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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

open allclose all

Basic Examples  (2)Summary of the most common use cases

Lifting filter:

In[1]:=1
✖
https://wolfram.com/xid/0pnkhua20w62wztu-bgqqc9
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0pnkhua20w62wztu-l3q2pc
Out[2]=2

Lifting transform equations:

In[1]:=1
✖
https://wolfram.com/xid/0pnkhua20w62wztu-lqsncz
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0pnkhua20w62wztu-r8gh13
Out[2]=2

Scope  (6)Survey of the scope of standard use cases

Use LiftingFilterData to compute LiftingWaveletTransform:

In[1]:=1
✖
https://wolfram.com/xid/0pnkhua20w62wztu-mhw9n6
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0pnkhua20w62wztu-lq4hpa
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0pnkhua20w62wztu-jmx50u
Out[3]=3

Tabulate lifting transform equations:

In[1]:=1
✖
https://wolfram.com/xid/0pnkhua20w62wztu-84txcj
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0pnkhua20w62wztu-ozqjtp
Out[2]=2

Tabulate inverse lifting transform equations:

In[3]:=3
✖
https://wolfram.com/xid/0pnkhua20w62wztu-hay232
Out[3]=3

Generate a function to compute a lifting wavelet transform:

In[1]:=1
✖
https://wolfram.com/xid/0pnkhua20w62wztu-dqs54t
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0pnkhua20w62wztu-pl6h0t
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0pnkhua20w62wztu-73huhe
Out[3]=3

Generate a function to compute an inverse lifting transform:

In[4]:=4
✖
https://wolfram.com/xid/0pnkhua20w62wztu-ojgd4x
Out[4]=4
In[5]:=5
✖
https://wolfram.com/xid/0pnkhua20w62wztu-1xe22c
Out[5]=5

Tabulate integer lifting transform equations:

In[1]:=1
✖
https://wolfram.com/xid/0pnkhua20w62wztu-kfpz21
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0pnkhua20w62wztu-z0qdqx
Out[2]=2

Tabulate inverse lifting transform equations:

In[3]:=3
✖
https://wolfram.com/xid/0pnkhua20w62wztu-h41t7a
Out[3]=3

Generate a function to compute a lifting wavelet transform:

In[1]:=1
✖
https://wolfram.com/xid/0pnkhua20w62wztu-9km7v9
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0pnkhua20w62wztu-ox1hxf
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0pnkhua20w62wztu-yjwup2
Out[3]=3

Generate a function to compute an inverse lifting transform:

In[4]:=4
✖
https://wolfram.com/xid/0pnkhua20w62wztu-v6m4fs
Out[4]=4
In[5]:=5
✖
https://wolfram.com/xid/0pnkhua20w62wztu-z883hj
Out[5]=5

Generate a matrix representation of lifting steps:

In[1]:=1
✖
https://wolfram.com/xid/0pnkhua20w62wztu-0dkdrl
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0pnkhua20w62wztu-3d2m7u
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0pnkhua20w62wztu-co0rxl
Out[3]=3

Generate a Laurent form representation of lifting steps:

In[4]:=4
✖
https://wolfram.com/xid/0pnkhua20w62wztu-f5xzgn
Out[4]=4

Generalizations & Extensions  (1)Generalized and extended use cases

Use LiftingWaveletTransform to compute a lifting transform:

In[1]:=1
✖
https://wolfram.com/xid/0pnkhua20w62wztu-u8tat0
In[2]:=2
✖
https://wolfram.com/xid/0pnkhua20w62wztu-8zveie

Compare wavelet coefficients:

In[3]:=3
✖
https://wolfram.com/xid/0pnkhua20w62wztu-4pr2cc
Out[3]=3

Options  (2)Common values & functionality for each option

Compiled  (2)

Use Compiled->True to optimize for machine-number computation:

In[1]:=1
✖
https://wolfram.com/xid/0pnkhua20w62wztu-cag419
Out[1]=1

Generate a compiled forward lifting transform function:

In[2]:=2
✖
https://wolfram.com/xid/0pnkhua20w62wztu-vf1j37
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0pnkhua20w62wztu-k4syff
In[4]:=4
✖
https://wolfram.com/xid/0pnkhua20w62wztu-4z3d1w
Out[4]=4

Suboptions can be used to control the compiled attributes:

In[1]:=1
✖
https://wolfram.com/xid/0pnkhua20w62wztu-e59c0w
Out[1]=1

A listable compiled function can run in parallel, giving an acceleration on multicore machines:

In[2]:=2
✖
https://wolfram.com/xid/0pnkhua20w62wztu-j8smmt
In[3]:=3
✖
https://wolfram.com/xid/0pnkhua20w62wztu-lg667i
In[4]:=4
✖
https://wolfram.com/xid/0pnkhua20w62wztu-00fcey
Out[4]=4

