TITLE(accessC @@ Get smoothed data from wavelet structure. )
The smoothed and original data from a wavelet decomposition structure
(returned from wd) are packed into a single vector in that structure.
This function extracts the data corresponding to a particular resolution level.
USAGE(
accessC(wd.structure, level=wd.structure\$levels, boundary=F)
)
ARGUMENTS(
ARG(wd.structure@@)
Wavelet decomposition structure from which you wish to extract the
smoothed or original data if the structure is from a wavelet decomposition,
or the reconstructed data if the structure is from a wavelet reconstruction.
ARG(level@@)
The level that you wish to extract. By default, this is the level with
most detail (in the case of structures from a decomposition this is the
original data, in the case of structures from a reconstruction this is the
top-level reconstruction).
ARG(boundary@@)
If this argument is T then all of the boundary correction values
will be returned as well (note: the length of the returned vector
may not be a power of 2). If boundary is false, then just the
coefficients will be returned. If the decomposition (or reconstruction)
was done with periodic boundary conditions then this option has
no effect.
)
PARA BOLD(VALUE)
A vector of the extracted data.
The wd (wr) function produces a wavelet decomposition (reconstruction)
structure.
For decomposition, the top level contains the original data, and
subsequent lower levels contain the successively smoothed data.
So if there are 2^m original data points, there will be m+1 levels
indexed 0,1,...,m. So
> accessC(wd.structure, level=m)
pulls out the original data, as does
> accessC(wd.structure)
To get hold of lower levels just specify the level that you're interested
in, e.g.
> accessC(wd.structure, level=2)
Gets hold of the second level.
For reconstruction, the top level contains the ultimate step in the
Mallat pyramid reconstruction algorithm, lower levels are intermediate
steps.
The need for this function is a consequence of the pyramidal structure
of Mallat's algorithm and the memory efficiency gain achieved by
storing the pyramid as a linear vector. AccessC obtains information about
where the smoothed data appears from the fl.dbase component of
wd.structure, in particular the array fl.dbase\$first.last.c which
gives a complete specification of index numbers and offsets for
wd.structure\$C.
Note that this and the accessD function only work with objects of class
'wd'.
Note also that this function only gets information from 'wd' class
objects. To put coefficients etc. into LANG(wd) structures you have to
use the "putC" function.
PARA BOLD(RELEASE)
Release 2.2
Copyright Guy Nason 1993
PARA BOLD(REFERENCES)
Any book on wavelets, especially
Chui, C. K. (1992)
An Introduction to Wavelets.
Academic Press, London.
Daubechies, I. (1988)
Orthonormal bases of compactly supported wavelets
Communications on Pure and Applied Mathematics, Vol. 41, 909-996
Mallat, S. G. (1989)
A theory for multiresolution signal decomposition: the wavelet representation
IEEE Transactions on Pattern Analysis and Machine Intelligence.
Vol. 11, Number 7 674-693.
PARA BOLD(SEE ALSO)
LANG(wr), LANG(wd), LANG(accessD), LANG(filter.select), LANG(plot.coefs), LANG(dyn.load)
LANG(hard.threshold), LANG(soft.threshold), LANG(putC), LANG(putD), LANG(draw)
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PARA BOLD( )
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EXAMPLES(
#
# Get the 3rd level of smoothed data from a decomposition
#
> accessC(wd(data), level=3)
#
# Plot the time series from a reconstruction
#
> tsplot(accessC(reconstruction))
)
PARA ITALIC(File automatically converted from S(-PLUS) help format)
