WaveletFilterCoefficients
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WaveletFilterCoefficients
gives the filter coefficients for the symbolic wavelet wave of type filt.
Details and Options
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- WaveletFilterCoefficients[wave,filt] gives a list of the form {{n,cn},{n+1,cn+1},…}, where n is the index and cn the corresponding filter coefficient.
- For orthogonal wavelets possible filters filt include: "PrimalLowpass" and "PrimalHighpass".
- The primal highpass filter coefficients satisfy
, where
are primal lowpass filter coefficients.
- The scaling function
and wavelet function
satisfy the relations:
-
(primal) scaling refinement equation (primal) wavelet refinement equation - For biorthogonal wavelets, possible filters filt include: "PrimalLowpass", "PrimalHighpass", "DualLowpass", and "DualHighpass".
- The primal highpass filter coefficients satisfy
, where
are dual lowpass filter coefficients. Dual highpass filter coefficients satisfy
, where
are primal lowpass filter coefficients.
- The primal scaling function
and wavelet function
satisfy the relations:
-
(primal) scaling refinement equation (primal) wavelet refinement equation - The dual scaling function
and dual wavelet function
satisfy:
-
(dual) scaling refinement equation (dual) wavelet refinement equation - For discrete wavelets with compact support, you can also produce LiftingFilterData objects used for LiftingWaveletTransform as well as generating compiled standalone wavelet transform code. The following filt values can be used:
-
"LiftingFilter" default lifting filter "AllLiftingFilter" all possible lifting filters "BestLiftingFilter" most stable lifting filter - With the option setting WorkingPrecision->prec, filter coefficients are computed using precision prec. By default, WorkingPrecision->MachinePrecision is used.
Examples
open allclose allBasic Examples (4)Summary of the most common use cases
Primal lowpass filter coefficients:
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https://wolfram.com/xid/0bmvb95zs3yjyoig9jq-lmmump
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Primal highpass filter coefficients:
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https://wolfram.com/xid/0bmvb95zs3yjyoig9jq-0e2bs6
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Dual lowpass filter coefficients:
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https://wolfram.com/xid/0bmvb95zs3yjyoig9jq-raub53
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Dual highpass filter coefficients:
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https://wolfram.com/xid/0bmvb95zs3yjyoig9jq-m71igw
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Scope (5)Survey of the scope of standard use cases
Compute primal lowpass filter coefficients:
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https://wolfram.com/xid/0bmvb95zs3yjyoig9jq-x5t4az
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Primal highpass filter coefficients:
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https://wolfram.com/xid/0bmvb95zs3yjyoig9jq-tovf4h
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Dual lowpass filter coefficients:
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https://wolfram.com/xid/0bmvb95zs3yjyoig9jq-ozjyj6
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Dual highpass filter coefficients:
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https://wolfram.com/xid/0bmvb95zs3yjyoig9jq-bzlj15
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"Properties" gives a list of available properties:
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https://wolfram.com/xid/0bmvb95zs3yjyoig9jq-jmfswx
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Properties for BiorthogonalSplineWavelet:
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https://wolfram.com/xid/0bmvb95zs3yjyoig9jq-8se554
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Options (2)Common values & functionality for each option
WorkingPrecision (2)
By default WorkingPrecision->MachinePrecision is used:
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https://wolfram.com/xid/0bmvb95zs3yjyoig9jq-jj9fjg
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https://wolfram.com/xid/0bmvb95zs3yjyoig9jq-6vi03j
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https://wolfram.com/xid/0bmvb95zs3yjyoig9jq-fste7p
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Use higher-precision filter computation:
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https://wolfram.com/xid/0bmvb95zs3yjyoig9jq-oxpk71
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https://wolfram.com/xid/0bmvb95zs3yjyoig9jq-f6wruc
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https://wolfram.com/xid/0bmvb95zs3yjyoig9jq-cwufym
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https://wolfram.com/xid/0bmvb95zs3yjyoig9jq-yp62kx
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Properties & Relations (3)Properties of the function, and connections to other functions
Lowpass filter coefficients sum to unity; :
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https://wolfram.com/xid/0bmvb95zs3yjyoig9jq-bs7miu
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Highpass filter coefficients sum to zero; :
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https://wolfram.com/xid/0bmvb95zs3yjyoig9jq-jaf8rr
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The lowpass and highpass filter coefficients are orthogonal; :
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https://wolfram.com/xid/0bmvb95zs3yjyoig9jq-8vwdxn
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Wolfram Research (2010), WaveletFilterCoefficients, Wolfram Language function, https://reference.wolfram.com/language/ref/WaveletFilterCoefficients.html.
Text
Wolfram Research (2010), WaveletFilterCoefficients, Wolfram Language function, https://reference.wolfram.com/language/ref/WaveletFilterCoefficients.html.
Wolfram Research (2010), WaveletFilterCoefficients, Wolfram Language function, https://reference.wolfram.com/language/ref/WaveletFilterCoefficients.html.
CMS
Wolfram Language. 2010. "WaveletFilterCoefficients." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/WaveletFilterCoefficients.html.
Wolfram Language. 2010. "WaveletFilterCoefficients." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/WaveletFilterCoefficients.html.
APA
Wolfram Language. (2010). WaveletFilterCoefficients. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WaveletFilterCoefficients.html
Wolfram Language. (2010). WaveletFilterCoefficients. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WaveletFilterCoefficients.html
BibTeX
@misc{reference.wolfram_2025_waveletfiltercoefficients, author="Wolfram Research", title="{WaveletFilterCoefficients}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/WaveletFilterCoefficients.html}", note=[Accessed: 19-February-2025
]}
BibLaTeX
@online{reference.wolfram_2025_waveletfiltercoefficients, organization={Wolfram Research}, title={WaveletFilterCoefficients}, year={2010}, url={https://reference.wolfram.com/language/ref/WaveletFilterCoefficients.html}, note=[Accessed: 19-February-2025
]}