emd {EMD}

Empirical Mode Decomposition

Description

This function performs empirical mode decomposition.

Usage

emd(xt, tt=NULL, tol=sd(xt)*0.1^2, max.sift=20, stoprule="type1",  
    boundary="periodic", sm="none", smlevels=c(1), spar=NULL, alpha=NULL, 
    check=FALSE, max.imf=10, plot.imf=FALSE, interm=NULL, weight=NULL)

Arguments

xt

observation or signal observed at time tt

tt

observation index or time index

tol

tolerance for stopping rule of sifting. If stoprule=type5, the number of iteration for S stoppage criterion.

max.sift

the maximum number of sifting

stoprule

stopping rule of sifting. The type1 stopping rule indicates that absolute values of envelope mean must be less than the user-specified tolerance level in the sense that the local average of upper and lower envelope is zero. The stopping rules type2, type3, type4 and type5 are the stopping rules given by equation (5.5) of Huang et al. (1998), equation (11a), equation (11b) and S stoppage of Huang and Wu (2008), respectively.

boundary

specifies boundary condition from “none", “wave", “symmetric", “periodic" or “evenodd". See Zeng and He (2004) for evenodd boundary condition.

sm

specifies whether envelop is constructed by interpolation, spline smoothing, kernel smoothing, or local polynomial smoothing. Use “none" for interpolation, “spline" for spline smoothing, “kernel" for kernel smoothing, or “locfit" for local polynomial smoothing. See Kim et al. (2012) for detalis.

smlevels

specifies which level of the IMF is obtained by smoothing other than interpolation.

spar

specifies user-supplied smoothing parameter of spline smoothing, kernel smoothing, or local polynomial smoothing.

alpha

deprecated.

check

specifies whether the sifting process is displayed. If check=TRUE, click the plotting area to start the next step.

max.imf

the maximum number of IMF's

plot.imf

specifies whether each IMF is displayed. If plot.imf=TRUE, click the plotting area to start the next step.

interm

specifies vector of periods to be excluded from the IMF's to cope with mode mixing.

weight

deprecated.

Details

This function performs empirical mode decomposition.

Value

imf

IMF's

residue

residue signal after extracting IMF's from observations xt

nimf

the number of IMF's

References

Huang, N. E., Shen, Z., Long, S. R., Wu, M. L. Shih, H. H., Zheng, Q., Yen, N. C., Tung, C. C. and Liu, H. H. (1998) The empirical mode decomposition and Hilbert spectrum for nonlinear and nonstationary time series analysis. Proceedings of the Royal Society London A, 454, 903–995.

Huang, N. E. and Wu, Z. (2008) A review on Hilbert-Huang Transform: Method and its applications to geophysical studies. Reviews of Geophysics, 46, RG2006.

Kim, D., Kim, K.-O. and Oh, H.-S. (2012) Extending the Scope of Empirical Mode Decomposition using Smoothing. EURASIP Journal on Advances in Signal Processing, 2012:168, doi: 10.1186/1687-6180-2012-168.

Zeng, K and He, M.-X. (2004) A simple boundary process technique for empirical mode decomposition. Proceedings of 2004 IEEE International Geoscience and Remote Sensing Symposium, 6, 4258–4261.

See Also

extrema, extractimf.

Examples

### Empirical Mode Decomposition
ndata <- 3000
tt2 <- seq(0, 9, length=ndata)
xt2 <- sin(pi * tt2) + sin(2* pi * tt2) + sin(6 * pi * tt2)  + 0.5 * tt2

try <- emd(xt2, tt2, boundary="wave")

### Ploting the IMF's
par(mfrow=c(try$nimf+1, 1), mar=c(2,1,2,1))
rangeimf <- range(try$imf)
for(i in 1:try$nimf) {
    plot(tt2, try$imf[,i], type="l", xlab="", ylab="", ylim=rangeimf,
    main=paste(i, "-th IMF", sep="")); abline(h=0)
}
plot(tt2, try$residue, xlab="", ylab="", main="residue", type="l", axes=FALSE); box()