brainwaver (version 1.6)

wave.trans: Computation of the wavelet transform

Description

Uses the wavelet decomposition implemented by Whitcher in the library waveslim. See all the details there.

Usage

wave.trans(x, method = "modwt", wf = "la8", n.levels = 4, boundary = "periodic")

Arguments

x

original vector to be decomposed

method

wavelet decomposition to be used, algorithm implemented in the waveslim package (Whitcher, 2000). By default, the Maximal Overlap Discrete Wavelet Transform is used "modwt". It is also possible to use the classical Discrete Wavelet Transform "dwt".

wf

name of the wavelet filter to use in the decomposition. By default this is set to "la8", the Daubechies orthonormal compactly supported wavelet of length $L=8$ (Daubechies, 1992), least asymmetric family.

n.levels

specifies the depth of the decomposition. This must be a number less than or equal to $log(length(x),2)$.

boundary

Character string specifying the boundary condition. If boundary=="periodic" the default, then the vector you decompose is assumed to be periodic on its defined interval, if boundary=="reflection", the vector beyond its boundaries is assumed to be a symmetric reflection of itself.

Value

Object of class "modwt", basically, a list with the following components

d?

Wavelet coefficient vectors.

s?

Scaling coefficient vector.

wavelet

Name of the wavelet filter used.

boundary

How the boundaries were handled.

Details

See the library package waveslim (Whitcher, 2000).

References

R. Gencay, F. Selcuk and B. Whitcher (2001) An Introduction to Wavelets and Other Filtering Methods in Finance and Economics, Academic Press.

D. B. Percival and A. T. Walden (2000) Wavelet Methods for Time Series Analysis, Cambridge University Press.

Examples

data(brain) # the result brain is a matrix
brain<-as.matrix(brain)

# WARNING : To process only the first five regions
brain<-brain[,1:5]

PreCG.R<-brain[,1]
# LA(8)
PreCG.R.la8 <- wave.trans(PreCG.R, wf="la8")
names(PreCG.R.la8) <- c("w1", "w2", "w3", "w4", "v4")
## plot partial MODWT for PreCG.R data
par(mfcol=c(6,1), pty="m", mar=c(5-2,4,4-2,2))
plot.ts(PreCG.R, axes=FALSE, ylab="", main="(a)")
for(i in 1:5)
  plot.ts(PreCG.R.la8[[i]], axes=FALSE, ylab=names(PreCG.R.la8)[i])
axis(side=1, at=seq(0,518,by=50),
  labels=c(0,"",100,"",200,"",300,"",400,"",500))