Internal EMD Functions

Description

The hilbert, unwrap, C_extrema2dC, extrema2dVC and imageplot.ts are internal EMD functions.

Details

These are not to be called by the user.

Imputation by the mean of the two adjacent values

Description

This function performs imputation by the mean of the two adjacent values for test dataset of cross-validation.

Usage

cvimpute.by.mean(y, impute.index)

Arguments

Details

This function performs imputation by the mean of the two adjacent values for test dataset of cross-validation. See Kim et al. (2012) for detalis.

Value

References

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.

See Also

cvtype, semd.

Generating test dataset index for cross-validation

Description

This function generates test dataset index for cross-validation.

Usage

cvtype(n, cv.bsize=1, cv.kfold, cv.random=FALSE)

Arguments

Details

This function provides index of test dataset according to various cross-validation scheme. One may construct K test datasets in a way that each testset consists of blocks of b consecutive data. Set cv.bsize = b for this. To select each fold at random, set cv.random = TRUE. See Kim et al. (2012) for detalis.

Value

matrix of which row is test dataset index for cross-validation

References

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.

Examples

# Traditional 4-fold cross-validation for 100 observations
cvtype(n=100, cv.bsize=1, cv.kfold=4, cv.random=FALSE)
# Random 4-fold cross-validation with block size 2 for 100 observations
cvtype(n=100, cv.bsize=2, cv.kfold=4, cv.random=TRUE)

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

Details

This function performs empirical mode decomposition.

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., 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()

Prediction by EMD and VAR model

Description

This function calculates prediction values and confidence limits using EMD and VAR (vector autoregressive) model.

Usage

emd.pred(varpred, trendpred, ci = 0.95, figure = TRUE) 

Arguments

Details

This function calculates prediction values and confidence limits using EMD and VAR (vector autoregressive) model. See Kim et al. (2008) for detalis.

Value

References

Kim, D, Paek, S.-H. and Oh, H.-S. (2008) A Hilbert-Huang Transform Approach for Predicting Cyber-Attacks. Journal of the Korean Statistical Society, 37, 277–283, doi:10.1016/j.jkss.2008.02.006.

Bidimenasional Empirical Mode Decomposition

Description

This function performs the bidimenasional empirical mode decomposition utilizing extrema detection based on the equivalence relation between neighboring pixels.

Usage

emd2d(z, x = NULL, y = NULL, tol = sd(c(z)) * 0.1^2, max.sift = 20, 
    boundary = "reflexive", boundperc = 0.3, max.imf = 5, sm = "none", 
    smlevels = 1, spar = NULL, weight = NULL, plot.imf = FALSE) 

Arguments

Details

This function performs the bidimenasional empirical mode decomposition utilizing extrema detection based on the equivalence relation between neighboring pixels. See Kim et al. (2012) for detalis.

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.

Kim, D., Park, M. and Oh, H.-S. (2012) Bidimensional Statistical Empirical Mode Decomposition. IEEE Signal Processing Letters, 19, 191–194, doi: 10.1109/LSP.2012.2186566.

See Also

extrema2dC, extractimf2d.

Examples

data(lena)
z <- lena[seq(1, 512, by=4), seq(1, 512, by=4)]
image(z, main="Lena", xlab="", ylab="", col=gray(0:100/100), axes=FALSE)

## Not run: 
lenadecom <- emd2d(z, max.imf = 4)
imageEMD(z=z, emdz=lenadecom, extrema=TRUE, col=gray(0:100/100))
## End(Not run)

### Test Image
ndata <- 128

x <- y <- seq(0, 9, length=ndata)
meanf1 <- outer(sin(2 * pi * x), sin(2 * pi * y))
meanf2 <- outer(sin(0.5 * pi * x), sin(0.5 * pi * y))
meanf <- meanf1 + meanf2

snr <- 2
set.seed(77)
zn <- meanf + matrix(rnorm(ndata^2, 0, sd(c(meanf))/snr), ncol=ndata)

rangezn <- range(c(meanf1, meanf2, meanf, zn))
par(mfrow=c(2,2), mar=0.1 + c(0, 0.25, 3, 0.25))
image(meanf1, main="high frequency component", xlab="", ylab="", zlim=rangezn, 
    col=gray(100:0/100), axes=FALSE)
image(meanf2, main="low frequency component", xlab="", ylab="", zlim=rangezn, 
    col=gray(100:0/100), axes=FALSE)
image(meanf, main="test image", xlab="", ylab="", zlim=rangezn, col=gray(100:0/100), axes=FALSE)
image(zn, main="noisy image", xlab="", ylab="", zlim=rangezn, col=gray(100:0/100), axes=FALSE)

