wd.object: Wavelet decomposition object (1D)

Description

These are objects of class "wd" They represent a decomposition of a function with respect to a wavelet basis.

Arguments

Value

The following components must be included in a legitimate wd object.
Ca vector containing each level's smoothed data. The wavelet transform works by applying both a smoothing filter and a bandpass filter to the previous level's smoothed data, the top level containing data at the highest resolution level. This the ``pyramid structure of Mallat''. Each of these levels are stored one after the other in this vector. The matrix fl.dbase$first.last.c determines exactly where each level is stored in the vector. Usually, accessC should be used to extract C components.
Dwavelet coefficients. If you were to write down the discrete wavelet transform of a function, then these D would be the coefficients of the wavelet basis functions. Like the C, they are also formed in a pyramidal manner, but stored in a linear array. The storage details are to be found in fl.dbase$first.last.d. Usually, accessD should be used to extract D components.
nlevelsThe number of resolution levels in the pyramidal decomposition that produces the coefficients. Therefore, 2^nlevels$\equiv 2^m$ is the number of data points used in the decomposition. This means there will be $m$ levels of wavelet coefficients (indexed $0,1,2,\dots, m-1$), and $m+1$ levels of smoothed data (indexed $0,1,2,\dots{},m$).
fl.dbaseThe first/last database associated with this decomposition. This is a list consisting of 2 integers, and 2 matrices. The matrices detail how the coefficients are stored in the C and D components of the wd.object.
In the decomposition `extra' coefficients are generated that help take care of the boundary effects, this database lists where these start and finish, so the "true" data can be extracted. See first.last for more information.
filtera list containing the details of the filter that did the decomposition
bchow the boundaries were handled

GENERATION

This class of objects is returned from the wd function to represent a wavelet decomposition of a function. Other functions also return a wd.object

METHODS

The "wd" class of objects has methods for the following generic functions: plot, threshold, summary, print, draw.

RELEASE

Details

To retain your sanity the C and D coefficients should be extracted by the accessC and accessD functions and put using the putC and putD functions, rather than by the $ operator.

Mind you, if you want to muck about with coefficients directly, then you'll have to do it yourself by working out what the fl.dbase list means.