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Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.10,0:00:04.09,Default,,0000,0000,0000,,Welcome to Module 10. \NThis is the end.
Dialogue: 0,0:00:04.09,0:00:07.29,Default,,0000,0000,0000,,This is the last model obviously and \Nshould show some perspective of where we
Dialogue: 0,0:00:07.29,0:00:11.16,Default,,0000,0000,0000,,can go with the stuff you have learned \Nfrom this online class.
Dialogue: 0,0:00:12.92,0:00:16.65,Default,,0000,0000,0000,,So it has four parts. \NWe're going to talk about courses that we
Dialogue: 0,0:00:16.65,0:00:22.58,Default,,0000,0000,0000,,give here at EPFL that follow up on the \NBasic Digital Signal Processing class.
Dialogue: 0,0:00:22.58,0:00:25.65,Default,,0000,0000,0000,,Then we'll talk about some research \Nprojects, where techniques that we have
Dialogue: 0,0:00:25.65,0:00:30.08,Default,,0000,0000,0000,,learned, are actually being used. \NWe're also going to talk about a few
Dialogue: 0,0:00:30.08,0:00:32.99,Default,,0000,0000,0000,,start-ups that came out of research from \Nthe lab, and finish with
Dialogue: 0,0:00:32.99,0:00:39.49,Default,,0000,0000,0000,,acknowledgements. \NModule 10.1.
Dialogue: 0,0:00:39.49,0:00:43.50,Default,,0000,0000,0000,,What sort of classes can you take once \Nyou have mastered Digital Signal
Dialogue: 0,0:00:43.50,0:00:47.53,Default,,0000,0000,0000,,Processing basics? \NWell, there is a classical course called
Dialogue: 0,0:00:47.53,0:00:51.74,Default,,0000,0000,0000,,Statistical Signal Processing. \NWe give, here, a class on Audio and
Dialogue: 0,0:00:51.74,0:00:55.98,Default,,0000,0000,0000,,Acoustic Signal Processing. \NWe have a follow up course, which is more
Dialogue: 0,0:00:55.98,0:01:00.81,Default,,0000,0000,0000,,Mathematical on the Foundations of Signal \NProcessing and we give a doctoral course
Dialogue: 0,0:01:00.81,0:01:07.87,Default,,0000,0000,0000,,on advanced topics. \NSo the first classical class in on
Dialogue: 0,0:01:07.87,0:01:12.63,Default,,0000,0000,0000,,statistical signal processing. \NSo why do we need statistical tools to
Dialogue: 0,0:01:12.63,0:01:15.98,Default,,0000,0000,0000,,process signals? \NWell, so far we have seen mostly
Dialogue: 0,0:01:15.98,0:01:19.67,Default,,0000,0000,0000,,deterministic signals. \NBut most deterministic signals, if they
Dialogue: 0,0:01:19.67,0:01:24.98,Default,,0000,0000,0000,,are measured, will be hampered by noise. \NSecond, signals change over time.
Dialogue: 0,0:01:24.98,0:01:29.43,Default,,0000,0000,0000,,So we need to adapt signal processing \Nmethods to changing conditions.
Dialogue: 0,0:01:30.45,0:01:35.61,Default,,0000,0000,0000,,And finally, to do estimation, so to find \Nsome information from a signal.
Dialogue: 0,0:01:35.61,0:01:39.44,Default,,0000,0000,0000,,So that's called optimal estimation, \Nrequires stochastic models and
Dialogue: 0,0:01:39.44,0:01:43.44,Default,,0000,0000,0000,,statistical techniques. \NWhat sort of problems can we address?
Dialogue: 0,0:01:43.44,0:01:47.99,Default,,0000,0000,0000,,So every communications problem that you \Ncan think of will need statistical signal
Dialogue: 0,0:01:47.99,0:01:53.49,Default,,0000,0000,0000,,processing. \NSo you saw the Wi-Fi system in module 9.
