Statistical signal properties and its variability

reflect changes in the signal and system that produced it.

Before we start talking about evaluation of the signal statistics,

we need to agree on that biomedical signal

distributed according to the normal distribution.

This is a main assumption in biomedical analysis.

According to this assumption ordinary data normalization widely used for data scaling.

The data is converted into notionally common scale from -1 to 1.

In most cases, the original data convert to

the data set with the zero average and variance close to 1

It allows us to remove an influence of

the current recoder and specific amplitude signal properties.

There are a huge amount of statistical methods

and it's really difficult to talk about all of them.

However, they are based on the signal properties like a mean value, or the median,

variance and distribution type,

co-variation, and correlation coefficient and so on.

We are dealing with the time space instead of

the frequency domain that corresponds to the spectral analysis.

You may find more information about

statistical methods in the literature from the list at the lecture notes.

For our task we will use simple metrics as mean, median,

and standard deviation calculated in moving window for different signal parts.

In the analysis of biomedical signals,

different types of time series are used.

For feature extraction, we need to determine some specific time and events basis.

We have different levels of data.

An original signal with a uniform sampling frequency for example, 250 Hz,

some signal properties, spectral and/or

statistical calculated at a different moving windows.

For example, in 10 seconds,

30 seconds, and so on.

It is similar to the low sampling frequency or rare time series,

but with uniform grid too.

We have some events and its properties and features for

each complex provide non-uniform grid time series.

Distance between events are not constant and changes from one event to the other.

Finally, properties for several events.

For example, average RR interval for last 3 complexes.

It will be also non-uniform time grid.

This multilevel structure is not intuitive,

but it's understanding is immensely important for effective data analysis.

The main problem is to combine all these layers into one data frame.

That is why I recommend you to create an additional parameter with the positions of

the calculated features in the original - the highest - time grid, say 250 Hz.

So, let us take a closer look at the layers with moving windows.

In the next video,

we'll create a layer with the features calculated in moving window and

we'll try to combine them with the original time grid together.