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accessC.wd

Get smoothed data from wavelet object (wd).

DESCRIPTION

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(wdobj, level=wdobj$levels, boundary=F)

REQUIRED ARGUMENTS

wdobj: Wavelet decomposition object from which you wish to extract the smoothed or original data if the object is from a wavelet decomposition, or the reconstructed data if the object is from a wavelet reconstruction.

OPTIONAL ARGUMENTS

level: The level that you wish to extract. By default, this is the level with most detail (in the case of objects from a decomposition this is the original data, in the case of structures from a reconstruction this is the top-level reconstruction).
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.

VALUE

A vector of the extracted data.

DETAILS

The wd (wr.wd) 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(wdobj, level=m)

pulls out the original data, as does

> accessC.wd(wdobj)

To get hold of lower levels just specify the level that you're interested in, e.g.

> accessC.wd(wdobj, 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 an wd object, in particular the array

fl.dbase$first.last.c

which gives a complete specification of index numbers and offsets for

wd.object$C.

Note that this function is method for the generic function accessC. When the wd object is definitely a wd class object then you only need use the generic version of this function.

Note also that this function only gets information from wd class objects. To insert coefficients into wd objects you have to use the putC function (or more precisely, the putC.wd method).

RELEASE

REFERENCES

Mallat, S. G. (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence. 11, 674--693.

Nason, G. P. and Silverman, B. W. (1994). The discrete wavelet transform in S. Journal of Computational and Graphical Statistics, 3, 163--191.

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))