Dialogue: 0,0:01:53.49,0:01:57.39,Default,,0000,0000,0000,,That's a typical example where noise is \Ndominant and you need to have,
Dialogue: 0,0:01:57.39,0:02:01.58,Default,,0000,0000,0000,,statisfical methods to recover signals \Nfrom noise.
Dialogue: 0,0:02:01.58,0:02:05.80,Default,,0000,0000,0000,,Then we have examples in biological \Nsignal processing, for example spikes
Dialogue: 0,0:02:05.80,0:02:09.65,Default,,0000,0000,0000,,working. \NAnd one classic other example is adaptive
Dialogue: 0,0:02:09.65,0:02:15.80,Default,,0000,0000,0000,,filtering for echo cancellation. \NIn module 5.12 we saw reverberation and
Dialogue: 0,0:02:15.80,0:02:21.68,Default,,0000,0000,0000,,the inverse called dereverberation. \NAnd this is used in for example hands
Dialogue: 0,0:02:21.68,0:02:26.55,Default,,0000,0000,0000,,free telephone communications, and \Nrequires adaptive filtering.
Dialogue: 0,0:02:28.24,0:02:32.15,Default,,0000,0000,0000,,Let's look at just one image here. \NIt's from biological signal processing.
Dialogue: 0,0:02:32.15,0:02:36.04,Default,,0000,0000,0000,,So there is a measurement here in the \Nbrain of a grasshopper, and it's to
Dialogue: 0,0:02:36.04,0:02:42.11,Default,,0000,0000,0000,,figure out when the olfactory system of \Nthe grasshopper is actually active.
Dialogue: 0,0:02:42.11,0:02:47.29,Default,,0000,0000,0000,,So there are some electrical probes here. \NHere are neural spikes coming out and you
Dialogue: 0,0:02:47.29,0:02:50.100,Default,,0000,0000,0000,,need to do two things which are \Nstatistical in nature.
Dialogue: 0,0:02:50.100,0:02:54.64,Default,,0000,0000,0000,,One is to classify the spikes, or if you \Nblow up here's a signal you're going to
Dialogue: 0,0:02:54.64,0:02:58.77,Default,,0000,0000,0000,,see these neural spikes and they have \Ndifferent types.
Dialogue: 0,0:02:58.77,0:03:03.54,Default,,0000,0000,0000,,But if you classify correctly you can \Nidentify Certain characteristic.
Dialogue: 0,0:03:03.54,0:03:07.08,Default,,0000,0000,0000,,And the other one is that you have \Nchanging characteristic over time.
Dialogue: 0,0:03:07.08,0:03:11.11,Default,,0000,0000,0000,,You might have very low activity here, \Nand some very high activity, so you would
Dialogue: 0,0:03:11.11,0:03:16.56,Default,,0000,0000,0000,,like to model this to figure out when a \Ncertain neuron is actually active.
Dialogue: 0,0:03:16.56,0:03:19.86,Default,,0000,0000,0000,,Okay, so they are two examples of \Nstatistical signal processing in the
Dialogue: 0,0:03:19.86,0:03:25.36,Default,,0000,0000,0000,,context of biological. \NSo, the outline of the class, is that we
Dialogue: 0,0:03:25.36,0:03:29.20,Default,,0000,0000,0000,,start with basic models, then we look at \Nthese exemplary applications, for
Dialogue: 0,0:03:29.20,0:03:34.86,Default,,0000,0000,0000,,example, Wireless Transmission, Echo \NCancellation and Spikes sorting.
