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Dialogue: 0,0:00:00.60,0:00:04.10,Default,,0000,0000,0000,,Hi, and welcome to module nine of digital \Nsignal processing.
Dialogue: 0,0:00:04.10,0:00:06.77,Default,,0000,0000,0000,,This is the last module in our class, and \Nthis is really where it all comes
Dialogue: 0,0:00:06.77,0:00:09.69,Default,,0000,0000,0000,,together. \NIn this module we will review the
Dialogue: 0,0:00:09.69,0:00:14.14,Default,,0000,0000,0000,,principles behind the success of digital \Ncommunication systems.
Dialogue: 0,0:00:14.14,0:00:17.56,Default,,0000,0000,0000,,And we will look at different \Ncommunication systems starting from the
Dialogue: 0,0:00:17.56,0:00:21.27,Default,,0000,0000,0000,,voice band modems that were popular a few \Nyears ago and that you can still hear
Dialogue: 0,0:00:21.27,0:00:24.93,Default,,0000,0000,0000,,when you use a fax machine, to the most \Nrecent incarnations like the ADSL box
Dialogue: 0,0:00:24.93,0:00:28.29,Default,,0000,0000,0000,,that you have in your home and that \Nyou're probably using to watch this
Dialogue: 0,0:00:28.29,0:00:34.71,Default,,0000,0000,0000,,video. \NDigital communication systems need no
Dialogue: 0,0:00:34.71,0:00:37.71,Default,,0000,0000,0000,,introduction. \NThe amount of information that we consume
Dialogue: 0,0:00:37.71,0:00:42.90,Default,,0000,0000,0000,,and that we produce every day is \Nstaggering by an historical standard.
Dialogue: 0,0:00:42.90,0:00:45.48,Default,,0000,0000,0000,,And what is even more amazing is that we \Ncan access this wealth of information
Dialogue: 0,0:00:45.48,0:00:49.14,Default,,0000,0000,0000,,from basically anyway via a small device, \Nlike the smartphoen that you have in your
Dialogue: 0,0:00:49.14,0:00:52.94,Default,,0000,0000,0000,,pocket. \NThere is actually a joke about that and
Dialogue: 0,0:00:52.94,0:00:55.70,Default,,0000,0000,0000,,suppose that someone from the \NRenaissance, like Leonardo, was
Dialogue: 0,0:00:55.70,0:00:59.67,Default,,0000,0000,0000,,teleported to today. \NAnd you'd have to explain to them what
Dialogue: 0,0:00:59.67,0:01:02.99,Default,,0000,0000,0000,,your smartphone does. \NWell you have to say this is a small
Dialogue: 0,0:01:02.99,0:01:06.47,Default,,0000,0000,0000,,device that allows me to access \Neverything that has been done, written
Dialogue: 0,0:01:06.47,0:01:11.40,Default,,0000,0000,0000,,about, or were said by mankind since the \Nbeginning of history.
Dialogue: 0,0:01:11.40,0:01:14.12,Default,,0000,0000,0000,,And I use it mainly to look at pictures \Nof cats.
Dialogue: 0,0:01:14.12,0:01:16.93,Default,,0000,0000,0000,,But jokes aside the truth remains that \Ncommunications systems, digital
Dialogue: 0,0:01:16.93,0:01:20.44,Default,,0000,0000,0000,,communications systems. \NAre really the pinnacle achievment of
Dialogue: 0,0:01:20.44,0:01:23.98,Default,,0000,0000,0000,,digital signal processing. \NSo in this module we'll start from the
Dialogue: 0,0:01:23.98,0:01:27.82,Default,,0000,0000,0000,,basic principles in module nine one and \Nwe'll see the kind of signals that we
Dialogue: 0,0:01:27.82,0:01:34.52,Default,,0000,0000,0000,,have to design in order to be able to \Ntransmit them over a physical channel.
Dialogue: 0,0:01:34.52,0:01:38.55,Default,,0000,0000,0000,,Now a physical channel whether it's a \Nwireless channel, whether it's a piece of
Dialogue: 0,0:01:38.55,0:01:42.57,Default,,0000,0000,0000,,wire or an optical fiber will always \Nimpose two fundamental constraints on the
Dialogue: 0,0:01:42.57,0:01:47.31,Default,,0000,0000,0000,,kind of signal that can transit over the \Nchannel.
Dialogue: 0,0:01:47.31,0:01:50.46,Default,,0000,0000,0000,,The first one is a bandwidth constraint, \Nwhich means that we will only have a
Dialogue: 0,0:01:50.46,0:01:55.33,Default,,0000,0000,0000,,certain range of frequencies over which \Nwe can send information.
Dialogue: 0,0:01:55.33,0:01:57.92,Default,,0000,0000,0000,,And the second constraint is a power \Nconstraint.
Dialogue: 0,0:01:57.92,0:02:01.64,Default,,0000,0000,0000,,It limits the amount of power that we can \Ninject onto the channel.
Dialogue: 0,0:02:01.64,0:02:05.64,Default,,0000,0000,0000,,So in module 9.2, we will tackle the \Nbanther constraint, in detail.
Dialogue: 0,0:02:05.64,0:02:08.72,Default,,0000,0000,0000,,And in module 9.3, we will look at the \Npower constraint.
Dialogue: 0,0:02:08.72,0:02:11.97,Default,,0000,0000,0000,,And we will see in the end how these two \Nconstraints limit the maximum amount of
Dialogue: 0,0:02:11.97,0:02:15.79,Default,,0000,0000,0000,,information that we can send over a \Nchannel.
Dialogue: 0,0:02:16.32,0:02:19.79,Default,,0000,0000,0000,,In Module 9.4, we will look at the \Nmodulation and demodulation techniques
Dialogue: 0,0:02:19.79,0:02:24.64,Default,,0000,0000,0000,,that are specially designed to transmit \Ndata over the telephone channel.