## Not run: 
out <- emd2d(zn, max.imf=3, sm="locfit", smlevels=1, spar=0.004125)
par(mfcol=c(3,1), mar=0.1 + c(0, 0.25, 0.25, 0.25)) 
image(out$imf[[1]], main="", xlab="", ylab="", col=gray(100:0/100), zlim=rangezn, axes=FALSE)
image(out$imf[[2]], main="", xlab="", ylab="", col=gray(100:0/100), zlim=rangezn, axes=FALSE)
image(out$imf[[3]], main="", xlab="", ylab="", col=gray(100:0/100), zlim=rangezn, axes=FALSE)
## End(Not run)

Denoising by EMD and Thresholding

Description

This function performs denoising by empirical mode decomposition and thresholding.

Usage

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

Details

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

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)

Intrinsic Mode Function

Description

This function extracts intrinsic mode function from given a signal.

Usage

extractimf(residue, tt=NULL, tol=sd(residue)*0.1^2, max.sift=20, 
    stoprule="type1", boundary="periodic", sm="none", spar=NULL, 
    alpha=NULL, check=FALSE, weight=NULL)

Arguments

Details

This function extracts intrinsic mode function from given a signal.

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., 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, emd.

Examples

### Generating a signal
ndata <- 3000
par(mfrow=c(1,1), mar=c(1,1,1,1))
tt2 <- seq(0, 9, length=ndata)
xt2 <- sin(pi * tt2) + sin(2* pi * tt2) + sin(6 * pi * tt2)  + 0.5 * tt2
plot(tt2, xt2, xlab="", ylab="", type="l", axes=FALSE); box()

### Extracting the first IMF by sifting process
tryimf <- extractimf(xt2, tt2, check=FALSE)

Bidimensional Intrinsic Mode Function

Description

This function extracts the bidimensional intrinsic mode function from given an image utilizing extrema detection based on the equivalence relation between neighboring pixels.

Usage

extractimf2d(residue, x=NULL, y=NULL, nnrow=nrow(residue), 
    nncol=ncol(residue), tol=sd(c(residue))*0.1^2, 
    max.sift=20, boundary="reflexive", boundperc=0.3,  
    sm="none", spar=NULL, weight=NULL, check=FALSE)

Arguments

Details

This function extracts the bidimensional intrinsic mode function from given image utilizing extrema detection based on the equivalence relation between neighboring pixels. See Kim et al. (2012) for detalis. See Kim et al. (2012) for detalis.

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.

Kim, D., Park, M. and Oh, H.-S. (2012) Bidimensional Statistical Empirical Mode Decomposition. IEEE Signal Processing Letters, 19, 191–194, doi: 10.1109/LSP.2012.2186566.

See Also

extrema2dC, emd2d.

Examples

data(lena)
z <- lena[seq(1, 512, by=4), seq(1, 512, by=4)]

## Not run: 
lenaimf1 <- extractimf2d(z, check=FALSE)
## End(Not run)

Finding Local Extrema and Zero-crossings

Description

This function indentifies extrema and zero-crossings.

Usage

extrema(y, ndata = length(y), ndatam1 = ndata - 1)

Arguments

Details

This function indentifies extrema and zero-crossings.

Value

See Also

extrema2dC, extractimf, emd.

Examples

y <- c(0, 1, 2, 1, -1, 1:4, 5, 6, 0, -4, -6, -5:5, -2:2)
#y <- c(0, 0, 0, 1, -1, 1:4, 4, 4, 0, 0, 0, -5:5, -2:2, 2, 2)
#y <- c(0, 0, 0, 1, -1, 1:4, 4, 4, 0, 0, 0, -5:5, -2:2, 0, 0)

plot(y, type = "b"); abline(h = 0)
extrema(y)

Finding Local Extrema

Description

This function finds the bidimensional local extrema based on the equivalence relation between neighboring pixels.