Dialogue: 0,0:03:34.86,0:03:38.28,Default,,0000,0000,0000,,You can go to the website of the class \Nhere, and see all the details and the
Dialogue: 0,0:03:38.28,0:03:44.32,Default,,0000,0000,0000,,outline. \NA second class we're giving, which builds
Dialogue: 0,0:03:44.32,0:03:48.47,Default,,0000,0000,0000,,up on digital signal processing is one on \Nsignal processing for audio and
Dialogue: 0,0:03:48.47,0:03:52.70,Default,,0000,0000,0000,,acoustics. \NThe objective is to understand acoustics,
Dialogue: 0,0:03:52.70,0:03:56.75,Default,,0000,0000,0000,,but also psychoacoustics, because signal \Nprocessing for acoustics has to deal with
Dialogue: 0,0:03:56.75,0:04:01.81,Default,,0000,0000,0000,,a human perceptual system. \NSo spatial hearing, for example, is very
Dialogue: 0,0:04:01.81,0:04:06.80,Default,,0000,0000,0000,,sophisticated and very important if you \Ndo multi-channel audio processing.
Dialogue: 0,0:04:06.80,0:04:11.18,Default,,0000,0000,0000,,Then, we want to understand manipulation \Nprocessing of audio signals.
Dialogue: 0,0:04:11.18,0:04:15.46,Default,,0000,0000,0000,,Last but not least, understand \Nstate-of-the-art methods in audio signal
Dialogue: 0,0:04:15.46,0:04:19.27,Default,,0000,0000,0000,,processing, including on consumer-only \Naudio.
Dialogue: 0,0:04:19.27,0:04:22.03,Default,,0000,0000,0000,,On the right side here we have a \Nbeautiful picture of a so-called
Dialogue: 0,0:04:22.03,0:04:26.11,Default,,0000,0000,0000,,spectrogram, a spectrogram is a local \NFourier analysis over time.
Dialogue: 0,0:04:26.11,0:04:29.90,Default,,0000,0000,0000,,So you move, here is time, here is the \Nspectrum, that changes over time.
Dialogue: 0,0:04:29.90,0:04:33.13,Default,,0000,0000,0000,,And here is a small piece of music, and \Nyou see all the harmonics and then we
Dialogue: 0,0:04:33.13,0:04:36.36,Default,,0000,0000,0000,,change the note. \NWe have other harmonics, and so on.
Dialogue: 0,0:04:36.36,0:04:40.64,Default,,0000,0000,0000,,So this is the most basic signal \Nprocessing for acoustics.
Dialogue: 0,0:04:40.64,0:04:43.45,Default,,0000,0000,0000,,But of course if you do it for \Nmulti-channels it's Becomes very
Dialogue: 0,0:04:43.45,0:04:47.45,Default,,0000,0000,0000,,complicated, and leads to sophisticated \Nprocessing techniques.
Dialogue: 0,0:04:48.89,0:04:54.24,Default,,0000,0000,0000,,Here is an example done by people in the \Nlab, on so called Auralization.
Dialogue: 0,0:04:54.24,0:04:58.38,Default,,0000,0000,0000,,So if a piece a music and you like to \Nsimulate its rendering, in different
Dialogue: 0,0:04:58.38,0:05:02.66,Default,,0000,0000,0000,,environments. \NSo here's a rendering which simulate a
Dialogue: 0,0:05:02.66,0:05:07.15,Default,,0000,0000,0000,,concert hall, here's a rendering which \Nsimulate a classroom, here's a rendering
Dialogue: 0,0:05:07.15,0:05:11.77,Default,,0000,0000,0000,,would be for example, for multimedia \Nsystem, and here's a rendering would be
Dialogue: 0,0:05:11.77,0:05:17.21,Default,,0000,0000,0000,,in an open public space. \NThese spaces are all very, very
Dialogue: 0,0:05:17.21,0:05:20.62,Default,,0000,0000,0000,,different, and then if you want to \Npredict how something sounds In a given
Dialogue: 0,0:05:20.62,0:05:24.18,Default,,0000,0000,0000,,environment then this is a perfect \Nsystem.
