WOLFRAM

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

gives the inverse transform using the wavelet wave.

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

Details and Options

Examples

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Basic Examples  (1)Summary of the most common use cases

Perform a continuous wavelet transform:

Out[2]=2

Inverse transform resynthesizes data from continuous wavelet coefficients:

Out[3]=3

Scope  (5)Survey of the scope of standard use cases

Basic Uses  (5)

Inverse transform ContinuousWaveletData from the forward transform:

Out[1]=1
Out[2]=2

The quality of the reconstruction depends on the number of octaves and voices:

Out[3]=3

Inverse transform modified ContinuousWaveletData:

Out[2]=2

Plot the inverse transform of original and modified coefficients:

Out[3]=3

Inverse transform selected octaves and voices only:

Out[2]=2

Inverse transform only the {2,5} coefficient:

Out[4]=4

Inverse transform the first octave {1,_}, setting other coefficients to zero:

Out[5]=5

Inverse transform an explicitly constructed ContinuousWaveletData object:

Out[1]=1
Out[2]=2

Unspecified coefficients are taken to be zero:

Out[3]=3

Specify a different wavelet to use in the inverse transform:

Out[2]=2

By default, the wavelet used in the forward transform is chosen:

Out[3]=3

Options  (4)Common values & functionality for each option

Method  (4)

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

Out[1]=1
Out[2]=2

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

Out[1]=1
Out[2]=2

Method option "LeastSquares" performs an exact inverse transform:

Out[1]=1
Out[2]=2

Method option "DeltaFunction" performs an approximate inverse transform:

Out[3]=3

Compare efficiency and accuracy of the two methods:

Out[2]=2

For large data, "LeastSquares" is slow:

Out[3]=3

Compare with the original data:

Out[4]=4

Use "DeltaFunction" for large data:

Out[5]=5

Compare with the original data:

Out[6]=6

Applications  (2)Sample problems that can be solved with this function

Scale & Time Filtering  (2)

Filter one scale or frequency from a signal:

Out[2]=2

Identify separate signal components on a scalogram:

Out[4]=4

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

Out[5]=5

Synthesize filtered data:

Out[6]=6

Filter data with both time- and scale-dependent features:

Out[2]=2

Identify signal components as a function of scale and time:

Out[3]=3
Out[4]=4

Excise transient feature using a step filter:

Out[6]=6

Show altered scalogram and synthesized filtered data:

Out[7]=7

Properties & Relations  (2)Properties of the function, and connections to other functions

InverseContinuousWaveletTransform synthesizes data from continuous wavelet coefficients:

Out[1]=1

The synthesis operation is approximately the inverse of the forward continuous transform:

Out[2]=2

InverseWaveletTransform gives the inverse of discrete forward transforms:

Out[3]=3

The inverse is exact for all orthogonal wavelets including HaarWavelet[]:

Out[4]=4

InverseContinuousWaveletTransform[,,octvoc] effectively zeros other coefficients:

Out[2]=2

Explicitly set other wavelet coefficients to zero:

Out[3]=3
Out[4]=4
Wolfram Research (2010), InverseContinuousWaveletTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseContinuousWaveletTransform.html.
Wolfram Research (2010), InverseContinuousWaveletTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseContinuousWaveletTransform.html.

Text

Wolfram Research (2010), InverseContinuousWaveletTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseContinuousWaveletTransform.html.

Wolfram Research (2010), InverseContinuousWaveletTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseContinuousWaveletTransform.html.

CMS

Wolfram Language. 2010. "InverseContinuousWaveletTransform." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InverseContinuousWaveletTransform.html.

Wolfram Language. 2010. "InverseContinuousWaveletTransform." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InverseContinuousWaveletTransform.html.

APA

Wolfram Language. (2010). InverseContinuousWaveletTransform. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseContinuousWaveletTransform.html

Wolfram Language. (2010). InverseContinuousWaveletTransform. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseContinuousWaveletTransform.html

BibTeX

@misc{reference.wolfram_2025_inversecontinuouswavelettransform, author="Wolfram Research", title="{InverseContinuousWaveletTransform}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/InverseContinuousWaveletTransform.html}", note=[Accessed: 30-March-2025 ]}

@misc{reference.wolfram_2025_inversecontinuouswavelettransform, author="Wolfram Research", title="{InverseContinuousWaveletTransform}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/InverseContinuousWaveletTransform.html}", note=[Accessed: 30-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_inversecontinuouswavelettransform, organization={Wolfram Research}, title={InverseContinuousWaveletTransform}, year={2010}, url={https://reference.wolfram.com/language/ref/InverseContinuousWaveletTransform.html}, note=[Accessed: 30-March-2025 ]}

@online{reference.wolfram_2025_inversecontinuouswavelettransform, organization={Wolfram Research}, title={InverseContinuousWaveletTransform}, year={2010}, url={https://reference.wolfram.com/language/ref/InverseContinuousWaveletTransform.html}, note=[Accessed: 30-March-2025 ]}