Usage

extrema2dC(z, nnrow=nrow(z), nncol=ncol(z))

Arguments

Details

This function finds the bidimensional local extrema based on the equivalence relation between neighboring pixels. See Kim et al. (2012) for detalis.

Value

References

Kim, D., Park, M. and Oh, H.-S. (2012) Bidimensional Statistical Empirical Mode Decomposition. IEEE Signal Processing Letters, 19, 191–194, doi: 10.1109/LSP.2012.2186566.

See Also

extrema, , extractimf2d, emd2d.

Examples

data(lena)
z <- lena[seq(1, 512, by=4), seq(1, 512, by=4)]

par(mfrow=c(1,3), mar=c(0, 0.5, 2, 0.5))
image(z, main="Lena", xlab="", ylab="", col=gray(0:100/100), axes=FALSE)    

example <- extrema2dC(z=z)
localmin <- matrix(256, 128, 128)
localmin[example$minindex] <- z[example$minindex]
image(localmin, main="Local minimum", xlab="", ylab="", col=gray(0:100/100), axes=FALSE)

localmax <- matrix(0, 128, 128)
localmax[example$maxindex] <- z[example$maxindex]
image(localmax, main="Local maximum", xlab="", ylab="", col=gray(0:100/100), axes=FALSE)

Hilbert Transform and Instantaneous Frequency

Description

This function calculates the amplitude and instantaneous frequency using Hilbert transform.

Usage

hilbertspec(xt, tt=NULL, central=FALSE)

Arguments

Details

This function calculates the amplitude and instantaneous frequency using Hilbert transform.

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.

Dasios, A., Astin, T. R. and McCann C. (2001) Compressional-wave Q estimation from full-waveform sonic data. Geophysical Prospecting, 49, 353–373.

See Also

spectrogram.

Examples

tt <- seq(0, 0.1, length = 2001)[1:2000]           
f1 <- 1776; f2 <- 1000
xt <- sin(2*pi*f1*tt) * (tt <= 0.033 | tt >= 0.067) + sin(2*pi*f2*tt)
 
### Before treating intermittence
interm1 <- emd(xt, tt, boundary="wave", max.imf=2, plot.imf=FALSE)  
### After treating intermittence
interm2 <- emd(xt, tt, boundary="wave", max.imf=2, plot.imf=FALSE, 
interm=0.0007)

par(mfrow=c(2,1), mar=c(2,2,2,1))
test1 <- hilbertspec(interm1$imf)
spectrogram(test1$amplitude[,1], test1$instantfreq[,1])

test2 <- hilbertspec(interm2$imf, tt=tt)
spectrogram(test2$amplitude[,1], test2$instantfreq[,1])

Plot of Bidimenasional Empirical Mode Decomposition Result

Description

This function draws plots of input image, IMF's, residue and extrema.

Usage

imageEMD(z = z, emdz, extrema = FALSE, ...)

Arguments

Details

This function draws plots of input image, IMF's, residue and extrema.

Examples

data(lena)
z <- lena[seq(1, 512, by=4), seq(1, 512, by=4)]
image(z, main="Lena", xlab="", ylab="", col=gray(0:100/100), axes=FALSE)

## Not run: 
lenadecom <- emd2d(z, max.imf = 4)
imageEMD(z=z, emdz=lenadecom, extrema=TRUE, col=gray(0:100/100))
## End(Not run)

Korea Stock Price Index 200

Description

the weekly KOSPI 200 index from January, 1990 to February, 2007.

Usage

data(kospi200)

Format

A list of date and KOSPI200 index

Details

See Kim and Oh (2009) for the analysis for kospi200 data using EMD.

References

Kim, D. and Oh, H.-S. (2009) A Multi-Resolution Approach to Non-Stationary Financial Time Series Using the Hilbert-Huang Transform. The Korean Journal of Applied Statistics, 22, 499–513.

Examples

data(kospi200)
names(kospi200)
plot(kospi200$date, kospi200$index, type="l")

Gray Lena image

Description

A 512x512 gray image of Lena.

Usage

data(lena)

Format

A 512x512 matrix.

Examples

data(lena)
image(lena, col=gray(0:100/100), axes=FALSE)

Gray John Lennon image

Description

A 256x256 gray image of John Lennon.

