getpacket.wst

Get packet of coefficients from a packet ordered non-decimated wavelet object (wst).

DESCRIPTION

USAGE

getpacket.wst(wst, level, index, type="D")

REQUIRED ARGUMENTS

wst

Packet-ordered non-decimated wavelet object from which you wish to extract the packet from.

level

The resolution level of the coefficients that you wish to extract.

index

The index number within the resolution level of the packet of coefficients that you wish to extract.

OPTIONAL ARGUMENTS

type

This argument must be either "C" or "D". If the argument is "C" then non-decimated father wavelet coefficients corresponding to the packet that you want are returned. If the argument is "D" then non-decimated mother wavelet coefficients are returned.

VALUE

A vector containing the packet of packet-ordered non-decimated wavelet coefficients that you wished to extract.

DETAILS

The wst function produces a packet-ordered non-decimated wavelet object: wst. The coefficients in this structure can be organised into a binary tree with each node in the tree containing a packet of coefficients.

Each packet is obtained by repeated application of the usual DG quadrature mirror filter with both even and odd dyadic decimation. See the detailed description given in Nason and Silverman, 1995.

This function enables whole packets of coefficients to be extracted at any resolution level. The index argument chooses a particular packet within each level and thus ranges from 0 to 2^{J-j} for j=0,..., J-1. Each packet corresponds to the wavelet coefficients with respect to different origins.

Note that both mother and father wavelet coefficient at different shifts are available by using the type argument.

RELEASE

Version 3.9 Copyright Guy Nason 1998

SEE ALSO

wst, wst object,

EXAMPLES

#
# Take the packet-ordered non-decimated transform of some random data 
#
> MyWST <- wst(rnorm(1:512))
#
# The above data set was 2^9 in length. Therefore there are
# coefficients at resolution levels 0, 1, 2, ..., and 8.
#
# The high resolution coefficients are at level 8.
# There should be 256 coefficients at level 8 in index location 0 and 1.
#
> length(getpacket(MyWST, level=8, index=0))
[1] 256
> length(getpacket(MyWST, level=8, index=1))
[1] 256
#
# There are also 256 FATHER wavelet coefficients at each of these two indices
# (origins)
#
> length(getpacket(MyWST, level=8, index=0, type="C"))
[1] 256
> length(getpacket(MyWST, level=8, index=1, type="C"))
[1] 256
#
# There should be 4 coefficients at resolution level 2
#
> getpacket(MyWST, level=2, index=0)
[1] -0.92103095  0.70125471  0.07361174 -0.43467375
#
# Here are the equivalent father wavelet coefficients
#
> getpacket(MyWST, level=2, index=0, type="C")
[1] -1.8233506 -0.2550734  1.9613138  1.2391913