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
Introduced in 2010
(8.0)