Usage

data(lennon)

Format

A 256x256 matrix.

Examples

data(lennon)
image(lennon, col=gray(100:0/100), axes=FALSE)

Statistical Empirical Mode Decomposition

Description

This function performs empirical mode decomposition using spline smoothing not interpolation for sifting process. The smoothing parameter is automatically detemined by cross-validation.

Usage

semd(xt, tt=NULL, cv.kfold, cv.tol=0.1^1, cv.maxiter=20, 
    emd.tol=sd(xt)*0.1^2, max.sift=20, stoprule="type1", boundary="periodic", 
    smlevels=1, max.imf=10)

Arguments

Details

This function performs empirical mode decomposition using spline smoothing not interpolation for sifting process. The smoothing parameter is automatically detemined by cross-validation. Optimization is done by golden section search. See Kim et al. (2012) for details.

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., 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

extractimf, emd.

Examples

ndata <- 2048
tt <- seq(0, 9, length=ndata)                 
xt <- sin(pi * tt) + sin(2* pi * tt) + sin(6 * pi * tt)  + 0.5 * tt 
set.seed(1)
xt <- xt + rnorm(ndata, 0, sd(xt)/5)

## Not run: 
### Empirical Mode Decomposition by Interpolation
emdbyint <- emd(xt, tt, max.imf = 5, boundary = "wave")
### Empirical Mode Decomposition by Smoothing
emdbysm <- semd(xt, tt, cv.kfold=4, boundary="wave", smlevels=1, max.imf=5)

par(mfcol=c(6,2), mar=c(2,2,2,1), oma=c(0,0,2,0))                              
rangext <- range(xt); rangeimf <- rangext - mean(rangext)
plot(tt, xt, xlab="", ylab="", main="signal", ylim=rangext, type="l")
mtext("Decomposition by EMD", side = 3, line = 2, cex=0.85, font=2)
plot(tt, emdbyint$imf[,1], xlab="", ylab="", main="imf 1", ylim=rangeimf,  type="l")
abline(h=0, lty=2)
plot(tt, emdbyint$imf[,2], xlab="", ylab="", main="imf 2", ylim=rangeimf,  type="l")
abline(h=0, lty=2)
plot(tt, emdbyint$imf[,3], xlab="", ylab="", main="imf 3", ylim=rangeimf,  type="l")
abline(h=0, lty=2)
plot(tt, emdbyint$imf[,4], xlab="", ylab="", main="imf 4", ylim=rangeimf,  type="l")
abline(h=0, lty=2)
plot(tt, emdbyint$imf[,5]+emdbyint$residue, xlab="", ylab="", main="remaining signal",
    ylim=rangext, type="l")

plot(tt, xt, xlab="", ylab="", main="signal", ylim=rangext, type="l")
mtext("Decomposition by SEMD", side = 3, line = 2, cex=0.85, font=2)
plot(tt, emdbysm$imf[,1], xlab="", ylab="", main="noise", ylim=rangeimf,  type="l")
abline(h=0, lty=2)
plot(tt, emdbysm$imf[,2], xlab="", ylab="", main="imf 1", ylim=rangeimf,  type="l")
abline(h=0, lty=2)
plot(tt, emdbysm$imf[,3], xlab="", ylab="", main="imf 2", ylim=rangeimf,  type="l")
abline(h=0, lty=2)
plot(tt, emdbysm$imf[,4], xlab="", ylab="", main="imf 3", ylim=rangeimf,  type="l")
abline(h=0, lty=2)
plot(tt, emdbysm$residue, xlab="", ylab="", main="residue", ylim=rangext, type="l")
## End(Not run)

Solar Irradiance Proxy Data

Description

solar irradiance proxy data.

Hoyt and Schatten (1993) reconstructed solar irradiance (from 1700 through 1997) using the amplitude of the 11-year solar cycle together with a long term trend estimated from solar-like stars. They put relatively more weight on the length of the 11-year cycle.

Lean et al. (1995) reconstructed solar irradiance (from 1610 through 2000) using the amplitude of the 11-year solar cycle and a long term trend estimated from solar-like stars.

