumstances you need to make that known to myself and to the office ahead of time okay there's no point telling me after the exam or after the test now another thing to note is that it's a two-hour test okay it's not just a one-hour test it's a two-hour test um there are a total of 15 questions and there are two parts to the test there's a part a and a part b part a looks like what you've seen before so it's sort of a canvas test with numerical and multiple choice um submissions or solutions so multiple choice and numerical so it's similar to the kind of test you had um back in in march so similar to test one but there's also a part b now for part b there are handwritten solutions okay so here i will expect you to either plot a sketch or to write an expression or to explain something okay so this is a different format something you're not um you're not you're not accustomed to and it won't be using your your familiar format on canvas so for that i've put together a little demo and you know the i expect you to spend some time um uh trying this demo out okay just to see if your computer can support it and if you're able to interact with these different styles of questions okay so you have two hours in total so one hour for each part so one hour for part a and one hour for part b the way it's structured is that the exam the test starts at 10 am you have an 11 am deadline for completing part a and a 12 p.m deadline for completing part b okay so if you finish part a early that will give you more time for part b but you shouldn't need an hour part b is only five questions and you shouldn't need an hour so two hours should be plenty if you have a support plan then you will have extra time for part a only okay part b the time is the same for everyone so back to lecture 11. so now we've digitized our data now we have data that's been sampled quantized and encoded we want to transmit it we've already looked at baseband transmission so baseband transmission is where you have a cable and you're trying to transmit along a cable and we've we've looked at that and we've spoken about data centers undersea cable fiber optic cables pcm regenerative repeaters and all that now we're going to look at band pass modulation so band pass modulation this is where you have a radio wave carrier so wireless okay so when i say radio wave i include microwave okay so we're now talking about wireless communication now there's i i've put together a short little short little video from a from a youtube clip online the link to the original clip is in my powerpoint on canvas i suggest you watch that if you want the whole the whole video clip but i've put together a a few minutes just to set uh the scene give you some context and introduce you to what we'll be talking about for the rest of this lecture so let's discuss the digital modulation techniques that are currently used more specifically let's see how the digital bit flow is converted to an electromagnetic wave the first digital technique is amplitude shift keying here based on the digital pulses the amplitude of the carrier signal is adjusted high amplitude relates to one and low amplitude relates to zero the next technique is called frequency shift keying here based on the value of digital pulses the frequency of the carrier signal is adjusted in this case high frequency relates to one and low frequency relates to zero the third technique is phase shift keying here the phase of the carrier signal is changed by 180 degrees when the digital pulse moves from one to zero or zero to one telecommunications technology is all about increasing data transfer speed and efficiency but if you use any of the digital modulation techniques explained previously you wouldn't get a high data transfer speed however there is a technique in physics which if you use it means you can practically send up to six bits of information as a single electromagnetic wave this technique is known as quadrature amplitude modulation in the case of digital qam a similar approach is used here instead of analog signals different combinations of bits are added together to produce a multiplexed signal let's see how a 16 qam works if you are familiar with digital technology you know that any form of data is just a collection of ones and zeros in 16 qam we can pack four bits together and send it as a single electromagnetic wave based on the values of the four bits this output will have different phase angles and amplitude this means the phase angle and amplitude of the multiplexed signal can completely represent four bits of data in 16 qam such 16-bit values can be represented by adjusting the phase and amplitude of the multiplexed signal and this single multiplexed signal is then used for the transmission you can see how the different amplitude and phase electromagnetic signals represent various four bits of data so you see when we have digital modulation essentially we're doing the same as we did with analog modulation we take a carrier at the transmitter and then we superimpose upon that high frequency carrier our message and our message happens to be digital so we modulate the carrier with our digital information so this information just happens to be digital and at the receiver we reverse that and we demodulate so really all we're trying to do is modify so you've seen this diagram before we're trying to modify or change some characteristic of our signal so what are the characteristics that we can change well there are only three things we can change we can either change the amplitude or the frequency or the phase of our carrier we can try um doing combinations of those we can change the amp frequency and phase we can change the frequency and the amplitude but most commonly what we do is we change the amplitude and phase so that's the