Dialogue: 0,0:05:25.79,0:05:29.41,Default,,0000,0000,0000,,Okay the outline of the class, spatial \Nhearing is the first important topic, and
Dialogue: 0,0:05:29.41,0:05:33.93,Default,,0000,0000,0000,,recording methodologies. \NThen multi-channel audio, in this class
Dialogue: 0,0:05:33.93,0:05:38.69,Default,,0000,0000,0000,,we always talk about the single signal \Nbut here in audio signal processing you
Dialogue: 0,0:05:38.69,0:05:44.78,Default,,0000,0000,0000,,can have dozens of channels or even \Nhundreds of channels.
Dialogue: 0,0:05:44.78,0:05:48.77,Default,,0000,0000,0000,,Talking about spacial filtering, coding, \Nwhich you're all familiar with MP3 which
Dialogue: 0,0:05:48.77,0:05:52.53,Default,,0000,0000,0000,,we discussed briefly as our much more \Nsophisticated methods for multi channel
Dialogue: 0,0:05:52.53,0:05:56.57,Default,,0000,0000,0000,,audio. \NLast but not least auralization to do
Dialogue: 0,0:05:56.57,0:06:01.75,Default,,0000,0000,0000,,stimulation of acoustic environments like \Nin the previous slide.
Dialogue: 0,0:06:01.75,0:06:05.10,Default,,0000,0000,0000,,Again, you have details on the website \Nfor the course.
Dialogue: 0,0:06:07.34,0:06:10.94,Default,,0000,0000,0000,,The next class we teach is called, \NMathematical Foundations of Signal
Dialogue: 0,0:06:10.94,0:06:14.16,Default,,0000,0000,0000,,Processing. \NAs we have seen in module six, the world
Dialogue: 0,0:06:14.16,0:06:17.59,Default,,0000,0000,0000,,is analog, but computation is on digital \Ncomputers.
Dialogue: 0,0:06:17.59,0:06:21.19,Default,,0000,0000,0000,,So how do we go From the analog world, \Nto, back to the analog world, using
Dialogue: 0,0:06:21.19,0:06:26.52,Default,,0000,0000,0000,,processing methodologies on computers. \NAnd the examples are audio as we've just
Dialogue: 0,0:06:26.52,0:06:29.94,Default,,0000,0000,0000,,seen, sensor networks that we are \Ngoing to discuss in a minute, imaging,
Dialogue: 0,0:06:29.94,0:06:34.53,Default,,0000,0000,0000,,light on digital cameras, computer \Ngraphics, and so on.
Dialogue: 0,0:06:34.53,0:06:38.55,Default,,0000,0000,0000,,And the key mathematical concepts we have \Nsort of Seen in this class at an
Dialogue: 0,0:06:38.55,0:06:43.17,Default,,0000,0000,0000,,elementary levels, so it's sampling and \Ninterpo-, sampling and interpolation or
Dialogue: 0,0:06:43.17,0:06:48.69,Default,,0000,0000,0000,,approximation and compression. \NNow, in this class we do this in much
Dialogue: 0,0:06:48.69,0:06:51.95,Default,,0000,0000,0000,,more detail. \NOkay, but the basic picture is the same
Dialogue: 0,0:06:51.95,0:06:56.13,Default,,0000,0000,0000,,as we saw in module six. \NYou have an analog world here that we
Dialogue: 0,0:06:56.13,0:07:00.91,Default,,0000,0000,0000,,inhabit, and we have a digital world \Nwhere we do the processing.
Dialogue: 0,0:07:02.88,0:07:06.35,Default,,0000,0000,0000,,So for example, questions are you want to \Nbuild a sensor network.
Dialogue: 0,0:07:06.35,0:07:10.17,Default,,0000,0000,0000,,Here is EPFL campus. \NYou want to measure temperature, how many
Dialogue: 0,0:07:10.17,0:07:14.50,Default,,0000,0000,0000,,sensors should you put on the campus to \Nsense temperature accurately?
Dialogue: 0,0:07:14.50,0:07:18.60,Default,,0000,0000,0000,,And once you have sensed the temperature, \Nhow should you reconstruct?
