Synthetic vs. Natural
This is a report on our investigation of Empirical Mode Decomposition (EMD). In it, we will cover the uses of EMD, the method of applying EMD to a signal, an example of EMD applied to an appropriate signal, and comparisons of this application to the application of other ways of analyzing signals.
EMD is a method of breaking down a signal without leaving the time domain. It can be compared to other analysis methods like Fourier Transforms and wavelet decomposition. The process is useful for analyzing natural signals, which are most often non-linear and non-stationary. This parts from the assumptions of the methods we have thus far learned (namely that the systems in question be LTI, at least in approximation).
EMD filters out functions which form a complete and nearly orthogonal basis for the original signal. Completeness is based on the method of the EMD; the way it is decomposed implies completeness. The functions, known as Intrinsic Mode Functions (IMFs), are therefore sufficient to describe the signal, even though they are not necessarily orthogonal. The reasons are described in Huang et al., published in the Royal Society Proceedings on Math, Physical, and Engineering Sciences: "...the real meaning here applies only locally. For some special data, the neighbouring components could certainly have sections of data carrying the same frequency at different time durations. But locally, any two components should be orthogonal for all practical purposes" (927).
The fact that the functions into which a signal is decomposed are all in the time-domain and of the same length as the original signal allows for varying frequency in time to be preserved. Obtaining IMFs from real world signals is important because natural processes often have multiple causes, and each of these causes may happen at specific time intervals. This type of data is evident in an EMD analysis, but quite hidden in the Fourier domain or in wavelet coefficients.
Some examples of data to which the EMD method may be applied quite effectively are seismic readings, results of neuroscience experiments, electrocardiograms (which we will examine later), gastroelectrograms, and sea-surface height (SSH) readings.