Applications  (4)Sample problems that can be solved with this function

Create an Executable for a Forward Lifting Transform  (1)

Compile a forward lifting transform into a standalone executable:

In[1]:=1
✖
https://wolfram.com/xid/0pnkhua20w62wztu-vmdokm
In[2]:=2
✖
https://wolfram.com/xid/0pnkhua20w62wztu-3nkkx6

Load necessary code-generation packages:

In[3]:=3
✖
https://wolfram.com/xid/0pnkhua20w62wztu-bcnnou
In[4]:=4
✖
https://wolfram.com/xid/0pnkhua20w62wztu-s2jjjb

Generate forward lifting transform C code:

In[5]:=5
✖
https://wolfram.com/xid/0pnkhua20w62wztu-gv4kg7

Generate a header file:

In[6]:=6
✖
https://wolfram.com/xid/0pnkhua20w62wztu-nb6mmj

Load precoded example main code to link the above files:

In[7]:=7
✖
https://wolfram.com/xid/0pnkhua20w62wztu-claac4

Generate a static executable:

In[8]:=8
✖
https://wolfram.com/xid/0pnkhua20w62wztu-uikr77

Generate a data file with first element indicating the dimension of the input vector:

In[9]:=9
✖
https://wolfram.com/xid/0pnkhua20w62wztu-c1gui1
In[10]:=10
✖
https://wolfram.com/xid/0pnkhua20w62wztu-wdkog1

Run the executable:

In[11]:=11
✖
https://wolfram.com/xid/0pnkhua20w62wztu-ezk7z2
In[12]:=12
✖
https://wolfram.com/xid/0pnkhua20w62wztu-trbz33
Out[12]=12
In[13]:=13
✖
https://wolfram.com/xid/0pnkhua20w62wztu-qrezpp

The executable creates an output file with coefficient values:

In[14]:=14
✖
https://wolfram.com/xid/0pnkhua20w62wztu-pr9hh9
In[15]:=15
✖
https://wolfram.com/xid/0pnkhua20w62wztu-9i52vk
Out[15]=15

Compare coefficient values:

In[16]:=16
✖
https://wolfram.com/xid/0pnkhua20w62wztu-gbewo0
Out[16]=16

Create an Executable for an Inverse Lifting Transform  (1)

Compile a forward lifting transform into a standalone executable:

In[1]:=1
✖
https://wolfram.com/xid/0pnkhua20w62wztu-w3roq1
In[2]:=2
✖
https://wolfram.com/xid/0pnkhua20w62wztu-w2ejul

Load necessary code-generation packages:

In[3]:=3
✖
https://wolfram.com/xid/0pnkhua20w62wztu-4cd92l
In[4]:=4
✖
https://wolfram.com/xid/0pnkhua20w62wztu-xzwkmn

Generate forward lifting transform C code:

In[5]:=5
✖
https://wolfram.com/xid/0pnkhua20w62wztu-lfv57v

Generate a header file:

In[6]:=6
✖
https://wolfram.com/xid/0pnkhua20w62wztu-xq5gme

Load precoded example main code to link the above files:

In[7]:=7
✖
https://wolfram.com/xid/0pnkhua20w62wztu-zudwp3

Generate a static executable:

In[8]:=8
✖
https://wolfram.com/xid/0pnkhua20w62wztu-uixav

Run the executable:

In[9]:=9
✖
https://wolfram.com/xid/0pnkhua20w62wztu-0p2gtp
In[10]:=10
✖
https://wolfram.com/xid/0pnkhua20w62wztu-qt3996
Out[10]=10
In[11]:=11
✖
https://wolfram.com/xid/0pnkhua20w62wztu-t5ak8r

The executable creates an output file with coefficient values:

In[12]:=12
✖
https://wolfram.com/xid/0pnkhua20w62wztu-csjbfv

Compare reconstructed data values:

In[13]:=13
✖
https://wolfram.com/xid/0pnkhua20w62wztu-lx67s2
In[14]:=14
✖
https://wolfram.com/xid/0pnkhua20w62wztu-wd646g
Out[14]=14

Create an Executable for a Forward Integer Lifting Transform  (1)

Compile a forward lifting transform into a standalone executable:

In[1]:=1
✖
https://wolfram.com/xid/0pnkhua20w62wztu-qz38fi
In[2]:=2
✖
https://wolfram.com/xid/0pnkhua20w62wztu-jf1e3x

Load necessary code-generation packages:

In[3]:=3
✖
https://wolfram.com/xid/0pnkhua20w62wztu-j4xhwr
In[4]:=4
✖
https://wolfram.com/xid/0pnkhua20w62wztu-6lyyty

Generate forward lifting transform C code:

In[5]:=5
✖
https://wolfram.com/xid/0pnkhua20w62wztu-n53rof

Generate a header file:

