BUILT-IN MATHEMATICA SYMBOL

LiftingFilterData

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

MORE INFORMATION

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 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 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

EXAMPLES

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Basic Examples (2)

Lifting filter:

Lifting transform equations:

Lifting filter:

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Lifting transform equations:

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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)

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:

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:

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:

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:

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

:

Taking a Dot product of matrix representation gives the polyphase matrix: