emd: Empirical Mode Decomposition

In EMD: Empirical Mode Decomposition and Hilbert Spectral Analysis

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()

Example output

Loading required package: fields
Loading required package: spam
Loading required package: grid
Spam version 1.4-0 (2016-08-29) is loaded.
Type 'help( Spam)' or 'demo( spam)' for a short introduction 
and overview of this package.
Help for individual functions is also obtained by adding the
suffix '.spam' to the function name, e.g. 'help( chol.spam)'.

Attaching package: 'spam'

The following objects are masked from 'package:base':

    backsolve, forwardsolve

Loading required package: maps
Loading required package: locfit
locfit 1.5-9.1 	 2013-03-22

EMD documentation built on Jan. 4, 2022, 1:08 a.m.