# 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 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 {w1,,wn-1} from coefficients with wavelet index {w1,,wn-1,wn}.
• • An explicit wind specification needs to be consistent. A wind specification is consistent if for each {w1,,wn} that is included no {w1,,wk} for k<n 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 r<n a new DiscreteWaveletData object is returned with n-r refinement levels.

# Examples

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## Basic Examples(3)

Perform a discrete wavelet transform:

 In:= Out= Inverse transform recovers the original data:

 In:= Out= DiscreteWaveletData representing modified wavelet image coefficients:

 In:= In:= Out= Inverse transform gives filtered image:

 In:= Out= DiscreteWaveletData representing an audio signal:

 In:= In:= Out= Inverse transform using refinement level 5 coefficients only:

 In:= Out= ## Possible Issues(1)

Introduced in 2010
(8.0)