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represents a reverse biorthogonal spline wavelet of order 4 and dual order 2.

represents a reverse biorthogonal spline wavelet of order n and dual order m.

Details

Examples

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Basic Examples  (6)Summary of the most common use cases

Primal scaling function:

Out[1]=1

Primal wavelet function:

Out[1]=1

Dual scaling function:

Out[1]=1

Dual wavelet function:

Out[1]=1

Primal filter coefficients:

Out[1]=1

Dual filter coefficients:

Out[1]=1

Scope  (17)Survey of the scope of standard use cases

Basic Uses  (10)

Compute primal lowpass filter coefficients:

Out[1]=1

Dual lowpass filter coefficients:

Out[1]=1

Primal highpass filter coefficients:

Out[1]=1

Dual highpass filter coefficients:

Out[1]=1

Lifting filter coefficients:

Out[1]=1
Out[2]=2

Generate a function to compute lifting wavelet transform:

Out[1]=1
Out[2]=2
Out[3]=3

Primal scaling function:

Out[1]=1

Dual scaling function:

Out[2]=2

Plot scaling function using different levels of recursion:

Out[1]=1

Primal wavelet function:

Out[1]=1

Dual wavelet function:

Out[2]=2

Plot wavelet function at different refinement scales:

Out[1]=1

Wavelet Transforms  (5)

Compute a DiscreteWaveletTransform:

Out[2]=2
Out[3]=3

View the tree of wavelet coefficients:

Out[4]=4

Get the dimensions of wavelet coefficients:

Out[5]=5

Plot the wavelet coefficients:

Out[6]=6

Compute a DiscreteWaveletPacketTransform:

Out[2]=2

View the tree of wavelet coefficients:

Out[3]=3

Get the dimensions of wavelet coefficients:

Out[4]=4

Plot the wavelet coefficients:

Out[5]=5

Compute a StationaryWaveletTransform:

View the tree of wavelet coefficients:

Out[3]=3

Get the dimensions of wavelet coefficients:

Out[4]=4

Plot the wavelet coefficients:

Out[5]=5

Compute a StationaryWaveletPacketTransform:

View the tree of wavelet coefficients:

Out[3]=3

Get the dimensions of wavelet coefficients:

Out[4]=4

Plot the wavelet coefficients:

Out[5]=5

Compute a LiftingWaveletTransform:

View the tree of wavelet coefficients:

Out[3]=3

Get the dimensions of wavelet coefficients:

Out[4]=4

Plot the wavelet coefficients:

Out[5]=5

Higher Dimensions  (2)

Multivariate scaling and wavelet functions are products of univariate ones:

Out[2]=2
Out[3]=3
Out[4]=4
Out[5]=5

Multivariate dual scaling and wavelet functions are products of univariate ones:

Out[2]=2
Out[3]=3
Out[4]=4
Out[5]=5

Properties & Relations  (19)Properties of the function, and connections to other functions

ReverseBiorthogonalSplineWavelet[1,1] is equivalent to HaarWavelet:

Out[1]=1
Out[2]=2

ReverseBiorthogonalSplineWavelet is equivalent to BiorthogonalSplineWavelet :

Out[1]=1

ReverseBiorthogonalSplineWavelet is equivalent to BiorthogonalSplineWavelet :

Out[2]=2

ReverseBiorthogonalSplineWavelet is equivalent to BiorthogonalSplineWavelet :

Out[3]=3

ReverseBiorthogonalSplineWavelet is equivalent to BiorthogonalSplineWavelet :

Out[4]=4

Lowpass filter coefficients sum to unity; :

Out[1]=1

Highpass filter coefficients sum to zero; :

Out[2]=2

Dual filter coefficients sum to unity; :

Out[1]=1

Dual highpass filter coefficients sum to zero; :

Out[2]=2

Scaling function integrates to unity; :

Out[1]=1

Dual scaling function integrates to unity; :

Out[2]=2

Wavelet function integrates to zero; :

Out[1]=1

Dual wavelet function integrates to zero; :

Out[2]=2

Scaling function has compact support {n1,n2}:

