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based on an earlier version of the Wolfram Language.
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LiftingFilterData

LiftingFilterData[...]
represents lifting-filter data used to compute forward and inverse lifting wavelet transforms.
  • LiftingFilterData can be used to generate standalone functions that compute forward and inverse lifting wavelet transforms.
  • Properties fprop to dynamically generate functions that compute a lifting transform:
"ForwardLiftingFunction"function representing forward lifting transform
"InverseLiftingFunction"function representing inverse lifting transform
"ForwardIntegerLiftingFunction"function representing forward integer lifting transform
"InverseIntegerLiftingFunction"function representing inverse integer lifting transform
  • LiftingFilterData can be used to specify the formal variables in the generated function, where e is the input vector, c is the coarse coefficient vector, and d is the detail coefficient vector.
  • Properties related to generating formatted lifting transform equations:
"ForwardLiftingTable"forward lifting transform equations
"InverseLiftingTable"inverse lifting transform equations
"ForwardIntegerLiftingTable"forward integer lifting transform equations
"InverseIntegerLiftingTable"inverse integer lifting transform equations
  • Properties lprop related to lifting factorization:
"LiftingLaurentForm"Laurent form representation of lifting equations
"LiftingMatrixList"matrix form representation of lifting equations
"LiftingMatrixForm"formatted matrix form representation of lifting equations
"PolyphaseMatrix"polyphase representation of wavelet family
  • LiftingFilterData can be used to specify the formal variable in the resulting polynomial and rational formulas.
  • Properties related to input wavelet:
"DualHighpass"dual high-pass filter coefficients
"DualLowpass"dual low-pass filter coefficients
"PrimalHighpass"primal high-pass filter coefficients
"PrimalLowpass"primal low-pass filter coefficients
"Wavelet"wavelet family used
Lifting filter:
Lifting transform equations:
Lifting filter:
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Lifting transform equations:
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Tabulate lifting transform equations:
Tabulate inverse lifting transform equations:
Generate a function to compute a lifting wavelet transform:
Generate a function to compute an inverse lifting transform:
Tabulate integer lifting transform equations:
Tabulate inverse lifting transform equations:
Generate a function to compute a lifting wavelet transform:
Generate a function to compute an inverse lifting transform:
Generate a matrix representation of lifting steps:
Generate a Laurent form representation of lifting steps:
Use LiftingWaveletTransform to compute a lifting transform:
Compare wavelet coefficients:
Use Compiled->True to optimize for machine-number computation:
Generate a compiled forward lifting transform function:
Suboptions can be used to control the compiled attributes:
A listable compiled function can run in parallel, giving an acceleration on multicore machines:
Compile a forward lifting transform into a standalone executable:
Load necessary code-generation packages:
Generate forward lifting transform C code:
Generate a header file:
Load precoded example main code to link the above files:
Generate a static executable:
Generate a data file with first element indicating the dimension of the input vector:
Run the executable:
The executable creates an output file with coefficient values:
Compare coefficient values:
Compile a forward lifting transform into a standalone executable:
Load necessary code-generation packages:
Generate forward lifting transform C code:
Generate a header file:
Load precoded example main code to link the above files:
Generate a static executable:
Run the executable:
The executable creates an output file with coefficient values:
Compare reconstructed data values:
Compile a forward lifting transform into a standalone executable:
Load necessary code-generation packages:
Generate forward lifting transform C code:
Generate a header file:
Load precoded example main code to link the above files:
Generate a static executable:
Generate a data file with first element indicating the dimension of the input vector:
Run the executable:
The executable creates an output file with coefficient values:
Compare coefficient values:
Compile a forward lifting transform into a standalone executable:
Load necessary code-generation packages:
Generate forward lifting transform C code:
Generate a header file:
Load precoded example main code to link the above files:
Generate a static executable:
Run the executable:
The executable creates an output file with coefficient values:
Compare reconstructed data values:
The determinant of a polyphase matrix is always :
Taking a Dot product of matrix representation gives the polyphase matrix:
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