amplitude and phase so the rest of this lecture is really just about how we do it and what we call it so the three things we do are amplitude modulation frequency modulation and phase modulation and we add these words we say it's amplitude shift keying frequency shift keying and phase shift keying and you you'll see why in a second so you have your data this is after sampling quantization and encoding you have your data for example one zero one and you superimpose that on your high frequency carrier so this is a an illustrative example it's a bit exaggerated the frequency isn't that high so here you can see that when you have a zero you have nothing but when you have a one you have a burst of high frequency carrier that's amplitude modulation basically so that's amplitude shift keying in frequency shift keying you have a high frequency when you have a one and a lower frequency when you have a zero and in frequency in phase shift keying you have a phase change so you have one phase for a one and the opposite phase for a zero so you end up with these phase changes so that's a little summary and now for a little bit more detail so when we say amplitude shift keying i've added another word here binary so binary amplitude shift keying is where we only have two levels a one and a zero because you know in digital data doesn't have to be a series of ones and zeros but if we're only looking at one and zero if we have binary then we're only going to have two levels and if we use those two levels and we simply multiply our high frequency carrier by a suitable lining coded signal so this signal is after line encoding then you end up with a signal here where again your data is encoded within the envelope of the product so this looks very much like dsb okay so it's just am it's amplitude modulation but digital but because we have nothing we have zero whenever there's a zero being transmitted and we have a burst of carrier when there's a one so it means we have carrier no carrier carrier no carry that is if our data just happens to look like that so we also refer to this as on off keying because it's on then off on then off now obviously if we had a different data stream like one one one one zero one zero one one this would vary accordingly but it still turns on and off depending on whether the digital data is one or a zero so we call that on off keying so that's your ask or binary amplitude shift keying now for frequency shift keying again we're looking at binary frequency shift keying so that's where we have two levels here the information isn't encoded in the amplitude it's encoded in the frequency so we have a low frequency high frequency low frequency high frequency so the in this case the low frequency corresponds to a 1 and the high frequency corresponds to zero one zero one zero so it looks a little bit like ask or it looks like the combination of two asks and we'll look at why and how that is in a few minutes so that was frequency shift keying or binary frequency shift keying for phase shift keying again we're looking at phase shift keying for two levels here what we have is depending on whether we have a one or a zero we either have one phase or the opposite phase so we have a 180 degree or pi radians shift in phase every time we have a change from one to zero okay so we have a two phases either 0 degrees or 180 degrees or pi radians so this is one way of doing phase shift keying there are variants that you need to know of we have something called differentially coded psk so instead of bpsk or just psk we have something called dpsk differentially coherent psk and here what we're encoding is the phase change so whenever we have a one in the digital data stream that translates into a phase change so the change the phase shifts every time there is a one when there is a zero then there is no change in phase so here we can tell whether our data stream contained ones or zeros based on whether we detect changes in phase or not so this is called dpsk so we're not encoding the data in the phase we're encoding it in the phase changes so a quick comparison based on what we've seen already ask is simple in terms of modulation and demodulation low bandwidth i'll show you why in a separate second and it's susceptible to interference for the same reasons that um amplitude modulation or analog amplitude modulation was also susceptible to interference and to noise so frequency shift keying requires a larger bandwidth you can probably imagine why again fm also required greater bandwidth than am but we'll look at the reasons why in a minute and frequency shift keying as you can imagine is more complex at both ends meaning at the transmitting and the receiving ends but it is more robust against interference and um [Music] also has a a lower bit error rate so let's look at how we actually modulate so when we talk about generation we're talking about modulation so remember when we spoke about analog modulation we introduced the properties we looked at power we looked at modulation demodulation and spectral requirements but we're going to do all of that in half an hour for digital modulation so have you seen a diagram like that before well it looks a lot like a dsb modulator okay it's almost exactly like a dsb modulator so what you have is a local carrier that's your local oscillator that's generating your high frequency signal and that's multiplied by your um line coded digital data and that gives you your ask signal it really couldn't be simpler than that now if we're going to look at the bandwidth requirements or the frequency domain version of this what you have here is the product of a rectangular wave multiplied by a high frequency carrier and in the frequency domain that's like a convolution between a pair of impulses and a sink function