Welcome to Module 10. This is the end.
This is the last model obviously and should show some perspective of where we
can go with the stuff you have learned from this online class.
So it has four parts. We're going to talk about courses that we
give here at EPFL that follow up on the Basic Digital Signal Processing class.
Then we'll talk about some research projects, where techniques that we have
learned, are actually being used. We're also going to talk about a few
start-ups that came out of research from the lab, and finish with
acknowledgements. Module 10.1.
What sort of classes can you take once you have mastered Digital Signal
Processing basics? Well, there is a classical course called
Statistical Signal Processing. We give, here, a class on Audio and
Acoustic Signal Processing. We have a follow up course, which is more
Mathematical on the Foundations of Signal Processing and we give a doctoral course
on advanced topics. So the first classical class in on
statistical signal processing. So why do we need statistical tools to
process signals? Well, so far we have seen mostly
deterministic signals. But most deterministic signals, if they
are measured, will be hampered by noise. Second, signals change over time.
So we need to adapt signal processing methods to changing conditions.
And finally, to do estimation, so to find some information from a signal.
So that's called optimal estimation, requires stochastic models and
statistical techniques. What sort of problems can we address?
So every communications problem that you can think of will need statistical signal
processing. So you saw the Wi-Fi system in module 9.
That's a typical example where noise is dominant and you need to have,
statisfical methods to recover signals from noise.
Then we have examples in biological signal processing, for example spikes
working. And one classic other example is adaptive
filtering for echo cancellation. In module 5.12 we saw reverberation and
the inverse called dereverberation. And this is used in for example hands
free telephone communications, and requires adaptive filtering.
Let's look at just one image here. It's from biological signal processing.
So there is a measurement here in the brain of a grasshopper, and it's to
figure out when the olfactory system of the grasshopper is actually active.
So there are some electrical probes here. Here are neural spikes coming out and you
need to do two things which are statistical in nature.
One is to classify the spikes, or if you blow up here's a signal you're going to
see these neural spikes and they have different types.
But if you classify correctly you can identify Certain characteristic.
And the other one is that you have changing characteristic over time.
You might have very low activity here, and some very high activity, so you would
like to model this to figure out when a certain neuron is actually active.
Okay, so they are two examples of statistical signal processing in the
context of biological. So, the outline of the class, is that we
start with basic models, then we look at these exemplary applications, for
example, Wireless Transmission, Echo Cancellation and Spikes sorting.
You can go to the website of the class here, and see all the details and the
outline. A second class we're giving, which builds
up on digital signal processing is one on signal processing for audio and
acoustics. The objective is to understand acoustics,
but also psychoacoustics, because signal processing for acoustics has to deal with
a human perceptual system. So spatial hearing, for example, is very
sophisticated and very important if you do multi-channel audio processing.
Then, we want to understand manipulation processing of audio signals.
Last but not least, understand state-of-the-art methods in audio signal
processing, including on consumer-only audio.
On the right side here we have a beautiful picture of a so-called
spectrogram, a spectrogram is a local Fourier analysis over time.
So you move, here is time, here is the spectrum, that changes over time.
And here is a small piece of music, and you see all the harmonics and then we
change the note. We have other harmonics, and so on.
So this is the most basic signal processing for acoustics.
But of course if you do it for multi-channels it's Becomes very
complicated, and leads to sophisticated processing techniques.
Here is an example done by people in the lab, on so called Auralization.
So if a piece a music and you like to simulate its rendering, in different
environments. So here's a rendering which simulate a
concert hall, here's a rendering which simulate a classroom, here's a rendering
would be for example, for multimedia system, and here's a rendering would be
in an open public space. These spaces are all very, very
different, and then if you want to predict how something sounds In a given
environment then this is a perfect system.
Okay the outline of the class, spatial hearing is the first important topic, and
recording methodologies. Then multi-channel audio, in this class
we always talk about the single signal but here in audio signal processing you
can have dozens of channels or even hundreds of channels.
Talking about spacial filtering, coding, which you're all familiar with MP3 which
we discussed briefly as our much more sophisticated methods for multi channel
audio. Last but not least auralization to do
stimulation of acoustic environments like in the previous slide.
Again, you have details on the website for the course.
The next class we teach is called, Mathematical Foundations of Signal
Processing. As we have seen in module six, the world
is analog, but computation is on digital computers.
So how do we go From the analog world, to, back to the analog world, using
processing methodologies on computers. And the examples are audio as we've just
seen, sensor networks that we are going to discuss in a minute, imaging,
light on digital cameras, computer graphics, and so on.
And the key mathematical concepts we have sort of Seen in this class at an
elementary levels, so it's sampling and interpo-, sampling and interpolation or
approximation and compression. Now, in this class we do this in much
more detail. Okay, but the basic picture is the same
as we saw in module six. You have an analog world here that we
inhabit, and we have a digital world where we do the processing.
So for example, questions are you want to build a sensor network.
Here is EPFL campus. You want to measure temperature, how many
sensors should you put on the campus to sense temperature accurately?
And once you have sensed the temperature, how should you reconstruct?
We're going to discuss this also in the research topic later on.
But that's a basic question of signal processing.
It's a sampling question. How many sensors?
And an interpolation question, how do we reconstruct the spatial field of
temperature over time? The course outline is, we do again,
Hildred space geometry, but now in great detail, so if you didn't enjoy Module
two, here in the current class. you may want to take this one but be
ready for some much more difficult stuff, but beautiful stuff in my view.
Then we discuss discrete-time systems and sequences, functions of continuous time
and systems on continuous time, and then there is a big part on sampling,
interpolation, and approximation. Finally we discuss some applications.
This class is based on the textbook that has been mentioned in this class, also
that is just coming out now, with Vetterli, Kovacevic and V.
Goyal it's called Foundations of Signal Processing and is also available open
access under this website. Last but not least, we give doctoral
courses here and doctoral courses are really at the state of the art of what is
being done in Signal Processing, what is being researched and published currently.
And it's based on the fact that the classical approach as discuss in
undergrad and masters level classes are sometimes limited and need to be
extended. To do state-of-the-art signal processing
research, this sometimes uses, quite sophisticated mathematical tools, that
you also need to understand and maybe apply, or, modify for a signal processing
problem. So here is an sample from a class like
this it's a compressed sensing, it has been mentioned in the forum, compressed
sensing is a very interesting technique where you try to acquire the analog world
by taking very, very few samples in particle or meta and you reconstruct
using regularization. So here's just a picture.
I don't have time to really explain it. But it's a picture where you solve a
linear system, essentially. But you solve it using different
regularization. So we worked always with the l 2 norm.
We measured the sum of squares of a sequence, for example.
There are other norms that are possible. The l 1, that's the sum of absolute
values, or the l infinity, that's the maximum value in sequence and if you
regularize a problem you solve your linear system using these different norms
you get very different solutions. And one of them happens to be very sparse
so if you are looking for a solution that has very few non zero terms then L1
regularization which is what hes using compressed sensing will give you an
interesting solution. We'll come back to this in the research
projects, because it is actually used currently in the lab to solve some very
interesting problems. Okay, so this Advanced Topics class
actually moves from topic to topic, so sometimes it's on Fourier and wavelet
processing, sometimes its on mathematical principles, sometimes it's on Simply
reading groups on advanced topics. Again, there is a website, and there is
volume 2 of Fourier and wavelets sequence here, which is the basis for the first
version of this class. Okay.
So that was an overview of the classes you could take if you were, for example,
at EPFL. Lots of that material is actually online,
so if you are interested, you can actually also learn it online from our
website.