InverseContinuousWaveletTransform

InverseContinuousWaveletTransform[cwd]

gives the inverse continuous wavelet transform of a ContinuousWaveletData object cwd.

InverseContinuousWaveletTransform[cwd,wave]

gives the inverse transform using the wavelet wave.

InverseContinuousWaveletTransform[cwd,wave,octvoc]

gives the inverse transform from the wavelet coefficients specified by octvoc.

Details and Options

Examples

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Basic Examples  (1)

Perform a continuous wavelet transform:

Inverse transform resynthesizes data from continuous wavelet coefficients:

Scope  (5)

Basic Uses  (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 {2,5} coefficient:

Inverse transform the first octave {1,_}, 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)

Method  (4)

By default, Method option "LeastSquares" is used for data less than length 512:

By default, Method option "DeltaFunction" is used for data greater than length 512:

Method option "LeastSquares" performs an exact inverse transform:

Method option "DeltaFunction" performs an approximate inverse transform:

Compare efficiency and accuracy of the two methods:

For large data, "LeastSquares" is slow:

Compare with the original data:

Use "DeltaFunction" for large data:

Compare with the original data:

Applications  (2)

Scale & Time Filtering  (2)

Filter one scale or frequency from a signal:

Identify separate signal components on a scalogram:

Remove the feature at small scales {3|4|5,_}:

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:

Properties & Relations  (2)

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[,,octvoc] effectively zeros other coefficients:

Explicitly set other wavelet coefficients to zero:

Introduced in 2010
 (8.0)