Dialogue: 0,0:02:24.64,0:02:28.20,Default,,0000,0000,0000,,And in Module 9.5, we will examine the \Nseveral signal processes and tricks that
Dialogue: 0,0:02:28.20,0:02:31.39,Default,,0000,0000,0000,,are put in place to implement a receiver, \Nwhich turns out to be much more
Dialogue: 0,0:02:31.39,0:02:35.62,Default,,0000,0000,0000,,complicated than the transmitter, because \Nthe receiver has to undo all the nasty
Dialogue: 0,0:02:35.62,0:02:40.75,Default,,0000,0000,0000,,things that happen to the signal. \NWhen it travels over the channel,
Dialogue: 0,0:02:40.75,0:02:44.67,Default,,0000,0000,0000,,including distortion and noise and so on. \NAs a matter of fact, module 9.5 is like a
Dialogue: 0,0:02:44.67,0:02:48.37,Default,,0000,0000,0000,,teaser that will probably whet your \Nappetite for more advanced signal
Dialogue: 0,0:02:48.37,0:02:54.56,Default,,0000,0000,0000,,processing techniques that you will be \Nable to study in more advanced classes.
Dialogue: 0,0:02:54.56,0:02:59.20,Default,,0000,0000,0000,,And finally in module 9.6, we will study \Nthe ADSL protocol.
Dialogue: 0,0:02:59.20,0:03:03.17,Default,,0000,0000,0000,,Now it turns out that ADSL is just one \Nbig DFT.
Dialogue: 0,0:03:03.17,0:03:06.87,Default,,0000,0000,0000,,And so, the fact that we can implement it \Nefficiently with the FFT algorithm, is
Dialogue: 0,0:03:06.87,0:03:10.23,Default,,0000,0000,0000,,really the reason behind the \Nextraordinary commercial success, of the
Dialogue: 0,0:03:10.23,0:03:15.32,Default,,0000,0000,0000,,ADSL setup box. \NYou will see that everything that we've
Dialogue: 0,0:03:15.32,0:03:18.18,Default,,0000,0000,0000,,studied so far really find it's place in \Nthe design of a sophisticated digital
Dialogue: 0,0:03:18.18,0:03:22.31,Default,,0000,0000,0000,,processing system. \NSo we hope you have enjoyed this initial
Dialogue: 0,0:03:22.31,0:03:26.86,Default,,0000,0000,0000,,ride into the world of digital signal \Nprocessing and hopefully we'll see each
Dialogue: 0,0:03:26.86,0:03:32.60,Default,,0000,0000,0000,,other again in more advanced classes in \Nthe future.
Dialogue: 0,0:03:32.60,0:03:36.75,Default,,0000,0000,0000,,Thank you. \NHi and welcome to module 9.1 of Digital
Dialogue: 0,0:03:36.75,0:03:39.96,Default,,0000,0000,0000,,Signal Processing. \NIn this module we will start to look at
Dialogue: 0,0:03:39.96,0:03:44.17,Default,,0000,0000,0000,,digital communication systems. \NIn particular, we will look at the many
Dialogue: 0,0:03:44.17,0:03:49.52,Default,,0000,0000,0000,,incarnations that a signal will undergo \Nfrom its source to its destination.
Dialogue: 0,0:03:49.52,0:03:51.83,Default,,0000,0000,0000,,This incarnations will travel through a \Nvariety.
Dialogue: 0,0:03:51.83,0:03:54.86,Default,,0000,0000,0000,,of different analog channel. \NAnd each channel will have a different
Dialogue: 0,0:03:54.86,0:03:58.54,Default,,0000,0000,0000,,set of constraints that the signal will \Nhave to submit itself to.
Dialogue: 0,0:03:58.54,0:04:02.13,Default,,0000,0000,0000,,And in this module we'll start to look \Nhow to design signals that fulfill the
Dialogue: 0,0:04:02.13,0:04:05.90,Default,,0000,0000,0000,,channel constraints. \NIf you remember in the beginning of this
Dialogue: 0,0:04:05.90,0:04:09.17,Default,,0000,0000,0000,,class we gave you a little overview of \Nthe major improvements and through put
Dialogue: 0,0:04:09.17,0:04:12.66,Default,,0000,0000,0000,,for channels that we implicitly use every \Nday.
Dialogue: 0,0:04:12.66,0:04:17.42,Default,,0000,0000,0000,,For instance, the transatlantic cables \Nthat allow telephoning from Europe to the
Dialogue: 0,0:04:17.42,0:04:21.84,Default,,0000,0000,0000,,Unites States have seen an improvement \NThat went from five bits per second in
Dialogue: 0,0:04:21.84,0:04:28.52,Default,,0000,0000,0000,,1866 with the first cable to 60 terabytes \Nper second last year.
Dialogue: 0,0:04:28.52,0:04:32.47,Default,,0000,0000,0000,,Similarly something you use every day at \Nhome, your modem that allows you to
Dialogue: 0,0:04:32.47,0:04:36.90,Default,,0000,0000,0000,,connect to the internet, has increased \Nits data rate from 1,200 bits per second
Dialogue: 0,0:04:36.90,0:04:44.30,Default,,0000,0000,0000,,in the 50s to 24 megabits per second with \Nthe current incarnation of ADSL.
Dialogue: 0,0:04:44.30,0:04:47.34,Default,,0000,0000,0000,,Now what are the reasons behind this \Nincredible success?
Dialogue: 0,0:04:47.34,0:04:51.37,Default,,0000,0000,0000,,Well, the first one clearly is the power \Nof the DSP paradigm.
Dialogue: 0,0:04:51.37,0:04:55.33,Default,,0000,0000,0000,,The fact that DSP works with integers \Nmeans that, for instance signals are very
Dialogue: 0,0:04:55.33,0:04:58.35,Default,,0000,0000,0000,,easy to regenerate. \NWe have seen an example in the
Dialogue: 0,0:04:58.35,0:05:00.85,Default,,0000,0000,0000,,introduction, and we will see it again in \Na second.
