accessC.wd: Get smoothed data from wavelet object (wd)

In wavethresh: Wavelets Statistics and Transforms

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

## S3 method for class 'wd'
accessC(wd, level = nlevelsWT(wd), boundary=FALSE, aspect, ...)

Arguments

wd	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.
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).
boundary	logical; if TRUE 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, this option has no effect.
aspect	Applies a function to the coefficients before return. Supplied as a text string which gets converted to a function. For example, "Mod" for complex-valued arguments
...	any other arguments

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

Value

A vector of the extracted data.

RELEASE

Version 3.5.3 Copyright Guy Nason 1994

Author(s)

G P Nason

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.

See Also

wr, wd, accessD, accessD.wd, filter.select, threshold, putC.wd, putD.wd.

Examples

## Get the 3rd level of smoothed data from a decomposition
dat <- rnorm(64)
accessC(wd(dat), level=3)

wavethresh documentation built on Nov. 16, 2022, 5:16 p.m.