emddenoise function

Denoising by EMD and Thresholding

This function performs denoising by empirical mode decomposition and thresholding.

emddenoise(xt, tt = NULL, cv.index, cv.level, cv.tol = 0.1^3, 
    cv.maxiter = 20, by.imf = FALSE, emd.tol = sd(xt) * 0.1^2, 
    max.sift = 20, stoprule = "type1", boundary = "periodic", 
    max.imf = 10)

Arguments

• xt: observation or signal observed at time tt
• tt: observation index or time index
• cv.index: test dataset index according to cross-validation scheme
• cv.level: levels to be thresholded
• cv.tol: tolerance for the optimization step of cross-validation
• cv.maxiter: maximum iteration for the optimization step of cross-validation
• by.imf: specifies whether shrinkage is performed by each IMS or not.
• emd.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.
• max.imf: the maximum number of IMF's

Details

This function performs denoising by empirical mode decomposition and cross-validation. See Kim and Oh (2006) for details.

Returns

• dxt: denoised signal

• optlambda: threshold values by cross-validation

• lambdaconv: sequence of lambda's by cross-validation

• perr: sequence of prediction error by cross-validation

• demd: denoised IMF's and residue

• niter: the number of iteration for optimal threshold value

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. and Oh, H.-S. (2006) Hierarchical Smoothing Technique by Empirical Mode Decomposition (Korean). The Korean Journal of Applied Statistics, 19 , 319--330.

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

cvtype, emd.

Examples

ndata <- 1024
tt <- seq(0, 9, length=ndata)
meanf <- (sin(pi*tt) + sin(2*pi*tt) + sin(6*pi*tt)) * (0.0<tt & tt<=3.0) + 
 (sin(pi*tt) + sin(6*pi*tt)) * (3.0<tt & tt<=6.0) +
 (sin(pi*tt) + sin(6*pi*tt) + sin(12*pi*tt)) * (6.0<tt & tt<=9.0)
snr <- 3.0
sigma <- c(sd(meanf[tt<=3]) / snr, sd(meanf[tt<=6 & tt>3]) / snr, 
sd(meanf[tt>6]) / snr)
set.seed(1)
error <- c(rnorm(sum(tt<=3), 0, sigma[1]), 
rnorm(sum(tt<=6 & tt>3), 0, sigma[2]), rnorm(sum(tt>6), 0, sigma[3]))
xt <- meanf + error 

cv.index <- cvtype(n=ndata, cv.kfold=2, cv.random=FALSE)$cv.index 

## Not run:

try10 <- emddenoise(xt, cv.index=cv.index, cv.level=2, by.imf=TRUE)

par(mfrow=c(2, 1), mar=c(2, 1, 2, 1))
plot(xt, type="l", main="noisy signal")
lines(meanf, lty=2)
plot(try10$dxt, type="l", main="denoised signal")
lines(meanf, lty=2)
## End(Not run)