Empirical Mode Decomposition

Empirical mode decomposition (EMD) is a data-adaptive multiresolution technique to decompose a signal into physically meaningful components. EMD can be used to analyze non-linear and non-stationary signals by separating them into components at different resolutions. Some of the common applications of empirical mode decomposition are in the fields of bearing fault detection, biomedical data analysis, power signal analysis, and seismic signals.

Vibration signal analyzed in MATLAB with empirical mode decomposition. (MATLAB code example)

Empirical mode decomposition can be used to perform time-frequency analysis while remaining in the time domain. The components are in the same time scale as the original signal, which makes them easier to analyze. Unlike other multiresolution analysis (MRA) techniques such as wavelet analysis, empirical mode decomposition recursively extracts different resolutions from the data itself without the use of fixed functions or filters.

Another way to explain EMD is to consider a signal as a fast oscillation superimposed on a slower one. After the fast oscillation is extracted, the EMD algorithm treats the remaining slower component as the new signal and again regards it as a fast oscillation superimposed on a slower one. The algorithm continues until some exit criterion is reached. The components in EMD are referred to as intrinsic mode functions (IMF).

A seismic signal analyzed and reconstructed with selected components with the Signal Multiresolution Analyzer app in MATLAB.

Using EMD, it is possible to eliminate specific components such as noise and reconstruct the signal. You can also extract relevant components for further analysis.

Wavelet Toolbox™ and  Signal Processing Toolbox™, for use with MATLAB®, provide EMD and other data-adaptive multiresolution analysis techniques. These techniques can be accessed through the Signal Multiresolution Analyzer app. The app makes it easy to compare results between techniques.

See also: wavelet transform, wavelet transforms videos, Signal Processing Toolbox, DSP System Toolbox™

Discrete Multiresolution Analysis