so this convolution of a sink function with a pair of impulses gives you a spectrum that looks like this so you've got your sync function centered at fc and you'll have another one centered at minus fc and i think it's useful to note that this is your bandwidth so your ask bandwidth will be similar to your bit rate okay so it'll be in be in the order of n times the sampling rate okay so for every bit per second you're going to need one hertz of bandwidth so this bandwidth is in the order of approximately your bit rate nfs now you can imagine if we had to demodulate this so they're talking about detection so this is demodulation so at the other end and again we're looking at non-coherent where have we seen that word before so non-coherent detection that means we're not using a local oscillator remember we spoke about envelope detection so this is a version of envelope detection for a um for a digital am signal so we're simply using a diode rectifier but we also need some kind of comparator in order to convert this output of the filter to our digital data because in the end this is what we're after we're after the digital data from where from where this originally came from why doesn't this look nice and clean like we agreed that ask should look like what why is it why does it look so strange well remember this is after the signal has traveled through the channel so we have a wireless propagation channel and then the signal will arrive here so it will have suffered from the effects of noise distortion attenuation interference etc then it goes into your recovery circuit and then we try to recover our original data is this perfect is this data um exactly the same as our original digital data it might be but often it isn't it's corrupted by errors these errors result in something called a bit error rate and we'll we'll speak a little bit about the bit error rate next lecture so that was non-coherent detection similar to an envelope detector now we're going to talk about coherent detection remember coherent detection is where we have a locally generated carrier so this is also known as synchronous detection or synchronous demodulation okay so where have we seen this before we saw this the dsb suppressed carrier and what does it consist of well it consists of a local carrier multiplier and a low pass filter the only thing we've added here is this comparator why have we done that it's so that we can have our crisp data our digital data recovered so there's some kind of sampling and thresholding going on that's what our comparator does to produce our digital data so it looks almost exactly like a dsp demodulator we just add that comparator now that was ask fsk is almost exactly the same you can imagine that our fsk signal is simply the sum of two ask signals so if you have a digital bit stream that looks like this 0 1 0 1 0 then if you take your zeros or your your ones let's let's let's start with the ones if you take your ones and you use an ask modulator using a a frequency let's call it f1 then that will give you this bit of your signal and if you use a different frequency f2 to generate another ask signal but this time you're generating it from the inverse of these so you need to take um you need to take this data stream and invert it in order to generate this so whenever there's a one here there'll be a zero here and whenever there's a zero here there's a one here a one here would be a zero there okay so these two one represents the data and one represents um not the data then they're added together and you end up with this composite signal now this is your fsk signal now in practice we don't generate our fsk that way but you can imagine that our fsk is simply two ask signals added together with this important not gate the reason i'm suggesting you look at it this way be is because it helps you to visualize how we demodulate fsk so this is generation of fsk in practice this is often done using a switch if we did have a switch we'd have two frequencies f1 and f2 here's omega one and omega two we would have these um phase discontinuities because of the switching in practice what we actually have is a voltage controlled oscillator so that rather than switching between two discrete frequencies what we have is an oscillator that will change its frequency depending on the amplitude of the input and here we have a better version of this without the discontinuities so you can imagine that this is how as fsk is generated in practice is generated like that which is just a better way of doing that now again what we always do is look at generation and detection detection is just another way of saying demodulation and again we're looking at non-coherent so we're looking at asynchronous so no carrier at the receiver so here you have your fsk signal and here we have two filters what kind of filters are these these are band pass filters and they're tuned to f1 and f2 so one will be tuned to this frequency and one will be tuned to that frequency what do you think these are that just looks like a rectifier followed by a low pass filter or a smoothing circuit so it's basically a a envelope detector so you can think of it as two ask detectors and then we have a comparator to check is the output greater at this end or this end so we know whether we had a one or a zero okay so if we imagine fsk as being a composite signal formed by two ask signals then you can imagine the detection of fm can happen simply by detecting two streams of ask after filtering using two frequencies so these would be the carrier frequencies used for the ones and the zeros the psk is slightly less easy but generation of psk so this is a psk modulator what does this look like it looks very much like a dsb modulator so simply multiplying our input signal our message digital