This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# InverseContinuousWaveletTransform

 InverseContinuousWaveletTransform[cwd] gives the inverse continuous wavelet transform of a ContinuousWaveletData object cwd. InverseContinuousWaveletTransformgives the inverse transform using the wavelet wave. InverseContinuousWaveletTransformgives the inverse transform from the wavelet coefficients specified by octvoc.
• The default wave is Automatic, which is taken to be cwd["Wavelet"].
• The default octvoc is Automatic, which is taken to be cwd["WaveletIndex"].
Perform a continuous wavelet transform:
Inverse transform resynthesizes data from continuous wavelet coefficients:
Perform a continuous wavelet transform:
 Out[2]=
Inverse transform resynthesizes data from continuous wavelet coefficients:
 Out[3]=
 Scope   (5)
Inverse transform ContinuousWaveletData from the forward transform:
The quality of the reconstruction depends on the number of octaves and voices:
Inverse transform modified ContinuousWaveletData:
Plot the inverse transform of original and modified coefficients:
Inverse transform selected octaves and voices only:
Inverse transform only the coefficient:
Inverse transform the first octave , setting other coefficients to zero:
Inverse transform an explicitly constructed ContinuousWaveletData object:
Unspecified coefficients are taken to be zero:
Specify a different wavelet to use in the inverse transform:
By default, the wavelet used in the forward transform is chosen:
 Options   (4)
By default, Method option is used for data less than length 512:
By default, Method option is used for data greater than length 512:
Method option performs an exact inverse transform:
Method option performs an approximate inverse transform:
Compare efficiency and accuracy of the two methods:
For large data, is slow:
Compare with the original data:
Use for large data:
Compare with the original data:
 Applications   (2)
Filter one scale or frequency from a signal:
Identify separate signal components on a scalogram:
Remove the feature at small scales :
Synthesize filtered data:
Filter data with both time- and scale-dependent features:
Identify signal components as a function of scale and time:
Excise transient feature using a step filter:
Show altered scalogram and synthesized filtered data:
InverseContinuousWaveletTransform synthesizes data from continuous wavelet coefficients:
The synthesis operation is approximately the inverse of the forward continuous transform:
InverseWaveletTransform gives the inverse of discrete forward transforms:
The inverse is exact for all orthogonal wavelets including HaarWavelet:
InverseContinuousWaveletTransform effectively zeros other coefficients:
Explicitly set other wavelet coefficients to zero:
New in 8