BUILT-IN MATHEMATICA SYMBOL

InverseContinuousWaveletTransform

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

gives the inverse transform using the wavelet wave.

InverseContinuousWaveletTransform

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

MORE INFORMATION

InverseContinuousWaveletTransform computes the inverse transform of continuous forward transforms such as ContinuousWaveletTransform.

The possible wavelets wave are the same as for ContinuousWaveletTransform.

The default wave is Automatic, which is taken to be cwd["Wavelet"].

The possible specifications for octvoc are the same as used by ContinuousWaveletData.

The default octvoc is Automatic, which is taken to be cwd["WaveletIndex"].

InverseContinuousWaveletTransform computes the inverse transform using only the wavelet coefficients specified by octvoc; other coefficients are set to be zero.

EXAMPLES

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Basic Examples (1)

Perform a continuous wavelet transform:

Inverse transform resynthesizes data from continuous wavelet coefficients:

Perform a continuous wavelet transform:

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In[2]:=

Out[2]=

Inverse transform resynthesizes data from continuous wavelet coefficients:

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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:

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

effectively zeros other coefficients:

Explicitly set other wavelet coefficients to zero: