TITLE(accessD @@ Get wavelet expansion coefficients from wavelet structure. )
The coefficients from a wavelet expansion in a wavelet decomposition structure
(returned from wd or wr) are packed into a single vector in that structure.
This function extracts the coefficients
corresponding to a particular resolution level.
USAGE(
accessD(wd.structure, level, boundary=F)
)
ARGUMENTS(
ARG(wd.structure@@)
Wavelet decomposition structure from which you wish to extract the
expansion coefficients.
ARG(level@@)
The level that you wish to extract. If the "original" data has
2^m data points then there are m possible levels that you could want
to access, indexed by 0,1,...,(m-1).
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 using periodic boundary handling then this option has no
effect.
)
PARA BOLD(VALUE)
A vector of the extracted coefficients. 
The wd (wr) function produces a wavelet decomposition (reconstruction)
structure.
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. AccessD obtains information about
where the coefficients appear from the fl.dbase component of
wd.structure, in particular the array fl.dbase\$first.last.d which
gives a complete specification of index numbers and offsets for
wd.structure\$D.
Note that this function and accessC only work on objects of class
LANG(wd). Also, you have to use putD to put wavelet coefficients into a
wd object.
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(accessC), LANG(filter.select), LANG(plot.coefs), LANG(dyn.load)
LANG(hard.threshold), 'soft.threshold', LANG(putC), LANG(putD), LANG(draw)
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PARA BOLD( )
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EXAMPLES(
#
# Get the 3rd level coefficients of a decomposition
#
> accessD(wd(data), level=3)
#
# Do a qqnorm plot to assess the normality of some coefficients
#
> qqnorm(accessD(wd(data), level=8))
)
PARA ITALIC(File automatically converted from S(-PLUS) help format)
