Computes the discrete wavelet transform coefficients for a univariate or multivariate time series.
dwt(X, filter="la8", n.levels, boundary="periodic", fast=TRUE)
A univariate or multivariate time series. Numeric vectors, matrices and data frames are also accepted.
Either a wt.filter
object, a character string
indicating which wavelet filter to use in the decomposition, or a
numeric vector of wavelet coefficients (not scaling coefficients). See
help(wt.filter)
for acceptable filter names.
An integer specifying the level of the decomposition. By default this is the value J such that the length of \(X\) is at least as great as the length of the level \(J\) wavelet filter, but less than the length of the level \(J+1\) wavelet filter. Thus, \(J \le \log{(\frac{N-1}{L-1}+1)}\), where \(N\) is the length of \(X\).
A character string indicating which boundary method to
use. boundary = "periodic"
and boundary = "reflection"
are the only supported methods at this time.
A logical flag which, if true, indicates that the pyramid algorithm is computed with an internal C function. Otherwise, only R code is used in all computations.
Returns an object of class dwt
, which is an S4 object with
slots
A list with element \(i\) comprised of a matrix containing the \(i\)th level wavelet coefficients.
A list with element \(i\) comprised of a matrix containing the \(i\)th level scaling coefficients.
A wt.filter
object containing information for
the filter used in the decomposition. See help(wt.filter)
for
details.
An integer value representing the level of wavelet decomposition.
A numeric vector indicating the number of boundary coefficients at each level of the decomposition.
A character string indicating the boundary method used in the decomposition. Valid values are "periodic" or "reflection".
The original time series, X
, in matrix format.
A character string indicating the class of the input
series. Possible values are "ts"
, "mts"
,
"numeric"
, "matrix"
, or "data.frame"
.
A list containing the attributes information of the
original time series, X
. This is useful if X
is an
object of class ts
or mts
and it is desired to retain
relevant time information. If the original time series, X
, is
a matrix or has no attributes, then attr.X
is an empty list.
A logical value indicating whether the wavelet and
scaling coefficients have been phase shifted so as to be aligned
with relevant time information from the original series. The value
of this slot is initially FALSE and can only be changed to TRUE via
the align
function, with the dwt
object as input.
A logical value indicating whether the center of energy
method was used in phase alignement of the wavelet and scaling
coefficients. By default, this value is FALSE (and will always be
FALSE when aligned
is FALSE) and will be set to true if the
dwt
object is phase shifted via the align
function and
center of energy method.
The discrete wavelet transform is computed via the pyramid
algorithm, using pseudocode written by Percival and Walden (2000),
pp. 100-101. When boundary="periodic"
the resulting wavelet and
scaling coefficients are computed without making changes to the
original series - the pyramid algorithm treats X
as if it is
circular. However, when boundary="reflection"
a call is made to
extend.series
, resulting in a new series which is reflected to
twice the length of the original series. The wavelet and scaling
coefficients are then computed by using a periodic boundary condition
on the reflected sereis, resulting in twice as many wavelet and
scaling coefficients at each level.
Percival, D. B. and A. T. Walden (2000) Wavelet Methods for Time Series Analysis, Cambridge University Press.
# NOT RUN {
# obtain the two series listed in Percival and Walden (2000), page 42
X1 <- c(.2,-.4,-.6,-.5,-.8,-.4,-.9,0,-.2,.1,-.1,.1,.7,.9,0,.3)
X2 <- c(.2,-.4,-.6,-.5,-.8,-.4,-.9,0,-.2,.1,-.1,.1,-.7,.9,0,.3)
# combine them and compute DWT
newX <- cbind(X1,X2)
wt <- dwt(newX, n.levels=3, boundary="reflection", fast=FALSE)
# }
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