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filter.select

Provide wavelet filter coefficients.

DESCRIPTION

This function stores the filter coefficients necessary for doing a discrete wavelet transform (and its inverse).

USAGE

filter.select(filter.number, family="DaubExPhase", constant=1)

REQUIRED ARGUMENTS

filter.number: This selects the desired filter, an integer that takes a value dependent upon the family that you select.

OPTIONAL ARGUMENTS

family: This selects the basic family that the wavelet comes from. The choices are DaubExPhase for Daubechies' extremal phase wavelets, DaubLeAsymm for Daubechies' ``least-asymmetric'' wavelets, Lawton for Lawton's complex-valued wavelets, LittlewoodPaley for a bad approximation to Littlewood-Paley wavelets.
constant: This constant is applied as a multiplier to all the coefficients. It can be a vector, and so you can adapt the filter coefficients to be whatever you want. (This is feature of negative utility, or ``there is less to this than meets the eye'' as my old PhD supervisor would say [GPN]).

VALUE

A list is returned with four components describing the filter:

H: A vector containing the filter coefficients.
G: A vector containing filter coefficients (if Lawton wavelets are selected, otherwise this is NULL).
name: A character string containing the name of the filter.
family: A character string containing the family of the filter.
filter.number The filter number used to select the filter from within a family.

DETAILS

This function contains at least three types of filter. Two types can be selected with family set to DaubExPhase, these wavelets are the Haar wavelet (selected by filter.number=1 within this family) and Daubechies ``extremal phase'' wavelets selected by filter.numbers ranging from 2 to 10). Setting family to DaubLeAsymm gives you Daubechies least asymmetric wavelets, but here the filter number ranges from 4 to 10. For Daubechies wavelets, filter.number corresponds to the N of that paper, the wavelets become more regular as the filter.number increases, but they are all of compact support.

Setting family equal to ``Lawton'' chooses complex-valued wavelets. The only wavelet available is the one with ``filter.number'' equal to 3.

The function compare.filters can be used to compare two filters.

The function support computes the support of compactly supported wavelets.

NOTE

The (Daubechies) filter coefficients should always sum to sqrt(2). This is a useful check on their validity.

RELEASE

EXAMPLES

This function is usually called by others. However, on occasion you may wish to look at the coefficients themselves.

#
# look at the filter coefficients for N=4 (by default Daubechies'
# least-asymmetric wavelets.)
#
> filter.select(4)
$H:
[1] -0.07576571 -0.02963553  0.49761867  0.80373875  0.29785780
[6] -0.09921954 -0.01260397  0.03222310

$G:
NULL

$name:
[1] "Daub cmpct on least asymm N=4"

$family:
[1] "DaubLeAsymm"

$filter.number:
[1] 4