hht (version 2.1.6)

EEMDResift: Resift averaged IMFs from EEMD

Description

Averaged IMFs produced by EEMD may not satisfy the strict definition of an IMF, and therefore they may not have meaningful Hilbert spectrograms. Huang and Wu (2008) suggest another round of sifting to ensure that the averaged IMFs are made to satisfy the IMF definition. This function resifts the averaged IMF set and saves the results based on rules described in the input resift.rule.

Usage

EEMDResift(EEMD.result, resift.rule, spectral.method = "arctan", 
    diff.lag = 1, tol = 5, max.sift = 200, stop.rule = "type5", 
    boundary = "wave", sm = "none", smlevels = c(1), 
    spar = NULL, max.imf = 100, interm = NULL)

Value

resift.result

The resifted results of the averaged IMF set and the individual Hilbert spectra of each resifted IMF.

Arguments

EEMD.result

The averaged IMF set and individual Hilbert spectra of EMD trials generated through EEMD.

resift.rule

How the resifting algorithm chooses which IMF to save

• Integer - Which IMF in the resifted set will be saved (so if resift.rule=1, the first IMF will be saved, the rest will be discarded)

• ``last'' - The last IMF will be saved (not terribly useful)

• ``max.var'' - The IMF with the most variance will be saved. This will get the most ``significant'' IMF out of each resifted set.

• ``all'' - Every single new IMF generated from resifting the averaged IMFs will be saved. There may be a lot of them!

spectral.method

See Sig2IMF.

diff.lag

See Sig2IMF.

tol

See Sig2IMF.

max.sift

See Sig2IMF.

stop.rule

See Sig2IMF.

boundary

See Sig2IMF.

sm

See Sig2IMF.

smlevels

See Sig2IMF.

spar

See Sig2IMF.

max.imf

See Sig2IMF.

interm

See Sig2IMF.

Author

Daniel Bowman

Details

The function EEMDCompile generates a list of averaged IMFs from EEMD trials. These averaged IMFs often do not satisfy the definition of an IMF, usually because some of them are mixtures of different time scales. This is a consequence of the noise perturbation method of EEMD, but it complicates the attempt to create a meaningful Hilbert spectrogram from the averaged IMF set. The resifting algorithm takes each averaged IMF and performs EMD, thereby splitting each one into multiple ``sub-IMFs'', each of which satisfy the strict definition of an IMF. The question then is: which of these sub-IMFs best represent the averaged IMF? The most rigorous solution is to set resift.rule to "all", but that tends to make a large number of sub-IMFs, many with very low amplitude. Another solution is to accept the sub-IMF with the most variance, as that probably represents the fundamental information content of the original averaged IMF.

See Also

EEMD, EEMDCompile

Examples

data(PortFosterEvent)

trials=10
nimf=10
noise.amp=6.4e-07
trials.dir="test"

set.seed(628)

#Run EEMD (this may take some time)
if (FALSE) EEMD(sig, tt, noise.amp, trials, nimf, noise.amp, trials.dir = trials.dir)

#Compile the results
if (FALSE) EEMD.result <- EEMDCompile(trials.dir, trials, nimf)


resift.rule="max.var"
if (FALSE) resift.result <- EEMDResift(EEMD.result, resift.rule)

#Plot the IMFs
time.span=c(5, 10)
imf.list=1:3
os=TRUE
res=TRUE
if (FALSE) PlotIMFs(resift.result, time.span, imf.list, os, res)