Dialogue: 0,0:07:18.60,0:07:22.28,Default,,0000,0000,0000,,We're going to discuss this also in the \Nresearch topic later on.
Dialogue: 0,0:07:22.28,0:07:24.51,Default,,0000,0000,0000,,But that's a basic question of signal \Nprocessing.
Dialogue: 0,0:07:24.51,0:07:26.67,Default,,0000,0000,0000,,It's a sampling question. \NHow many sensors?
Dialogue: 0,0:07:26.67,0:07:32.46,Default,,0000,0000,0000,,And an interpolation question, how do we \Nreconstruct the spatial field of
Dialogue: 0,0:07:32.46,0:07:37.75,Default,,0000,0000,0000,,temperature over time? \NThe course outline is, we do again,
Dialogue: 0,0:07:37.75,0:07:42.43,Default,,0000,0000,0000,,Hildred space geometry, but now in great \Ndetail, so if you didn't enjoy Module
Dialogue: 0,0:07:42.43,0:07:48.49,Default,,0000,0000,0000,,two, here in the current class. \Nyou may want to take this one but be
Dialogue: 0,0:07:48.49,0:07:54.28,Default,,0000,0000,0000,,ready for some much more difficult stuff, \Nbut beautiful stuff in my view.
Dialogue: 0,0:07:54.28,0:07:59.76,Default,,0000,0000,0000,,Then we discuss discrete-time systems and \Nsequences, functions of continuous time
Dialogue: 0,0:07:59.76,0:08:04.20,Default,,0000,0000,0000,,and systems on continuous time, and then \Nthere is a big part on sampling,
Dialogue: 0,0:08:04.20,0:08:11.32,Default,,0000,0000,0000,,interpolation, and approximation. \NFinally we discuss some applications.
Dialogue: 0,0:08:11.32,0:08:15.28,Default,,0000,0000,0000,,This class is based on the textbook that \Nhas been mentioned in this class, also
Dialogue: 0,0:08:15.28,0:08:19.94,Default,,0000,0000,0000,,that is just coming out now, with \NVetterli, Kovacevic and V.
Dialogue: 0,0:08:19.94,0:08:25.46,Default,,0000,0000,0000,,Goyal it's called Foundations of Signal \NProcessing and is also available open
Dialogue: 0,0:08:25.46,0:08:32.06,Default,,0000,0000,0000,,access under this website. \NLast but not least, we give doctoral
Dialogue: 0,0:08:32.06,0:08:35.84,Default,,0000,0000,0000,,courses here and doctoral courses are \Nreally at the state of the art of what is
Dialogue: 0,0:08:35.84,0:08:42.12,Default,,0000,0000,0000,,being done in Signal Processing, what is \Nbeing researched and published currently.
Dialogue: 0,0:08:42.12,0:08:46.49,Default,,0000,0000,0000,,And it's based on the fact that the \Nclassical approach as discuss in
Dialogue: 0,0:08:46.49,0:08:51.22,Default,,0000,0000,0000,,undergrad and masters level classes are \Nsometimes limited and need to be
Dialogue: 0,0:08:51.22,0:08:56.34,Default,,0000,0000,0000,,extended. \NTo do state-of-the-art signal processing
Dialogue: 0,0:08:56.34,0:09:00.63,Default,,0000,0000,0000,,research, this sometimes uses, quite \Nsophisticated mathematical tools, that
Dialogue: 0,0:09:00.63,0:09:05.05,Default,,0000,0000,0000,,you also need to understand and maybe \Napply, or, modify for a signal processing
Dialogue: 0,0:09:05.05,0:09:11.12,Default,,0000,0000,0000,,problem. \NSo here is an sample from a class like
Dialogue: 0,0:09:11.12,0:09:15.15,Default,,0000,0000,0000,,this it's a compressed sensing, it has \Nbeen mentioned in the forum, compressed
Dialogue: 0,0:09:15.15,0:09:19.29,Default,,0000,0000,0000,,sensing is a very interesting technique \Nwhere you try to acquire the analog world
Dialogue: 0,0:09:19.29,0:09:22.95,Default,,0000,0000,0000,,by taking very, very few samples in \Nparticle or meta and you reconstruct
Dialogue: 0,0:09:22.95,0:09:28.51,Default,,0000,0000,0000,,using regularization. \NSo here's just a picture.
