LiftingFilterData

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

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Basic 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)

Compiled  (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)

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:

Wolfram Research (2010), LiftingFilterData, Wolfram Language function, https://reference.wolfram.com/language/ref/LiftingFilterData.html.

Text

Wolfram Research (2010), LiftingFilterData, Wolfram Language function, https://reference.wolfram.com/language/ref/LiftingFilterData.html.

BibTeX

@misc{reference.wolfram_2021_liftingfilterdata, author="Wolfram Research", title="{LiftingFilterData}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/LiftingFilterData.html}", note=[Accessed: 23-September-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_liftingfilterdata, organization={Wolfram Research}, title={LiftingFilterData}, year={2010}, url={https://reference.wolfram.com/language/ref/LiftingFilterData.html}, note=[Accessed: 23-September-2021 ]}

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