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# LiftingFilterData

LiftingFilterData[...]
represents lifting-filter data used to compute forward and inverse lifting wavelet transforms.

## Details and OptionsDetails 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

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

Lifting filter:

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Lifting transform equations:

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### Properties & Relations (2)Properties & Relations (2)

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