Dialogue: 0,0:05:00.85,0:05:04.44,Default,,0000,0000,0000,,Also digital filters allow us to \Nimplement very precise phase control, and
Dialogue: 0,0:05:04.44,0:05:10.32,Default,,0000,0000,0000,,we will see how important phase is in the \Ndetection of a transmitted signal.
Dialogue: 0,0:05:10.32,0:05:16.28,Default,,0000,0000,0000,,And finally, we can seamlessly integrate \Nadaptive algorithms into a DSP system.
Dialogue: 0,0:05:16.28,0:05:22.19,Default,,0000,0000,0000,,Adaptive algorithms are algorithmic \Nprocedures that adapt their behavior.
Dialogue: 0,0:05:22.19,0:05:25.45,Default,,0000,0000,0000,,As a function of the received signal. \NThese are very hard things to do in
Dialogue: 0,0:05:25.45,0:05:28.95,Default,,0000,0000,0000,,analog hardware, but very easy to do in \Ndigital hardware.
Dialogue: 0,0:05:28.95,0:05:32.74,Default,,0000,0000,0000,,As a reminder of what happens when we use \Ndigital signals for communication, think
Dialogue: 0,0:05:32.74,0:05:38.00,Default,,0000,0000,0000,,of the problem of transmitting a string \Nof binary digits over an analog channel.
Dialogue: 0,0:05:38.00,0:05:41.75,Default,,0000,0000,0000,,To do that, we build a very simple \Nsignal, an analog signal, where we
Dialogue: 0,0:05:41.75,0:05:46.38,Default,,0000,0000,0000,,associate the values plus 5 volts to the \Nsymbol 0.
Dialogue: 0,0:05:46.38,0:05:50.47,Default,,0000,0000,0000,,And minus 5 volts to symbol one. \NNow the signal is analog, but it encodes
Dialogue: 0,0:05:50.47,0:05:54.83,Default,,0000,0000,0000,,binary information, namely it encodes a \Nstring of integers.
Dialogue: 0,0:05:54.83,0:05:59.23,Default,,0000,0000,0000,,When we transmit this over wire, two \Nthings happen.
Dialogue: 0,0:05:59.23,0:06:03.64,Default,,0000,0000,0000,,The signal gets attenuated and noise gets \Nadded to the signal.
Dialogue: 0,0:06:03.64,0:06:07.92,Default,,0000,0000,0000,,So what we'll receive at the other end of \Nthe channel is The original signal
Dialogue: 0,0:06:07.92,0:06:12.61,Default,,0000,0000,0000,,attenuated by effect of G, summed to some \Nrandom noise that corrupts the original
Dialogue: 0,0:06:12.61,0:06:17.36,Default,,0000,0000,0000,,signal. \NNow, if we want to regenerate the signal,
Dialogue: 0,0:06:17.36,0:06:21.20,Default,,0000,0000,0000,,the first thing we do is, undo the \Nattenuation.
Dialogue: 0,0:06:21.20,0:06:25.50,Default,,0000,0000,0000,,So we multiply the received signal by, a \Ngain factor, that is the reciprocal of
Dialogue: 0,0:06:25.50,0:06:28.88,Default,,0000,0000,0000,,the attenuation. \NSo we multiply the signal by g, we obtain
Dialogue: 0,0:06:28.88,0:06:32.30,Default,,0000,0000,0000,,a signal that has, once again the \Namplitude of the original signal but in
Dialogue: 0,0:06:32.30,0:06:38.39,Default,,0000,0000,0000,,so doing we also amplified noise. \NAnd so, we have very unclean levels here,
Dialogue: 0,0:06:38.39,0:06:44.64,Default,,0000,0000,0000,,which could cause all sorts of problems. \NBut since we know that signal is bi level
Dialogue: 0,0:06:44.64,0:06:49.77,Default,,0000,0000,0000,,all we need to do is threshold. \NThis signal, and when we see that it's
Dialogue: 0,0:06:49.77,0:06:53.76,Default,,0000,0000,0000,,positive, we set it plus 5. \NAnd when we see that it's negative, we
Dialogue: 0,0:06:53.76,0:06:57.31,Default,,0000,0000,0000,,set it minus 5. \NThis is easily accomplished in digital
Dialogue: 0,0:06:57.31,0:07:03.50,Default,,0000,0000,0000,,domain by taking the sign of the signal \Nbefore undoing the attenuation factor.
Dialogue: 0,0:07:03.50,0:07:05.83,Default,,0000,0000,0000,,And this is the signal that we get at the \Nother end of the transmission channel.
Dialogue: 0,0:07:07.40,0:07:12.20,Default,,0000,0000,0000,,And we can repeat this procedure as many \Ntimes as we need and that explains why we
Dialogue: 0,0:07:12.20,0:07:16.36,Default,,0000,0000,0000,,can send so much information over very, \Nvery long cables that go all the way
Dialogue: 0,0:07:16.36,0:07:22.36,Default,,0000,0000,0000,,under the ocean. \NThe second success factor for digital
Dialogue: 0,0:07:22.36,0:07:28.50,Default,,0000,0000,0000,,communications today comes from the \Nalgorithmic nature of DSP techniques.
Dialogue: 0,0:07:28.50,0:07:31.77,Default,,0000,0000,0000,,We have seen an example in image coding, \Nin JPEG, where signal processing
Dialogue: 0,0:07:31.77,0:07:35.92,Default,,0000,0000,0000,,techniques such as the discreet cosign \Ntransform could be matched seamlessly to
Dialogue: 0,0:07:35.92,0:07:42.40,Default,,0000,0000,0000,,information theory techniques that \Ninvolve the compression of bit streams.
Dialogue: 0,0:07:42.40,0:07:46.40,Default,,0000,0000,0000,,And this interplay between these two \Ntechniques from different domains.
Dialogue: 0,0:07:46.40,0:07:48.98,Default,,0000,0000,0000,,Creates such powerful compression \Nalgorithms.
