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
- 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[cwd,wave,octvoc] computes the inverse transform using only the wavelet coefficients specified by octvoc; other coefficients are set to be zero.
Examples
open allclose allBasic Examples (1)
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:
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,_}:
Filter data with both time- and scale-dependent features:
Identify signal components as a function of scale and time:
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:
Text
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.
APA
Wolfram Language. (2010). InverseContinuousWaveletTransform. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseContinuousWaveletTransform.html