wr.wd {wavethresh} | R Documentation

## Wavelet reconstruction for wd class objects (inverse discrete wavelet transform).

### Description

This function performs the reconstruction stage of Mallat's pyramid algorithm (Mallat 1989), i.e. the discrete inverse wavelet transform. The actual transform is performed by some C code, this is dynamically linked into S (if your machine can do this).

### Usage

    wr.wd(wd, start.level = 0, verbose = FALSE, bc = wd$bc,
            return.object = FALSE, filter.number = wd$filter$filter.number,
            family = wd$filter$family, ...)

### Arguments

`wd` | A wavelet decomposition object as returned by `wd`, and described in the help for that function and the help for `wd.object`.
`start.level` | The level you wish to start reconstruction at. The is usually the first (level 0). This argument is ignored for a wd object computed using the ``wavelets on the interval'' transform (i.e. using the `bc="interval"` option of `wd`.
`verbose` | Controls the printing of "informative" messages whilst the computations progress. Such messages are generally annoying so it is turned off by default.
`bc` | The boundary conditions used. Usually these are determined by those used to create the supplied wd object, but you sometimes change them with possibly silly results.
`filter.number` | The filter number of the wavelet used to do the reconstruction. Again, as for bc, you should probably leave this argument alone. Ignored if the bvc component of the `wd` object is "`interval`".
`family` | The type of wavelet used to do the reconstruction. You can change this argument from the default but it is probably NOT wise. Ignored if the bvc component of the `wd` object is "`interval`".
`return.object` | If this is F then the top level of the reconstruction is returned (this is the reconstructed function at the highest resolution). Otherwise if it is T the whole wd reconstructed object is returned. Ignored if the `bvc` component of the `wd` object is "`interval`".
`...` | any other arguments

### Details

The code implements Mallat's inverse pyramid algorithm. In the reconstruction the quadrature mirror filters G and H are supplied with c0 and d0, d1, ... d(m- 1) (the wavelet coefficients) and rebuild c1,..., cm.

If the `bc` component of the `wd` object is "`interval`" then the `wr.int` function which implements the inverse ``wavelet on the interval'' transform due to Cohen, Daubechies and Vial, 1993 is used instead.

### Value

Either a vector containing the top level reconstruction or an object of class wd containing the results of the reconstruction, details to be found in help for `wd.object`.

### RELEASE

Version 3 Copyright Guy Nason 1994 Integration of ``wavelets on the interval'' code by Piotr Fryzlewicz and Markus Monnerjahn was at Version 3.9.6, 1999.

### See Also

`wd`, `wr.int`, `accessC`, `accessD`, `filter.select`, `plot.wd`, `threshold`

### Examples

    #
    # Take the wd object generated in the examples to wd (called wds)
    #
    # Invert this wd object
    #
    #yans <- wr(wds)
    #
    # Compare it to the original, called y
    #
    #sum((yans-y)^2)
    #[1] 9.805676e-017
    #
    # A very small number
    #

[Package wavethresh version 4.0-2 Index]