Dialogue: 0,0:07:48.98,0:07:52.75,Default,,0000,0000,0000,,Other everyday examples can be found in \NCDs or DVDs.
Dialogue: 0,0:07:52.75,0:07:57.30,Default,,0000,0000,0000,,Where you have encoding of acoustic or \Nvideo information matched to powerful
Dialogue: 0,0:07:57.30,0:08:02.23,Default,,0000,0000,0000,,error correcting codes. \NSo that DVDs or CDs that are scratched or
Dialogue: 0,0:08:02.23,0:08:05.73,Default,,0000,0000,0000,,dusty still play. \NAnd in communications systems.
Dialogue: 0,0:08:05.73,0:08:09.60,Default,,0000,0000,0000,,Techniques such as trellis coded \Nmodulation and Viterbi decoding are used
Dialogue: 0,0:08:09.60,0:08:13.17,Default,,0000,0000,0000,,to exploit all the capacity of an analog \Ncommunication channel.
Dialogue: 0,0:08:13.17,0:08:16.82,Default,,0000,0000,0000,,The third success factor for digital \Ncommunications is related to hardware
Dialogue: 0,0:08:16.82,0:08:20.27,Default,,0000,0000,0000,,advancements. \NWe can have today miniaturized devices
Dialogue: 0,0:08:20.27,0:08:24.24,Default,,0000,0000,0000,,that we can keep in our pocket, we can \Nhave general purpose platforms used to
Dialogue: 0,0:08:24.24,0:08:28.40,Default,,0000,0000,0000,,develop advanced communication systems, \Nso we don't need to develop specific
Dialogue: 0,0:08:28.40,0:08:34.86,Default,,0000,0000,0000,,hardware for each different task. \NAnd communication devices have become
Dialogue: 0,0:08:34.86,0:08:39.28,Default,,0000,0000,0000,,very power efficient, so that we can have \NLarge data centers, or central offices
Dialogue: 0,0:08:39.28,0:08:45.32,Default,,0000,0000,0000,,that process an enormous number of \Ncommunication channels in peril.
Dialogue: 0,0:08:45.32,0:08:49.26,Default,,0000,0000,0000,,So let's have a look at what happens when \Nyou place a call from your mobile phone
Dialogue: 0,0:08:49.26,0:08:55.12,Default,,0000,0000,0000,,to someone that has their phone at home. \NThe information is first sent over the
Dialogue: 0,0:08:55.12,0:08:59.34,Default,,0000,0000,0000,,air to the closest base station where it \Nis now converted to a different format
Dialogue: 0,0:08:59.34,0:09:05.17,Default,,0000,0000,0000,,and sent over copper wires to a switch. \NThe switch is designed to find the
Dialogue: 0,0:09:05.17,0:09:10.27,Default,,0000,0000,0000,,routing pattern that will send the \Ninformation to the final destination.
Dialogue: 0,0:09:10.27,0:09:14.11,Default,,0000,0000,0000,,The switch will send information over \Nwhat is going to most likely an optic
Dialogue: 0,0:09:14.11,0:09:17.91,Default,,0000,0000,0000,,fiber channel to the global telephone \Nnetwork.
Dialogue: 0,0:09:17.91,0:09:21.13,Default,,0000,0000,0000,,The telephone network will route your \Ninformation to the central office that is
Dialogue: 0,0:09:21.13,0:09:25.37,Default,,0000,0000,0000,,closest to the person you'll calling. \NThe central office will then send the
Dialogue: 0,0:09:25.37,0:09:28.97,Default,,0000,0000,0000,,same information in yet a different \Nformat over a coax cable to the switch
Dialogue: 0,0:09:28.97,0:09:32.98,Default,,0000,0000,0000,,that is closest to the telephone that is \Nbeing called and finally from the closest
Dialogue: 0,0:09:32.98,0:09:39.23,Default,,0000,0000,0000,,switch to the phone in the house. \NThere is what is called the last smile
Dialogue: 0,0:09:39.23,0:09:45.54,Default,,0000,0000,0000,,which is a longish piece of copper wire. \NSo, you see at every change of channel
Dialogue: 0,0:09:45.54,0:09:51.38,Default,,0000,0000,0000,,many many things can happen. \NThe signal can be converted to digital
Dialogue: 0,0:09:51.38,0:09:55.34,Default,,0000,0000,0000,,again and then back to analog. \NThe modulation schemes and the signal
Dialogue: 0,0:09:55.34,0:09:58.47,Default,,0000,0000,0000,,formats that we will have to use on this \Ndifferent stretches of the channel will
Dialogue: 0,0:09:58.47,0:10:02.76,Default,,0000,0000,0000,,have to adopt to the physical \Ncharacteristics of the medium.
Dialogue: 0,0:10:02.76,0:10:06.60,Default,,0000,0000,0000,,Every analog channel. \NHas two unescapable limits that we have
Dialogue: 0,0:10:06.60,0:10:10.70,Default,,0000,0000,0000,,to reckon with. \NThe first is a bandwith constraint.
Dialogue: 0,0:10:10.70,0:10:14.35,Default,,0000,0000,0000,,The signals that we can send over an \Nanalog channel will have to be limited to
Dialogue: 0,0:10:14.35,0:10:18.80,Default,,0000,0000,0000,,a certain frequency band, and the second \Nlimit is the fact that we cannot use
Dialogue: 0,0:10:18.80,0:10:23.84,Default,,0000,0000,0000,,arbitrary power over that band. \NThere will be limits on the power of the
Dialogue: 0,0:10:23.84,0:10:27.64,Default,,0000,0000,0000,,signal we can send. \NThe maximum amount of informatin we will
Dialogue: 0,0:10:27.64,0:10:31.99,Default,,0000,0000,0000,,be able to send with the channel given \Nthis contraints is called a capicity of
Dialogue: 0,0:10:31.99,0:10:35.65,Default,,0000,0000,0000,,the channel. \NWe will see a remarkable result of
Dialogue: 0,0:10:35.65,0:10:38.60,Default,,0000,0000,0000,,information theory later on that exactly \Nquantifies the capcity of the channel
Dialogue: 0,0:10:38.60,0:10:41.83,Default,,0000,0000,0000,,given it's signal to noise ratio and it's \Nbandwidth.
