# dwt

##### Discrete Wavelet Transform

Computes the discrete wavelet transform coefficients for a univariate or multivariate time series.

- Keywords
- ts

##### Usage

`dwt(X, filter="la8", n.levels, boundary="periodic", fast=TRUE)`

##### Arguments

- X
A univariate or multivariate time series. Numeric vectors, matrices and data frames are also accepted.

- filter
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.- n.levels
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 \(X\).

- boundary
A character string indicating which boundary method to use.

`boundary = "periodic"`

and`boundary = "reflection"`

are the only supported methods at this time.- fast
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.

##### Details

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.

##### Value

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.

##### References

Percival, D. B. and A. T. Walden (2000) *Wavelet Methods for Time
Series Analysis*, Cambridge University Press.

##### See Also

##### Examples

```
# 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)
# }
```

*Documentation reproduced from package wavelets, version 0.3-0.1, License: GPL (>= 2)*