Synthetic vs. Natural
- The EMD will break down a signal into its component IMFs.
- An IMF is a function that:
- has only one extreme between zero crossings, and
- has a mean value of zero.
- In order to describe the process, we borrow from our poster the following section:
The Sifting Process
- The sifting process is what EMD uses to decomposes the signal into IMFs.
The sifting process is as follows:
For a signal X(t), let m1 be the mean of its upper and lower envelopes as determined from a cubic-spline interpolation of local maxima and minima. The locality is determined by an arbitrary parameter; the calculation time and the effectiveness of the EMD depends greatly on such a parameter.
- The first component h1 is computed:
- In the second sifting process, h1 is treated as the data, and m11 is the mean of h1ís upper and lower envelopes:
- This sifting procedure is repeated k times, until h1k is an IMF, that is:
- Then it is designated as c1=h1k, the first IMF component from the data, which contains the shortest period component of the signal.
We separate it from the rest of the data:
X(t)-c1 = r1
The procedure is repeated on rj:
r1-c2 = r2,....,rn-1 - cn = rn
- The result is a set of functions; the number of functions in the set depends on the original signal.
- For a visualization of the sifting process, check out this mpeg we found while looking for information on our topic.