Dialogue: 0,0:10:41.83,0:10:46.11,Default,,0000,0000,0000,,As communication system engineers we are \Ngiven the specifications of a chennel.
Dialogue: 0,0:10:46.11,0:10:51.12,Default,,0000,0000,0000,,And we want to design a system that sends \Nas much information over this channel.
Dialogue: 0,0:10:51.12,0:10:56.48,Default,,0000,0000,0000,,And as reliably as possible give this \Nunescapeable capacity constraint.
Dialogue: 0,0:10:56.48,0:11:00.56,Default,,0000,0000,0000,,Amount of information and reliability are \Nconcepts that are still a little fuzzy
Dialogue: 0,0:11:00.56,0:11:04.58,Default,,0000,0000,0000,,for the time being. \NThey will become clearer later on but we
Dialogue: 0,0:11:04.58,0:11:08.80,Default,,0000,0000,0000,,can certainly look at the intuition \Nbehind this problem.
Dialogue: 0,0:11:08.80,0:11:11.71,Default,,0000,0000,0000,,For instance, if we look at the \Nrelationship between bandwidth and
Dialogue: 0,0:11:11.71,0:11:15.27,Default,,0000,0000,0000,,capacity, we can do this very simple \Nthought experiment.
Dialogue: 0,0:11:15.27,0:11:19.21,Default,,0000,0000,0000,,Suppose we are going to transmit \Ninformation encoded as a sequence of
Dialogue: 0,0:11:19.21,0:11:23.29,Default,,0000,0000,0000,,digital samples over a continuous time \Nchannel.
Dialogue: 0,0:11:23.29,0:11:27.50,Default,,0000,0000,0000,,So, what we do we take the samples we \Ninterpolate the samples with a certain
Dialogue: 0,0:11:27.50,0:11:31.72,Default,,0000,0000,0000,,sampling period Ts now if we make Ts very \Nsmall it means that we can send more
Dialogue: 0,0:11:31.72,0:11:37.21,Default,,0000,0000,0000,,samples per second. \NBut if we make Ts small we know that the
Dialogue: 0,0:11:37.21,0:11:40.93,Default,,0000,0000,0000,,bandwidth will grow as the reciprocal of \NTs you remember the formula for
Dialogue: 0,0:11:40.93,0:11:47.30,Default,,0000,0000,0000,,interpolate signal. \NIn the sampling theorem, it says that the
Dialogue: 0,0:11:47.30,0:11:53.94,Default,,0000,0000,0000,,analog spectrum will be zero outside of a \Nband that goes from omega n to minus
Dialogue: 0,0:11:53.94,0:11:59.28,Default,,0000,0000,0000,,omega n. \NAnd omega n is Pi over Ts.
Dialogue: 0,0:11:59.28,0:12:02.83,Default,,0000,0000,0000,,If we make ts small the bandwidth will \Ngrow with 1 over Ts.
Dialogue: 0,0:12:04.30,0:12:08.27,Default,,0000,0000,0000,,So we see, that capacity, and the amount \Nof information that we can send per
Dialogue: 0,0:12:08.27,0:12:13.66,Default,,0000,0000,0000,,second, are related in some way. \NSimilarly, the relationship between the
Dialogue: 0,0:12:13.66,0:12:18.82,Default,,0000,0000,0000,,power constraint and capacity, can be \Nappreciated, because we can never do away
Dialogue: 0,0:12:18.82,0:12:22.23,Default,,0000,0000,0000,,with noise. \NSo, at the receiver, when we send the
Dialogue: 0,0:12:22.23,0:12:26.50,Default,,0000,0000,0000,,sequence of integers for instance, we \Nwill have to guess What has been set
Dialogue: 0,0:12:26.50,0:12:32.31,Default,,0000,0000,0000,,after it has been corrupted by noise. \NSo suppose we have a channel that
Dialogue: 0,0:12:32.31,0:12:36.18,Default,,0000,0000,0000,,introduces a noise variance of 1 and \Nsuppose we are transmitting the integer
Dialogue: 0,0:12:36.18,0:12:40.37,Default,,0000,0000,0000,,between 1 and 10. \NIf the variance is 1 lots of transmitted
Dialogue: 0,0:12:40.37,0:12:44.53,Default,,0000,0000,0000,,integers will have and error that will \Nsend them very close to the next integer
Dialogue: 0,0:12:44.53,0:12:48.48,Default,,0000,0000,0000,,in line. \NSo suppose I'm sending the integers
Dialogue: 0,0:12:48.48,0:12:53.78,Default,,0000,0000,0000,,between 1 and 10. \NAnd so I'm sending say one but because of
Dialogue: 0,0:12:53.78,0:12:57.69,Default,,0000,0000,0000,,the noise the one will be 1.75 for \Ninstance.
Dialogue: 0,0:12:57.69,0:13:01.90,Default,,0000,0000,0000,,So I'm not really sure if what was sent \Nwas one or was two.
Dialogue: 0,0:13:01.90,0:13:05.90,Default,,0000,0000,0000,,And then the strategies say okay. \NLet's transmit only odd numbers.