line encoded in this case with our high frequency carrier and that will give us that it looks a bit like a s k but it's not on off keying so you've got something for a one and something for a zero the the difference so rather than having nothing for a zero it's because here rather than having a signal that looks like this where you have zero this time you don't have zero you have a a positive or a negative so the positive gives you one phase the negative gives you another phase so you end up with this 180 degree or pi radian phase and the zero degree phase depending on whether you have a one or a zero being transmitted so you have these phase shifts so that's psk now whether it's dpsk or bpsk there can be different variations on this signal on this block diagram and how this exactly represents or how it relates to our data so the trick was to use a bipolar digital message so that you don't have zeros so what we always want to do remember in our very first lecture we said one of the characteristics or the desirable characteristics of a communication system is that we have a high data throughput that's another way of saying fast data transmission we want to transmit a lot of data in a short amount of time so to maximize data throughput what we want to do is to transmit as much information in as short a time as possible so that often means we want to transmit more than one bit at a time so is it possible to transmit two bits or more using the same portion of carrier so thinking about ask we spoke about bpsk where we have two levels what if we had four levels then we'd have four ask so instead of saying bpsk where b represents binary we would say sorry instead of saying b a s k where the b represents binary we would have four ask or four level ask so four levels will require two bits so two bits per digital symbol so our symbol will consist off two bits so two bits could be zero zero it could be zero one could be one zero it could be one one so these this is our alphabet of four possible symbols one two three four different symbols so four different levels so that's one level that's another level that's another level and that's another level that's these are our four levels so rather than have on off keying where you have a burst of carrier for a one and no carrier for a zero this time it looks a little bit closer to am doesn't it it looks like a dsb with a large carrier so it looks like we have the message encoded in the envelope so it looks like am the spectrum is probably going to look like am we're going to have a carrier component probably going to have side bands an upper side band and a lower sideband but the advantage is that now we can transmit data twice as fast we can do something similar with um phase as well so we're able to encode two bits using qpsk so depending on what our symbol is again same symbol zero zero zero one one zero one one so we have an alphabet of four symbols just like we had our four symbols here and the result is the same we have twice the symbol rate so the baud rate is just another way of saying the symbol rate and the data rate is twice the baud rate so we have twice as many bits per second as we have symbols per second what we can also do is combine amplitude and phase into something called or quadrature amplitude modulation now this is a really useful way to increase the data throughput or the data rate even further because we use eight different phases not just four and two different amplitudes if you multiply the two that gives you sixteen different symbols so four bits so we have zero zero zero zero zero zero zero one all the way to one one one one so four bits sixteen symbols where do we use this well it's used in mobile communications it's used in broadband it's used in some types of satellite communications we'll look at that in a minute but it comes with a big advantage and a disadvantage so it comes at the cost of an increased error rate but it allows you to transmit um [Music] four times more data [Music] per second compared to binary versions of amplitude modulation or phase modulation so you need to know some of the applications of these so where do we use ask ask is used for infrared modulation so things like television remotes okay so relatively low frequencies fsk used to be used so for dial-up internet so you might remember might have seen on tv old internet connections where we use telephone lines so the kind of modulation we used because the telephone lines weren't designed for internet they weren't designed for high-speed data they were intended for voice communication so they had to be adapted um for use for dial-up internet so we used something called audio fsk nowadays fsk you'll only come across it in things like caller id on your wired landline or it's part of bluetooth so bluetooth isn't fsk but fsk is involved in bluetooth communications psk is much more common so if you if you ever used wi-fi or enhanced gsm then psk is a big part of that now qualm is um so quadrature amplitude modulation what we spoke about before and qpsk that is involved in gps mobile satellite comms um etc so um a lot of 4g and parts of 5g involve qpsk and qualm so that brings us to the end of today's lecture so we've spoken about different types of amplitude frequency and phase modulation [Music] so digital band pass modulation we spoke about how it's generated how it's detected and a little bit about what they look like in the frequency domain we spoke about emory ask psk qpsk and qualm and we'll look at multiple access and multiplexing in our next and final lecture so just as a reminder we are now here that was lecture 11. lecture 12 is our final lecture and the test is on the 12th of may so i hope you found that helpful wherever you are whatever you're doing make sure you stay safe