10.1 - Signal processing courses you can take from here

From the official description of 10.. videos:

Goodbye!

As a parting message, we prepared an extra Module (yes, a "bonus feature", just like in DVDs!) with the following purposes:

give you some pointers if you want to learn more about signal processing
show you some of the cool research topics in signal processing that are currently being pursued in our lab
show you how signal processing translates to the real world by introducing several startups founded by current and former members of our lab

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.