Dialogue: 0,0:13:05.90,0:13:09.54,Default,,0000,0000,0000,,So instead of everything I will not just \Nbe at 0, we'll transmit 1 and then I will
Dialogue: 0,0:13:09.54,0:13:14.78,Default,,0000,0000,0000,,not transmit 2 but I will transmit 3. \NSo I'm increasing the gap between
Dialogue: 0,0:13:14.78,0:13:19.66,Default,,0000,0000,0000,,possible symbols and so the noise that \Nbefore Had probably me misguessing the
Dialogue: 0,0:13:19.66,0:13:24.46,Default,,0000,0000,0000,,transmission of 1, will still be small \Nenough to bring me back to the original
Dialogue: 0,0:13:24.46,0:13:29.34,Default,,0000,0000,0000,,signal. \NNow it is rather intuitive that, all
Dialogue: 0,0:13:29.34,0:13:33.30,Default,,0000,0000,0000,,other things being equal. \NA signal with a wider range will have a
Dialogue: 0,0:13:33.30,0:13:36.57,Default,,0000,0000,0000,,larger power. \NSo, if I want to keep the power constant,
Dialogue: 0,0:13:36.57,0:13:40.27,Default,,0000,0000,0000,,I will still have to send symbols between \Nzero and 10, but now there are only half
Dialogue: 0,0:13:40.27,0:13:43.74,Default,,0000,0000,0000,,as many odd integers between zero and 10 \Nthat there are integers, and so the
Dialogue: 0,0:13:43.74,0:13:49.21,Default,,0000,0000,0000,,amount of information that I can send per \Nunit of time.
Dialogue: 0,0:13:49.21,0:13:52.45,Default,,0000,0000,0000,,will be halved. \NLet's now look at some common
Dialogue: 0,0:13:52.45,0:13:57.70,Default,,0000,0000,0000,,communication channels and see what their \Npower and bandwidth constraints are.
Dialogue: 0,0:13:57.70,0:14:01.69,Default,,0000,0000,0000,,Maybe the simplest communication channel \Nthat we're still familiar with, is the AM
Dialogue: 0,0:14:01.69,0:14:05.51,Default,,0000,0000,0000,,radio channel. \NAM stands for amplitude modulation, and
Dialogue: 0,0:14:05.51,0:14:08.48,Default,,0000,0000,0000,,indeed the radio transmitter is very \Nsimple.
Dialogue: 0,0:14:08.48,0:14:12.13,Default,,0000,0000,0000,,We take an analog signal, it can be voice \Nor music, we do a low-pass filtering
Dialogue: 0,0:14:12.13,0:14:15.96,Default,,0000,0000,0000,,operation to limit its bandwidth, And \Nthen we do a very, very simple sinusoidal
Dialogue: 0,0:14:15.96,0:14:20.48,Default,,0000,0000,0000,,modulation with the cosine of a given \Ncarrier.
Dialogue: 0,0:14:20.48,0:14:23.29,Default,,0000,0000,0000,,The result in modulated signal, is simply \Nput to an antenna, and it will be
Dialogue: 0,0:14:23.29,0:14:27.60,Default,,0000,0000,0000,,propogated in the radial spectrum. \NThe radial spectrum is a very scarce
Dialogue: 0,0:14:27.60,0:14:29.63,Default,,0000,0000,0000,,resource. \NThere's only one radial spectrum,
Dialogue: 0,0:14:29.63,0:14:33.22,Default,,0000,0000,0000,,everybody has to share it. \NTherefore, every frequency band in the
Dialogue: 0,0:14:33.22,0:14:38.60,Default,,0000,0000,0000,,spectrum, is strictly regulated by law. \NIn the case of AM, the band is from 530
Dialogue: 0,0:14:38.60,0:14:43.99,Default,,0000,0000,0000,,kilohertz to 1.7 megahertz. \NThis is divided into 8 kilohertz wide
Dialogue: 0,0:14:43.99,0:14:47.54,Default,,0000,0000,0000,,channels. \NAnd each radio station gets allocated a
Dialogue: 0,0:14:47.54,0:14:51.35,Default,,0000,0000,0000,,specific channel. \NThe power is limited by law for a variety
Dialogue: 0,0:14:51.35,0:14:54.13,Default,,0000,0000,0000,,of reasons. \NThe first is that the propagation
Dialogue: 0,0:14:54.13,0:14:58.76,Default,,0000,0000,0000,,patterns for AM waves is very different \Nduring the day, and during the night.
Dialogue: 0,0:14:58.76,0:15:02.26,Default,,0000,0000,0000,,In particular at night time, AM radio \Nwaves travel much further than during the
Dialogue: 0,0:15:02.26,0:15:05.41,Default,,0000,0000,0000,,day. \NSo, they can create all source of
Dialogue: 0,0:15:05.41,0:15:09.38,Default,,0000,0000,0000,,interferences in distant places if the \Npower is not limited.
Dialogue: 0,0:15:09.38,0:15:12.30,Default,,0000,0000,0000,,Also you don't want radio stations to use \Ntoo much power because it wouldn't be
Dialogue: 0,0:15:12.30,0:15:15.18,Default,,0000,0000,0000,,healthy for people live in the vicinity \Nof the transmitter and on the channel
Dialogue: 0,0:15:15.18,0:15:19.10,Default,,0000,0000,0000,,where all are familiar with is the \Ntelephone channel.
Dialogue: 0,0:15:19.10,0:15:22.18,Default,,0000,0000,0000,,The telephone network is more properly \Ncalled the switched telephone network
Dialogue: 0,0:15:22.18,0:15:25.10,Default,,0000,0000,0000,,because instead of taking the \Ncombinatorial approach and having each
Dialogue: 0,0:15:25.10,0:15:28.62,Default,,0000,0000,0000,,phone connected to every other phone in \Nthe world.
Dialogue: 0,0:15:28.62,0:15:30.78,Default,,0000,0000,0000,,What happens is that when you call on \Nother phone.
