# Wolfram Language & System 10.0 (2014)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# InverseWaveletTransform

gives the inverse wavelet transform of a DiscreteWaveletData object dwd.

InverseWaveletTransform[dwd,wave]
gives the inverse transform using the wavelet wave.

InverseWaveletTransform[dwd,wave,wind]
gives the inverse transform from the wavelet coefficients specified by wind.

## Details and OptionsDetails and Options

• InverseWaveletTransform computes the inverse transform of discrete forward transforms such as DiscreteWaveletTransform etc.
• The possible wavelets wave are the same as for the forward wavelet transforms.
• The default wave is Automatic, which is taken to be dwd["Wavelet"].
• The possible specifications for wind are the same as used by DiscreteWaveletData.
• The default wind is Automatic, which is taken to be dwd["BasisIndex"].
• InverseWaveletTransform[dwd,wave,wind] computes the inverse transform using only the wavelet coefficients specified by wind; other coefficients are set to be zero.
• The inverse transform works recursively by computing coefficients with wavelet index from coefficients with wavelet index .
• An explicit wind specification needs to be consistent. A wind specification is consistent if for each that is included no for is included.
• InverseWaveletTransform[dwd,wave,r] can be used to inverse transform the r lowest levels of the wavelet tree.
• The default level r is given by the number of refinement levels n in dwd. With a new DiscreteWaveletData object is returned with refinement levels.

## ExamplesExamplesopen allclose all

### Basic Examples  (2)Basic Examples  (2)

Perform a discrete wavelet transform:

 Out[1]=

Inverse transform recovers the original data:

 Out[2]=

DiscreteWaveletData representing modified wavelet image coefficients:

 Out[2]=

Inverse transform gives filtered image:

 Out[3]=

### Possible Issues  (1)Possible Issues  (1)

Introduced in 2010
(8.0)