WiSEBoot (version 1.4.0)

SimulatedSNR9Series: Simulated Wavelet Signals with SNR=9

Description

A matrix containing simulated signals with noise added such that the signal-to-noise ratio (SNR) is 9. If the signal vector is called $Y$, and $Y$ is of length $2^J$, we have defined the SNR within the $J0=j$ threshold as $$SNR=(1/2^J)( (/(2^j-1)) / (\sigma^2/(2^J - 2^j -1)))$$ where $\sigma^2$ is the variance of the noise. These series are obtained by adding white noise to the smooth data in SimulatedSmoothSeries. Each column contains a wavelet coefficient threshold level and rows contain observations.

Usage

data("SimulatedSNR9Series")

format

The format is: num [1:1024, 1:9] -0.01879 -0.01635 -0.01096 -0.00814 -0.00423 ... - attr(*, "dimnames")=List of 2 ..$ : NULL ..$ : chr [1:9] "J0.0" "J0.1" "J0.2" "J0.3" ...

Details

The columns contain noisy series with signals in different wavelet coefficient threshold levels. Series are available for signal thresholds of $J0$ in {0, 1, 2, 3, 4, 5, 6, 7, 8}. The rows are the data observations. Thus, each smooth series is of length $2^{10}=1024$. The names of each column indicate the threshold ($J0$) in the smooth series. For example, the 3rd column, named J0.2, has a threshold of $J0=2$ in the signal, and thus 0-valued wavelet coefficients for all mother wavelet coefficients finer than level 2 in the signal. Notice, the white noise added to the signal creates non-zero coefficients above the threshold. The original smooth series were generated using 'wd' and 'wr' with the family="DaubLeAsymm", filter.number=8, bc="periodic" options in the 'wavethresh' package.

References

wavethresh-package, SimulatedSmoothSeries

Examples

data(SimulatedSNR9Series)

##See if WiSEBoot selects the correct threshold for this data (J0=3)
## R=10 bootstrap samples is not recommended.  For demonstration only.
bootObj <- WiSEBoot(SimulatedSNR9Series[,4], R=10)
bootObj$MSECriteria

##Look at the noisy data compared to the true smooth
data(SimulatedSmoothSeries)
plot(seq(1, 2^10), SimulatedSNR9Series[ , 6], main="Threshold of J0=5", 
     col="lightgray", xlab="Time", ylab="Observations", type="l")
lines(seq(1, 2^10), SimulatedSmoothSeries[ ,6], col="red", lwd=2)