This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# 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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 Scope   (6)
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:
 Options   (2)
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:
 Applications   (4)
Compile a forward lifting transform into a standalone executable:
Generate forward lifting transform C code:
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:
Generate forward lifting transform C code:
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:
Generate forward lifting transform C code:
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:
Generate forward lifting transform C code:
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:
New in 8