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\name{wst}
\alias{wst}
\title{Packet-ordered non-decimated wavelet transform.}
\description{
Computes the packet-ordered non-decimated wavelet transform (TI-transform). This algorithm is functionally equivalent to the time-ordered non-decimated wavelet transform (computed by \code{\link{wd}} with the \code{type="station"} argument).
}
\usage{
wst(data, filter.number=10, family="DaubLeAsymm", verbose=FALSE)
}
\arguments{
\item{data}{A vector containing the data you wish to decompose. The length of this vector must be a power of 2.}
\item{filter.number}{This selects the smoothness of wavelet that you want to use in the decomposition. By default this is 10, the Daubechies least-asymmetric orthonormal compactly supported wavelet with 10 vanishing moments.
Note: as of version 4.6 you can use the Lina-Mayrand complex-valued
compactly supported wavelets.
}
\item{family}{specifies the family of wavelets that you want to use. The options are "DaubExPhase" and "DaubLeAsymm".}
\item{verbose}{Controls the printing of "informative" messages whilst the computations progress. Such messages are generally annoying so it is turned off by default.}
}
\details{
The packet-ordered non-decimated wavelet transform is more properly known as the TI-transform described by Coifman and Donoho, 1995. A description of this implementation can be found in Nason and Silverman, 1995.
The coefficients produced by this transform are exactly the same as those produced by the \code{\link{wd}} function with the \code{type="station"} option \emph{except} in that function the coefficients are \emph{time-ordered}. In the \code{wst} function the coefficients are produced by a wavelet packet like algorithm with a \emph{cyclic rotation} step instead of processing with the father wavelet mirror filter at each level.
The coefficients produced by this function are useful in curve estimation problems in conjunction with the thresholding function \code{\link{threshold.wst}} and either of the inversion functions \code{\link{AvBasis.wst}} and \code{\link{InvBasis.wst}} The coefficients produced by the \code{time-ordered non-decimated wavelet transform} are more useful for time series applications: e.g. the evolutionary wavelet spectrum computation performed by \code{\link{ewspec}}.
Note that a time-ordered non-decimated wavelet transform object may be converted into a packet-ordered non-decimated wavelet transform object (and vice versa) by using the \code{\link{convert}} function.
}
\value{
An object of class: \code{\link{wst}}. The help for the \code{\link{wst}} describes the intricate structure of this class of object.
}
\section{RELEASE}{Version 3.5.3 Copyright Guy Nason 1995 }
\seealso{
\code{\link{wst.object}}, \code{\link{threshold.wst}}, \code{\link{AvBasis.wst}}, \code{\link{InvBasis.wst}}, \code{\link{filter.select}}, \code{\link{convert}}, \code{\link{ewspec}}, \code{\link{plot.wst}},
}
\examples{
#
# Let's look at the packet-ordered non-decimated wavelet transform
# of the data we used to do the time-ordered non-decimated wavelet
# transform exhibited in the help page for wd.
#
test.data <- example.1()$y
#
# Plot it to see what it looks like (piecewise polynomial)
#
\dontrun{ts.plot(test.data)}
#
# Now let's do the packet-ordered non-decimated wavelet transform.
#
TDwst <- wst(test.data)
#
# And let's plot it....
#
\dontrun{plot(TDwst)}
#
# The coefficients in this plot at each resolution level are the same
# as the ones in the non-decimated transform plot in the wd
# help page except they are in a different order. For more information
# about how the ordering works in each case see
# Nason, Sapatinas and Sawczenko, 1998.
#
# Next examples
# ------------
# The chirp signal is also another good examples to use.
#
#
# Generate some test data
#
test.chirp <- simchirp()$y
\dontrun{ts.plot(test.chirp, main="Simulated chirp signal")}
#
# Now let's do the packet-ordered non-decimated wavelet transform.
# For a change let's use Daubechies extremal phase wavelet with 6
# vanishing moments (a totally arbitrary choice, please don't read
# anything into it).
#
chirpwst <- wst(test.chirp, filter.number=6, family="DaubExPhase")
\dontrun{plot(chirpwst, main="POND WT of Chirp signal")}
}
\keyword{math}
\keyword{smooth}
\keyword{nonlinear}
\author{G P Nason}
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