Estimate the correlation dimension of a uniformly sampled signal in the Live Editor

The **Estimate Correlation Dimension** task lets you
interactively estimate the correlation dimension of a uniformly sampled signal. The task
automatically generates MATLAB^{®} code for your live script. For more information about Live Editor tasks
generally, see Add Interactive Tasks to a Live Script (MATLAB).

Correlation dimension is the measure of dimensionality of the space occupied by a set of random points. Correlation dimension is estimated as the slope of the correlation integral versus the range of radius of similarity. Use correlation dimension as a characteristic measure to distinguish between deterministic chaos and random noise, to detect potential faults.

To add the **Estimate Correlation Dimension** task to a live
script in the MATLAB Editor:

On the

**Live Editor**tab, select**Task**>**Estimate Correlation Dimension**.In a code block in your script, type a relevant keyword, such as

`correlation dimension`

or`correlation dimension`

. Select`Estimate Correlation Dimension`

from the suggested command completions.

`Signal`

— Uniformly sampled time-domain signalarray | timetable

Select a uniformly sampled time-domain signal in array or timetable format from the
MATLAB workspace. If the signal has multiple columns, the
**Estimate Correlation Dimension** task computes the
correlation dimension by treating it as a multivariate signal. If the signal is a row
vector, then the **Estimate Correlation Dimension** task
treats it as a univariate signal.

`Signal Type`

— Type of selected signal'

`Time Domain`

' | '`Phase space`

'Specify the type of the selected signal as either '`Time Domain`

'
or '`Phase space`

'. If you specify the signal type as:

'

`Time Domain`

', then also specify the embedding dimension and time lag for your signal.'

`Phase space`

', then the**Estimate Correlation Dimension**task automatically infers the embedding dimension and time lag using the phase space information.

`Embedding Dimension`

— Number of dimensions of phase space vectorsscalar | vector

Specify the number of dimensions of phase space vectors as a scalar or vector from
the MATLAB workspace. When you specify the embedding dimension as a scalar, then the
**Estimate Correlation Dimension** task uses the same
embedding dimension value to estimate the value of correlation dimension for all the
columns of the uniformly sampled signal.

The `Embedding Dimension`

drop down is active only when you
specify the signal type as '`Time Domain`

'. For phase space signals,
the **Estimate Correlation Dimension** task automatically
computes the embedding dimension from the phase space data.

If you do not know the value of embedding dimension for your signal, then you can
compute it using the **Reconstruct Phase
Space** task.

`Time Lag`

— Time lag between successive phase vectorsscalar | vector

Specify time lag between successive phase vectors as a scalar or vector from the
MATLAB workspace. When you specify the time lag as a scalar, then the
**Estimate Correlation Dimension** task uses the same
time delay value to estimate the value of correlation dimension for all the columns of
the uniformly sampled signal. If you specify the embedding dimension as a vector, then
specify the time lag also as a vector of the same length.

The `Time Lag`

drop down is active only when you specify
the signal type as '`Time Domain`

'. For phase space signals, the
**Estimate Correlation Dimension** task automatically
computes the time lag from the phase space data.

If you do not know the value of time lag for your signal, then you can compute it
using the **Reconstruct Phase
Space** task.

`Similarity Radius Min`

— Minimum radius of similarity`max radius/1000`

(default) | scalarSpecify the minimum radius of similarity to be used to compute the number of with-in range points for correlation dimension estimation. Try different values such that the linear fit line aligns with the original data line in the plot.

`Similarity Radius Max`

— Maximum radius of similarity`0.2*sqrt(trace(cov(signal)))`

(default) | scalarSpecify the maximum radius of similarity to be used to compute the number of with-in range points for correlation dimension estimation. Try different values such that the linear fit line aligns with the original data line in the plot.

`Number of Points`

— Number of points between the minimum and maximum radius10 (default) | positive scalar integer

Specify the number of points between the maximum and minimum radius of similarity. Choose an appropriate number of points based on the resolution required to compute the correlation dimension.

`Output Display`

— Toggle result display in the Live Editor outputon (default) | off

Toggle to display the value of correlation dimension in the Live Editor output.

Reconstruct Phase
Space | `approximateEntropy`

| `correlationDimension`

| `lyapunovExponent`

| `phaseSpaceReconstruction`