10-Beryllium (10Be) is measured in polar ice from 1424 through 1985. 10-Beryllium (10Be) is produced in the atmosphere by incoming cosmic ray flux, which in turn is influenced by the solar activity. The higher the solar activity, the lower the flux of cosmic radiation entering the earth atmosphere and therefore the lower the production rate of 10Be. The short atmospheric lifetime of 10Be of one to two years (Beer et al. 1994) allows the tracking of solar activity changes and offers an alternative way to the sunspot based techniques for the analysis of the amplitude and length of the solar cycle as well as for low frequency variations.

Usage

data(solar.hs)
data(solar.lean)
data(beryllium)

Format

A list of year and solar (solar irradiance proxy data) for solar.hs and solar.lean A list of year and be (10-Beryllium) for beryllium

References

Beer, J., Baumgartner, S., Dittrich-Hannen, B., Hauenstein, J., Kubik, P., Lukasczyk, C., Mende, W., Stellmacher, R. and Suter, M. (1994) Solar variability traced by cosmogenic isotopes. In: Pap, J.M., FrQohlich, C., Hudson, H.S., Solanki, S. (Eds.), The Sun as a Variable Star: Solar and Stellar Irradiance Variations, Cambridge University Press, Cambridge, 291–300.

Beer, J., Mende, W. and Stellmacher, R. (2000) The role of the sun in climate forcing. Quaternary Science Reviews, 19, 403–415.

Hoyt, D. V and, Schatten, K. H. (1993) A discussion of plausible solar irradiance variations, 1700–1992. Journal of Geophysical Research, 98 (A11), 18,895–18,906.

Lean, J. L., Beer, J. and Bradley, R. S. (1995) Reconstruction of solar irradiance since 1610: Implications for climate change. Geophysical Research Letters, 22 (23), 3195–3198.

Oh, H-S, Ammann, C. M., Naveau, P., Nychka, D. and Otto-Bliesner, B. L. (2003) Multi-resolution time series analysis applied to solar irradiance and climate reconstructions. Journal of Atmospheric and Solar-Terrestrial Physics, 65, 191–201.

Examples

data(solar.hs)
names(solar.hs)
plot(solar.hs$year, solar.hs$solar, type="l")

data(solar.lean)
names(solar.lean)
plot(solar.lean$year, solar.lean$solar, type="l")

data(beryllium)
names(beryllium)
plot(beryllium$year, beryllium$be, type="l")

Spectrogram

Description

This function produces image of amplitude by time index and instantaneous frequency. The horizontal axis represents time, the vertical axis is instantaneous frequency, and the color of each point in the image represents amplitude of a particular frequency at a particular time.

Usage

spectrogram(amplitude, freq, tt = NULL, multi = FALSE, 
nlevel = NULL, size = NULL) 

Arguments

Details

This function produces image of amplitude by time index and instantaneous frequency. The horizontal axis represents time, the vertical axis is instantaneous frequency, and the color of each point in the image represents amplitude of a particular frequency at a particular time.

Value

image

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.

See Also

hilbertspec.

Examples

tt <- seq(0, 0.1, length = 2001)[1:2000]           
f1 <- 1776; f2 <- 1000
xt <- sin(2*pi*f1*tt) * (tt <= 0.033 | tt >= 0.067) + sin(2*pi*f2*tt)
 
### Before treating intermittence
interm1 <- emd(xt, tt, boundary="wave", max.imf=2, plot.imf=FALSE)  
### After treating intermittence
interm2 <- emd(xt, tt, boundary="wave", max.imf=2, plot.imf=FALSE, 
interm=0.0007)

par(mfrow=c(2,1), mar=c(2,2,2,1))
test1 <- hilbertspec(interm1$imf)
spectrogram(test1$amplitude[,1], test1$instantfreq[,1])

test2 <- hilbertspec(interm2$imf, tt=tt)
spectrogram(test2$amplitude[,1], test2$instantfreq[,1])

Sunspot Data

Description

sunspot from 1610 through 1995.

Usage

data(sunspot)

Format

A list of year and sunspot

References

Oh, H-S, Ammann, C. M., Naveau, P., Nychka, D. and Otto-Bliesner, B. L. (2003) Multi-resolution time series analysis applied to solar irradiance and climate reconstructions. Journal of Atmospheric and Solar-Terrestrial Physics, 65, 191–201.

Examples

data(sunspot)
names(sunspot)
plot(sunspot$year, sunspot$sunspot, type="l")