Dialogue: 0,0:09:28.51,0:09:32.06,Default,,0000,0000,0000,,I don't have time to really explain it. \NBut it's a picture where you solve a
Dialogue: 0,0:09:32.06,0:09:36.25,Default,,0000,0000,0000,,linear system, essentially. \NBut you solve it using different
Dialogue: 0,0:09:36.25,0:09:40.16,Default,,0000,0000,0000,,regularization. \NSo we worked always with the l 2 norm.
Dialogue: 0,0:09:40.16,0:09:43.44,Default,,0000,0000,0000,,We measured the sum of squares of a \Nsequence, for example.
Dialogue: 0,0:09:43.44,0:09:47.25,Default,,0000,0000,0000,,There are other norms that are possible. \NThe l 1, that's the sum of absolute
Dialogue: 0,0:09:47.25,0:09:51.10,Default,,0000,0000,0000,,values, or the l infinity, that's the \Nmaximum value in sequence and if you
Dialogue: 0,0:09:51.10,0:09:55.26,Default,,0000,0000,0000,,regularize a problem you solve your \Nlinear system using these different norms
Dialogue: 0,0:09:55.26,0:10:01.73,Default,,0000,0000,0000,,you get very different solutions. \NAnd one of them happens to be very sparse
Dialogue: 0,0:10:01.73,0:10:05.57,Default,,0000,0000,0000,,so if you are looking for a solution that \Nhas very few non zero terms then L1
Dialogue: 0,0:10:05.57,0:10:09.54,Default,,0000,0000,0000,,regularization which is what hes using \Ncompressed sensing will give you an
Dialogue: 0,0:10:09.54,0:10:14.87,Default,,0000,0000,0000,,interesting solution. \NWe'll come back to this in the research
Dialogue: 0,0:10:14.87,0:10:17.75,Default,,0000,0000,0000,,projects, because it is actually used \Ncurrently in the lab to solve some very
Dialogue: 0,0:10:17.75,0:10:23.29,Default,,0000,0000,0000,,interesting problems. \NOkay, so this Advanced Topics class
Dialogue: 0,0:10:23.29,0:10:26.94,Default,,0000,0000,0000,,actually moves from topic to topic, so \Nsometimes it's on Fourier and wavelet
Dialogue: 0,0:10:26.94,0:10:30.87,Default,,0000,0000,0000,,processing, sometimes its on mathematical \Nprinciples, sometimes it's on Simply
Dialogue: 0,0:10:30.87,0:10:36.60,Default,,0000,0000,0000,,reading groups on advanced topics. \NAgain, there is a website, and there is
Dialogue: 0,0:10:36.60,0:10:40.63,Default,,0000,0000,0000,,volume 2 of Fourier and wavelets sequence \Nhere, which is the basis for the first
Dialogue: 0,0:10:40.63,0:10:45.71,Default,,0000,0000,0000,,version of this class. \NOkay.
Dialogue: 0,0:10:45.71,0:10:49.17,Default,,0000,0000,0000,,So that was an overview of the classes \Nyou could take if you were, for example,
Dialogue: 0,0:10:49.17,0:10:52.39,Default,,0000,0000,0000,,at EPFL. \NLots of that material is actually online,
Dialogue: 0,0:10:52.39,0:10:55.57,Default,,0000,0000,0000,,so if you are interested, you can \Nactually also learn it online from our
Dialogue: 0,0:10:55.57,0:10:57.19,Default,,0000,0000,0000,,website.