Out[1]=1

Dual scaling function has compact support {nd1,nd2}:

Out[3]=3

Corresponding wavelet function has support {(n1 nd2+1)/2, (n2 nd1+1)/2}:

Out[5]=5
Out[6]=6

Dual wavelet function has support {(nd1 n2+1)/2, (nd2 n1+1)/2}:

Out[7]=7
Out[8]=8

satisfies the recursion equation :

Plot the components and the sum of the recursion:

Out[4]=4

satisfies the recursion equation :

Plot the components and the sum of the recursion:

Out[4]=4

satisfies the recursion equation :

Plot the components and the sum of the recursion:

Out[4]=4

satisfies the recursion equation :

Plot the components and the sum of the recursion:

Out[4]=4

Frequency response for is given by :

The filter is a lowpass filter:

Out[2]=2

Fourier transform of is given by :

Out[3]=3

Frequency response for is given by :

The filter is a dual lowpass filter:

Out[2]=2

Fourier transform of is given by :

Out[3]=3

Frequency response for is given by :

The filter is a lowpass filter:

Out[2]=2

Fourier transform of is given by :

Out[4]=4

Frequency response for is given by :

The filter is a lowpass filter:

Out[2]=2

Fourier transform of is given by :

Out[4]=4

Neat Examples  (2)Surprising or curious use cases

Plot translates and dilations of scaling function:

Out[2]=2
Out[3]=3

Plot translates and dilations of wavelet function:

Out[2]=2
Out[3]=3
Wolfram Research (2010), ReverseBiorthogonalSplineWavelet, Wolfram Language function, https://reference.wolfram.com/language/ref/ReverseBiorthogonalSplineWavelet.html.
Wolfram Research (2010), ReverseBiorthogonalSplineWavelet, Wolfram Language function, https://reference.wolfram.com/language/ref/ReverseBiorthogonalSplineWavelet.html.

Text

Wolfram Research (2010), ReverseBiorthogonalSplineWavelet, Wolfram Language function, https://reference.wolfram.com/language/ref/ReverseBiorthogonalSplineWavelet.html.

Wolfram Research (2010), ReverseBiorthogonalSplineWavelet, Wolfram Language function, https://reference.wolfram.com/language/ref/ReverseBiorthogonalSplineWavelet.html.

CMS

Wolfram Language. 2010. "ReverseBiorthogonalSplineWavelet." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ReverseBiorthogonalSplineWavelet.html.

Wolfram Language. 2010. "ReverseBiorthogonalSplineWavelet." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ReverseBiorthogonalSplineWavelet.html.

APA

Wolfram Language. (2010). ReverseBiorthogonalSplineWavelet. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ReverseBiorthogonalSplineWavelet.html

Wolfram Language. (2010). ReverseBiorthogonalSplineWavelet. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ReverseBiorthogonalSplineWavelet.html

BibTeX

@misc{reference.wolfram_2025_reversebiorthogonalsplinewavelet, author="Wolfram Research", title="{ReverseBiorthogonalSplineWavelet}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/ReverseBiorthogonalSplineWavelet.html}", note=[Accessed: 07-June-2025 ]}

@misc{reference.wolfram_2025_reversebiorthogonalsplinewavelet, author="Wolfram Research", title="{ReverseBiorthogonalSplineWavelet}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/ReverseBiorthogonalSplineWavelet.html}", note=[Accessed: 07-June-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_reversebiorthogonalsplinewavelet, organization={Wolfram Research}, title={ReverseBiorthogonalSplineWavelet}, year={2010}, url={https://reference.wolfram.com/language/ref/ReverseBiorthogonalSplineWavelet.html}, note=[Accessed: 07-June-2025 ]}

@online{reference.wolfram_2025_reversebiorthogonalsplinewavelet, organization={Wolfram Research}, title={ReverseBiorthogonalSplineWavelet}, year={2010}, url={https://reference.wolfram.com/language/ref/ReverseBiorthogonalSplineWavelet.html}, note=[Accessed: 07-June-2025 ]}