XLSTAT: Ensemble empirical mode decomposition in Excel

This article shows you how to decompose a time series using the empirical mode decomposition (EMD)  and its noise-assisted version, the EEMD, in Excel using XLSTAT.

 

Dataset for Example

The attached dataset used to illustrate the ensemble empirical mode decomposition is an example of electrocardiogram data from the MIT-BIH Normal Sinus Rhythm database. It consists of the first 700 observations, which were recorded with a sampling interval of 0.0078125 seconds.

This tutorial aims to decompose this complex signal into a finite and relatively small number of components, also known as IMFs, for intrinsic mode functions.

 

Setting Up

• Open XLSTAT.

• Click on the Forecasting/ Time series analysis menu and select the Time series transformation feature.

In the General tab:

• Select the values of the time series and the date data.

• Check the Check intervals  option to make sure there is no gap in the data.

In the Options tab:

• Check the EMD / EEMD option. Enter the ensemble size to use for the EEMD (200 in our example).

• To run a regular empirical mode decomposition set the ensemble size to 1.

• Enter the noise strength as a percentage that is relative to the standard deviation of the original time series. A 20% noise strength is common when running an ensemble empirical mode decomposition. To run a regular EMD set the noise strength to 0%.

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet.

 

Interpreting the Results

The following table is the main output of the EEMD. It contains the extracted intrinsic mode functions, which all yield frequency information, that can be analyzed using Hilbert spectrums. This decomposition method can also be used to denoise signals or detect anomalies when the IMFs are used as inputs in complicated models.

Eight intrinsic mode functions, including the residual, were extracted from the EEMD. The following charts correspond to the first two components of the decomposition and represent those that yield the highest frequencies.