represents lifting-filter data used to compute forward and inverse lifting wavelet transforms.
LiftingFilterData
represents lifting-filter data used to compute forward and inverse lifting wavelet transforms.
Details and Options
- LiftingFilterData can be produced by WaveletFilterCoefficients from different wavelet families.
- The following wavelet families can be used: BiorthogonalSplineWavelet , CDFWavelet , CoifletWavelet , DaubechiesWavelet , HaarWavelet , ReverseBiorthogonalSplineWavelet , SymletWavelet .
- 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 [{fprop,{e,c,d}}] 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.
- LiftingFilterData [fprop,Compiled->copts] can be used to generate a compiled function, where copts are the option values accepted by Compiled .
- 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 [{lprop,z}] can be used to specify the formal variable in the resulting polynomial and rational formulas.
- Properties related to input wavelet:
-
"DualHighpass" dual highpass filter coefficients"DualLowpass" dual lowpass filter coefficients"PrimalHighpass" primal highpass filter coefficients"PrimalLowpass" primal lowpass filter coefficients"Wavelet" wavelet family used
Examples
open all close allBasic Examples (2)
Lifting filter:
Lifting transform equations:
Scope (6)
Use LiftingFilterData to compute LiftingWaveletTransform :
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:
Generalizations & Extensions (1)
Use LiftingWaveletTransform to compute a lifting transform:
Compare wavelet coefficients:
Options (2)
Applications (4)
Create an Executable for a Forward Lifting Transform (1)
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:
Create an Executable for an Inverse Lifting Transform (1)
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:
Create an Executable for a Forward Integer Lifting Transform (1)
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:
Create an Executable for an Inverse Integer Lifting Transform (1)
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:
Properties & Relations (2)
The determinant of a polyphase matrix is always 1:
Taking a Dot product of matrix representation gives the polyphase matrix:
Related Guides
History
Text
Wolfram Research (2010), LiftingFilterData, Wolfram Language function, https://reference.wolfram.com/language/ref/LiftingFilterData.html.
CMS
Wolfram Language. 2010. "LiftingFilterData." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/LiftingFilterData.html.
APA
Wolfram Language. (2010). LiftingFilterData. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LiftingFilterData.html
BibTeX
@misc{reference.wolfram_2025_liftingfilterdata, author="Wolfram Research", title="{LiftingFilterData}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/LiftingFilterData.html}", note=[Accessed: 10-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_liftingfilterdata, organization={Wolfram Research}, title={LiftingFilterData}, year={2010}, url={https://reference.wolfram.com/language/ref/LiftingFilterData.html}, note=[Accessed: 10-January-2026]}