Dialogue: 0,0:15:30.78,0:15:34.72,Default,,0000,0000,0000,,Your phone is connected to the central \Noffice, and the central office determines
Dialogue: 0,0:15:34.72,0:15:38.44,Default,,0000,0000,0000,,which parts of the network have to be \Nconnected together so that your call can
Dialogue: 0,0:15:38.44,0:15:44.15,Default,,0000,0000,0000,,be routed to the destination phone. \NSo, the piece of wire that connects you
Dialogue: 0,0:15:44.15,0:15:47.99,Default,,0000,0000,0000,,to the central office is up to, maybe \Nsay, a couple of kilometers long, and is
Dialogue: 0,0:15:47.99,0:15:52.80,Default,,0000,0000,0000,,called the last mile. \NThe central office today is a bunch of
Dialogue: 0,0:15:52.80,0:15:57.20,Default,,0000,0000,0000,,digital switches, in the old days was \Nmechanical rotary switches The network
Dialogue: 0,0:15:57.20,0:16:00.98,Default,,0000,0000,0000,,can be anything from optical fiber to \Nsatellite links to anything else in
Dialogue: 0,0:16:00.98,0:16:08.49,Default,,0000,0000,0000,,between, and here you have the symmetric \Npart where you get to your destination.
Dialogue: 0,0:16:08.49,0:16:14.42,Default,,0000,0000,0000,,The telephone channel is conventionally \Nlimited from 300 hertz to 3,000 hertz.
Dialogue: 0,0:16:14.42,0:16:18.31,Default,,0000,0000,0000,,These are historical limits that depend \Non the kind of hardware that was used In
Dialogue: 0,0:16:18.31,0:16:22.21,Default,,0000,0000,0000,,the old days in central office and in the \Nnetwork.
Dialogue: 0,0:16:22.21,0:16:26.50,Default,,0000,0000,0000,,Today these limits are historical \Nartifact but they are kept because anyway
Dialogue: 0,0:16:26.50,0:16:30.79,Default,,0000,0000,0000,,voice communications are perfectly \Nintelligible within this band And with
Dialogue: 0,0:16:30.79,0:16:36.68,Default,,0000,0000,0000,,the reduced band, you can multiplex. \NNamely, you can put together very many
Dialogue: 0,0:16:36.68,0:16:41.26,Default,,0000,0000,0000,,communications on a wider channel. \NThe power that you can send on a
Dialogue: 0,0:16:41.26,0:16:47.45,Default,,0000,0000,0000,,telephone wire is limited from 0.2 to 0.7 \Nvolts, or root mean square.
Dialogue: 0,0:16:47.45,0:16:50.74,Default,,0000,0000,0000,,And this a strictly enforced limit to \Nmake sure that you don't send signals
Dialogue: 0,0:16:50.74,0:16:54.16,Default,,0000,0000,0000,,that can burn the equipment at the \Ncentral office.
Dialogue: 0,0:16:54.16,0:16:57.51,Default,,0000,0000,0000,,And the signal to noise ratio is rather \Ngood because the analog part of the
Dialogue: 0,0:16:57.51,0:17:00.59,Default,,0000,0000,0000,,telephone network operates in the bass \Nband and there's not a lot of
Dialogue: 0,0:17:00.59,0:17:05.67,Default,,0000,0000,0000,,interference in the low frequencies. \NSo let's how we're going to go about
Dialogue: 0,0:17:05.67,0:17:10.25,Default,,0000,0000,0000,,designing a communications system. \NProbably the most important concept here,
Dialogue: 0,0:17:10.25,0:17:13.80,Default,,0000,0000,0000,,is that we're going to adopt the \Nall-digital paradigm.
Dialogue: 0,0:17:13.80,0:17:16.92,Default,,0000,0000,0000,,What this means is that, we will keep \Neverything in the digital domain until we
Dialogue: 0,0:17:16.92,0:17:20.83,Default,,0000,0000,0000,,hit the physical channel. \NAnd if we were to describe this as a
Dialogue: 0,0:17:20.83,0:17:25.64,Default,,0000,0000,0000,,block diagram, it would look like this. \NWe have a binary bit stream, can
Dialogue: 0,0:17:25.64,0:17:31.25,Default,,0000,0000,0000,,represent any sort of views or data. \NWe have a transmitter that operates
Dialogue: 0,0:17:31.25,0:17:36.70,Default,,0000,0000,0000,,entirely in digital domain that generates \Na discreet time signal s of n.
Dialogue: 0,0:17:36.70,0:17:39.27,Default,,0000,0000,0000,,The last element in the transmission \Nchain.
Dialogue: 0,0:17:39.27,0:17:42.93,Default,,0000,0000,0000,,Is a digital to analog converter \Noperating at a given frequency, or at the
Dialogue: 0,0:17:42.93,0:17:46.47,Default,,0000,0000,0000,,given period as you prefer, that \Ntransforms this signal into an analog
Dialogue: 0,0:17:46.47,0:17:52.79,Default,,0000,0000,0000,,signal that we can send over the channel. \NSo remember the channel constraints.
Dialogue: 0,0:17:52.79,0:17:55.21,Default,,0000,0000,0000,,Look a little bit like a filter design \Nproblem.
Dialogue: 0,0:17:55.21,0:18:00.40,Default,,0000,0000,0000,,We have a band width that is specified in \Nterms of a maximum and minimum frequency.
Dialogue: 0,0:18:00.40,0:18:05.30,Default,,0000,0000,0000,,So we can only operate over this band. \NAnd then we have a power constraint that
Dialogue: 0,0:18:05.30,0:18:09.18,Default,,0000,0000,0000,,restricts the power associated with the \Nsignal that we produce.
Dialogue: 0,0:18:09.18,0:18:13.80,Default,,0000,0000,0000,,So if you want to convert this to our old \Ndigital paradigm the first thing to do is
Dialogue: 0,0:18:13.80,0:18:16.77,Default,,0000,0000,0000,,to convert the specs into discreet time \Nspecs.
Dialogue: 0,0:18:16.77,0:18:21.17,Default,,0000,0000,0000,,So we choose a frequency for the D2A \Nconverted, fs, this will be our niquist
Dialogue: 0,0:18:21.17,0:18:26.68,Default,,0000,0000,0000,,frequency, fs over 2, and with this we \Ncan convert the specs.