In[6]:=6
✖
https://wolfram.com/xid/0pnkhua20w62wztu-u68s47

Load precoded example main code to link the above files:

In[7]:=7
✖
https://wolfram.com/xid/0pnkhua20w62wztu-8cj2l0

Generate a static executable:

In[8]:=8
✖
https://wolfram.com/xid/0pnkhua20w62wztu-vbir7b

Generate a data file with first element indicating the dimension of the input vector:

In[9]:=9
✖
https://wolfram.com/xid/0pnkhua20w62wztu-xafk9e
In[10]:=10
✖
https://wolfram.com/xid/0pnkhua20w62wztu-iuus3c

Run the executable:

In[11]:=11
✖
https://wolfram.com/xid/0pnkhua20w62wztu-r4onku
In[12]:=12
✖
https://wolfram.com/xid/0pnkhua20w62wztu-sy6v0y
Out[12]=12
In[13]:=13
✖
https://wolfram.com/xid/0pnkhua20w62wztu-lej7c7

The executable creates an output file with coefficient values:

In[14]:=14
✖
https://wolfram.com/xid/0pnkhua20w62wztu-dijp6h
In[15]:=15
✖
https://wolfram.com/xid/0pnkhua20w62wztu-kz3tnv
Out[15]=15

Compare coefficient values:

In[16]:=16
✖
https://wolfram.com/xid/0pnkhua20w62wztu-myidl0
Out[16]=16

Create an Executable for an Inverse Integer Lifting Transform  (1)

Compile a forward lifting transform into a standalone executable:

In[1]:=1
✖
https://wolfram.com/xid/0pnkhua20w62wztu-8d34s5
In[2]:=2
✖
https://wolfram.com/xid/0pnkhua20w62wztu-gi49in

Load necessary code-generation packages:

In[3]:=3
✖
https://wolfram.com/xid/0pnkhua20w62wztu-bmqxlq
In[4]:=4
✖
https://wolfram.com/xid/0pnkhua20w62wztu-b521lv

Generate forward lifting transform C code:

In[5]:=5
✖
https://wolfram.com/xid/0pnkhua20w62wztu-vvkozy

Generate a header file:

In[6]:=6
✖
https://wolfram.com/xid/0pnkhua20w62wztu-54uv6k

Load precoded example main code to link the above files:

In[7]:=7
✖
https://wolfram.com/xid/0pnkhua20w62wztu-beauxl

Generate a static executable:

In[8]:=8
✖
https://wolfram.com/xid/0pnkhua20w62wztu-1c46a3

Run the executable:

In[9]:=9
✖
https://wolfram.com/xid/0pnkhua20w62wztu-xft09
In[10]:=10
✖
https://wolfram.com/xid/0pnkhua20w62wztu-nck3jz
Out[10]=10
In[11]:=11
✖
https://wolfram.com/xid/0pnkhua20w62wztu-q0qeg4

The executable creates an output file with coefficient values:

In[12]:=12
✖
https://wolfram.com/xid/0pnkhua20w62wztu-1o9m5g

Compare reconstructed data values:

In[13]:=13
✖
https://wolfram.com/xid/0pnkhua20w62wztu-fivevt
In[14]:=14
✖
https://wolfram.com/xid/0pnkhua20w62wztu-bcvyaa
Out[14]=14

Properties & Relations  (2)Properties of the function, and connections to other functions

The determinant of a polyphase matrix is always 1:

In[1]:=1
✖
https://wolfram.com/xid/0pnkhua20w62wztu-v2vqgt
In[2]:=2
✖
https://wolfram.com/xid/0pnkhua20w62wztu-0owz4o
Out[2]=2

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

In[1]:=1
✖
https://wolfram.com/xid/0pnkhua20w62wztu-ozvkw3
In[2]:=2
✖
https://wolfram.com/xid/0pnkhua20w62wztu-wwqtme
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0pnkhua20w62wztu-w7lmut
Out[3]=3
Wolfram Research (2010), LiftingFilterData, Wolfram Language function, https://reference.wolfram.com/language/ref/LiftingFilterData.html.
✖
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.

✖
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.

✖
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

✖
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: 25-March-2025 ]}

✖
@misc{reference.wolfram_2025_liftingfilterdata, author="Wolfram Research", title="{LiftingFilterData}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/LiftingFilterData.html}", note=[Accessed: 25-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_liftingfilterdata, organization={Wolfram Research}, title={LiftingFilterData}, year={2010}, url={https://reference.wolfram.com/language/ref/LiftingFilterData.html}, note=[Accessed: 25-March-2025 ]}

✖
@online{reference.wolfram_2025_liftingfilterdata, organization={Wolfram Research}, title={LiftingFilterData}, year={2010}, url={https://reference.wolfram.com/language/ref/LiftingFilterData.html}, note=[Accessed: 25-March-2025 ]}