wd.object {wavethresh} | R Documentation |
These are objects of class "wd" They represent a decomposition of a function with respect to a wavelet basis.
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.
The following components must be included in a legitimate wd
object.
C |
a 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$first.last.c determines exactly where each
level is stored in the vector.Usually, accessC should be used to extract C
components.
|
D |
wavelet coefficients. If you were to write down the discrete
wavelet transform of a function, then these D would be the
coefficients of the wavelet basis functions. Like the C, they are
also formed in a pyramidal manner, but stored in a linear array.
The storage details are to be found in fl.dbase$first.last.d .Usually, accessD should be used to extract D
components.
|
nlevels |
The number of resolution levels in the pyramidal decomposition that produces
the coefficients. Therefore, 2^nlevels = 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,..., m-1), and m+1 levels of smoothed data
(indexed 0,1,2,...{},m).
|
fl.dbase |
The 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.
|
filter |
a list containing the details of the filter that did the decomposition |
bc |
how the boundaries were handled |
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
The "wd"
class of objects has methods for the following generic
functions:
plot
, threshold
, summary
, print
, draw
.
Release 2.2 Copyright Guy Nason 1993
wd
for examples and background.