BUILT-IN MATHEMATICA SYMBOL
StationaryWaveletPacketTransform
- StationaryWaveletPacketTransform gives a DiscreteWaveletData object.
- Properties of the DiscreteWaveletData dwd can be found using dwd["prop"], and a list of available properties can be found using dwd["Properties"].
- StationaryWaveletPacketTransform is a generalization of StationaryWaveletTransform where the full tree of wavelet coefficients is computed.
- The data can be a rectangular array of any depth.
- By default, input image is converted to an image of type
.
- The resulting wavelet coefficients are arrays of the same depth and dimensions as the input data.
- The possible wavelets wave include:
-
- The default wave is HaarWavelet[].
- With higher settings for the refinement level r, larger scale features are resolved.
- The default refinement level r is given by
![min(TemplateBox[{{{InterpretationBox[{log, _, DocumentationBuild`Utils`Private`Parenth[2]}, Log2, AutoDelete -> True], (, n, )}, +, {1, /, 2}}}, Floor],4)](Files/StationaryWaveletPacketTransform.en/2.png "min(TemplateBox[{{{InterpretationBox[{log, _, DocumentationBuild`Utils`Private`Parenth[2]}, Log2, AutoDelete -> True], (, n, )}, +, {1, /, 2}}}, Floor],4)")
, where 
is the minimum dimension of data.
- With refinement level Full, r is given by
![TemplateBox[{{{InterpretationBox[{log, _, DocumentationBuild`Utils`Private`Parenth[2]}, Log2, AutoDelete -> True], (, n, )}, +, {1, /, 2}}}, Floor]](Files/StationaryWaveletPacketTransform.en/4.png "TemplateBox[{{{InterpretationBox[{log, _, DocumentationBuild`Utils`Private`Parenth[2]}, Log2, AutoDelete -> True], (, n, )}, +, {1, /, 2}}}, Floor]")
.
- The tree of wavelet coefficients at level
consists of coarse coefficients 
and detail coefficients 
, with 
representing the input data.
-
- The forward transform is given by
, 
, 
, and 
, where 
is the filter length for the corresponding wspec and 
is the length of input data.
- The inverse transform is given by
.
- The
are lowpass filter coefficients and 
are highpass filter coefficients that are defined for each wavelet family.
- The following options can be given:
-
- StationaryWaveletPacketTransform uses periodic padding of data.
- InverseWaveletTransform gives the inverse transform.
- By default, InverseWaveletTransform uses coefficients represented by dwd["BasisIndex"] for reconstruction. Use WaveletBestBasis to compute and set an optimal basis.
Compute a stationary wavelet packet transform:
| Out[1]= |  |
The resulting DiscreteWaveletData represents a full tree of wavelet coefficients:
| Out[2]= |  |
The inverse transform reconstructs the input:
| Out[3]= |  |
Transform an Image object:
| Out[1]= |  |
Use 
to extract coefficient images:
| Out[2]= |  |
Compute the inverse transform:
| Out[3]= |  |
Transform a sampled Sound object:
| Out[1]= |  |
| Out[2]= |  |
| Out[3]= |  |
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