Good afternoon to the sixth lecture on biomedical signal analysis and today we're actually starting

into the analysis part of biomedical signals. Last week we talked about measurement, so

one brief lecture on that. We talked about the definition of measurement, about some

measurement possibilities, so different electrode types and also about biopotential electrodes.

We talked about ECG measurement in detail, so what is a 12 channel ECG and what is Wilson's

central terminal and Eindhoven's triangle. We talked about measurement of human movement

as an important symptom, both measured with inertial systems and 3D video. And we also

talked about measurement error sources. And the last point is very important for our topic

that we start into today, so you want to get rid of these error sources as part of your

biomedical signal analysis tasks and that's what we are going to start talking about today.

So, in this third part of the lecture we are going to have a few definitions and basic

discussions first of all. I'm sorry that this overview is broken, we'll fix that, but in

the whole analysis class we will have five different subchapters, so one of them has

disappeared so these subchapters should not appear. But it's going to be filtering for

artifact removal, it's going to be wavelet analysis, event detection, waveform analysis

and then we are going to talk about machine learning, so automated decision making at

the end. That's our fifth chapter that has disappeared here. And starting with filtering

for artifact removal, we are going to talk about filter concepts, about signal analysis

concepts that help you upgrade your signals that you measure in order to prepare them

for subsequent analysis. Now in this filtering part we will talk about several signal types,

most of them electric but some of them also electronic or acoustic, digital, optical and

what we want to do with filtering is to reject signal frequencies or vibrations that are

hindering to our analysis while we let other frequencies pass. So that's the content for

the filtering subchapter. And this chapter will be with us until Christmas, so for the

next four lecture units, so this and the next three lecture units. Before I go into the

problem statement, I want to let you arrive a little bit. So for a second don't look at

the slides but maybe think about a possible application of biomedical signal analysis

that you might want to work on in the future. What I want to bring across today as the main

message is that whatever you build, you need a lot of these tools that we are going to

talk about but you also need a certain process knowledge and that is even more important

to understand than the content of this and the following lectures. It's what I always

preach about but what can't be said often enough that you need to have a full understanding

of the process you're looking at and meaning that if you for example analyze ECG signals

and you should know about the generation of these signals, you should know about the measurement

of these signals but you should also know all the steps that are involved in analysis,

in filtering, in event detection, in whatever is there to come. That is because in all these

steps you have certain assumptions and we were going to talk about a lot of these assumptions

today that play a role in those processes. So for example, a lot of the things that we

are talking about today assume that processes are normal distributed. Who knows what a normal

distribution is? Yeah, what is it? What are the two defining parameters for a Gaussian

distribution? We have mean and the variance.

And that's the spell shape curve. So what is this? As an example, what could this be?

You have heard about this in mathematics education but I want to make it very concrete. I want

to talk about examples, not about only concepts. So what could X be in this case when I show

a distribution? Yeah? It's a random variable and so that's a concept? What could it be

concretely? Yeah? What was the second one? Yeah, H is a good example. So as everybody

enters the store, good morning, good afternoon, we could randomly sample the H. So this will

give you a normal distribution if we have enough samples and there's like 40 of you

in the room. So we will get in this case 40 discrete X's. That's some kind of measurement.

So for example, X equals H. And the P of X is the probability that you observe a certain