Dialogue: 0,0:18:26.68,0:18:30.57,Default,,0000,0000,0000,,Maximum frequency will be pi, and our \Nminimum and maximum frequency bands will
Dialogue: 0,0:18:30.57,0:18:34.39,Default,,0000,0000,0000,,be omega min and omega max using the \Nrelation.
Dialogue: 0,0:18:34.39,0:18:41.99,Default,,0000,0000,0000,,Omega equal to 2 pi f over fs. \NAnd you can put here, f min or f.
Dialogue: 0,0:18:41.99,0:18:45.58,Default,,0000,0000,0000,,Now, here are some working hypotheses \Nthat are common to most transmission
Dialogue: 0,0:18:45.58,0:18:49.27,Default,,0000,0000,0000,,systems you will ever see. \NWe start from a bitstream.
Dialogue: 0,0:18:49.27,0:18:52.42,Default,,0000,0000,0000,,And we will convert this bitstream into a \Nsequence of symbols.
Dialogue: 0,0:18:52.42,0:18:56.10,Default,,0000,0000,0000,,For samples a of n, via something called \Na mapper.
Dialogue: 0,0:18:56.10,0:19:02.50,Default,,0000,0000,0000,,What the mapper does is associate group \Nof bits to a specific symbol.
Dialogue: 0,0:19:02.50,0:19:05.61,Default,,0000,0000,0000,,Just to give you a concrete example \Nassume we're going to map each group of
Dialogue: 0,0:19:05.61,0:19:10.20,Default,,0000,0000,0000,,bits to its decimal value. \NWe want to model the sequence of symbols
Dialogue: 0,0:19:10.20,0:19:13.38,Default,,0000,0000,0000,,as a white random sequence and in order \Nto do so, we have to assume that the
Dialogue: 0,0:19:13.38,0:19:17.28,Default,,0000,0000,0000,,bitstream is a completely random \Nsequence.
Dialogue: 0,0:19:17.28,0:19:20.43,Default,,0000,0000,0000,,Now, this is not necessarily the case, \Nfor instance, imagine you're digitizing
Dialogue: 0,0:19:20.43,0:19:22.65,Default,,0000,0000,0000,,audio and you have long stretches of \Nsilence.
Dialogue: 0,0:19:22.65,0:19:26.12,Default,,0000,0000,0000,,This will result into a long sequence of \Nzeros.
Dialogue: 0,0:19:26.12,0:19:29.84,Default,,0000,0000,0000,,And so, what we do is we put a scrambler \Nin the line.
Dialogue: 0,0:19:29.84,0:19:33.36,Default,,0000,0000,0000,,What a scrambler does. \NIt transforms a sequence of bits into a
Dialogue: 0,0:19:33.36,0:19:37.14,Default,,0000,0000,0000,,sequence that looks like a random \Nsequence but this randomization is
Dialogue: 0,0:19:37.14,0:19:42.44,Default,,0000,0000,0000,,completely invariable at a receiver. \NSo, we start with the sequence of zeroes
Dialogue: 0,0:19:42.44,0:19:45.18,Default,,0000,0000,0000,,for instance. \NWe put into the scrambler, it's going to
Dialogue: 0,0:19:45.18,0:19:48.76,Default,,0000,0000,0000,,look like a completely random sequence of \Nzeroes and one but it's done
Dialogue: 0,0:19:48.76,0:19:51.13,Default,,0000,0000,0000,,algorithmically so we can invert this \Nrandomization on the receiver and
Dialogue: 0,0:19:51.13,0:19:56.30,Default,,0000,0000,0000,,retrieve the original bitstream.. \NWith this we can consider the sequence of
Dialogue: 0,0:19:56.30,0:20:00.45,Default,,0000,0000,0000,,symbol a of n as a wide sequence. \NAnd now we need to convert the sequence
Dialogue: 0,0:20:00.45,0:20:03.84,Default,,0000,0000,0000,,into a continuous time signal within the \Nconstraints.
Dialogue: 0,0:20:03.84,0:20:06.90,Default,,0000,0000,0000,,So here's the updated transmission \Nscheme.
Dialogue: 0,0:20:06.90,0:20:11.57,Default,,0000,0000,0000,,User data goes into a scrambler. \NThis is a random binary sequence.
Dialogue: 0,0:20:11.57,0:20:15.23,Default,,0000,0000,0000,,The mapper converts groups of bits to \Nsymbols.
Dialogue: 0,0:20:15.23,0:20:19.73,Default,,0000,0000,0000,,And then we have to decide what to do in \Nhere before converting this into an
Dialogue: 0,0:20:19.73,0:20:23.40,Default,,0000,0000,0000,,analog signal. \NThe first problem is Fulfilling the
Dialogue: 0,0:20:23.40,0:20:27.11,Default,,0000,0000,0000,,bandwidth constraint. \NIf we assume that the data is randomized
Dialogue: 0,0:20:27.11,0:20:31.26,Default,,0000,0000,0000,,and therefore the symbol sequence is a \Nwide sequence, we know that the power
Dialogue: 0,0:20:31.26,0:20:35.55,Default,,0000,0000,0000,,spectral density is simply equal to the \Nvariance and so the power of the signal
Dialogue: 0,0:20:35.55,0:20:39.45,Default,,0000,0000,0000,,will be constant over the entire \Nfrequency band but we actually need to
Dialogue: 0,0:20:39.45,0:20:47.58,Default,,0000,0000,0000,,fit it into the small band here as \Nspecified by the bandwidth constraint.
Dialogue: 0,0:20:47.58,0:20:51.87,Default,,0000,0000,0000,,So, how do we do this. \NWell in order to do that we need to
Dialogue: 0,0:20:51.87,0:20:56.91,Default,,0000,0000,0000,,introduce a new technique called up \Nsampling and we will see this in the next
Dialogue: 0,0:20:56.91,0:20:59.42,Default,,0000,0000,0000,,module.