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wst objects

(Packet ordered) Nondecimated wavelet transform decomposition objects.

DESCRIPTION

These are objects of class

wst

They represent a decomposition of a function with respect to a set of (all possible) shifted wavelets.

GENERATION

This class of objects is returned from the wst function which computes the packets-ordered non-decimated wavelet transform (effectively all possible shifts of the standard discrete wavelet transform).

Many other functions return an object of class wst.

METHODS

The wst class of objects has methods for the following generic functions: AvBasis, InvBasis, LocalSpec, MaNoVe, accessC, accessD, convert draw. getpacket. image. nlevels nullevels, plot, print, putC, putD, putpacket, summary, threshold.

INHERITANCE

None (yet).

STRUCTURE

The following components must be included in a legitimate `wst' object.

wp: a matrix containing the packet ordered non-decimated wavelet coefficients. Each row of the matrix contains coefficients with respect to a particular resolution level. There are nlevels(wst)+1 rows in the matrix. Row nlevels(wst)+1 (the ``bottom'') row contains the ``original'' data used to produce the wavelet packet coefficients. Rows nlevels(wst) to row 1 contain coefficients at resolution levels nlevels(wst)-1 to 0 (so the first row contains coefficients at resolution level 0).
The columns contain the coefficients with respect to packets. A different packet length exists at each resolution level. The packet length at resolution level i is given by 2^i. However, the getpacket.wst function should be used to access individual packets from a wst object.
Carray: A matrix of the same dimensions and format as wp but containing the father wavelet coefficients.
nlevels: The number of levels in the decomposition. If you raise 2 to the power of nlevels you get the number of data points used in the decomposition.
filter: a list containing the details of the filter that did the decomposition (equivalent to the return value from the filter.select function).
date: The date that the transform was performed or the wst was modified.

DETAILS

To retain your sanity we recommend that the coefficients from a wst object be extracted in one of two ways:

use getpacket.wst to obtain individual packets of either father or mother wavelet coefficients.
use accessD.wst to obtain all mother coefficients at a particular resolution level.
use accessC.wst to obtain all father coefficients at a particular resolution level.

You can obtain the coefficients directly from the wst$wp component (mother) or wst$Carray component (father) but you have to understand their organization described above.