ReverseBiorthogonalSplineWavelet []
represents a reverse biorthogonal spline wavelet of order 4 and dual order 2.
ReverseBiorthogonalSplineWavelet [n,m]
represents a reverse biorthogonal spline wavelet of order n and dual order m.
ReverseBiorthogonalSplineWavelet
ReverseBiorthogonalSplineWavelet []
represents a reverse biorthogonal spline wavelet of order 4 and dual order 2.
ReverseBiorthogonalSplineWavelet [n,m]
represents a reverse biorthogonal spline wavelet of order n and dual order m.
Details
- ReverseBiorthogonalSplineWavelet defines a family of biorthogonal wavelets.
- ReverseBiorthogonalSplineWavelet [n,m] is defined for positive integers m and n where m+n is even.
- The scaling function () and wavelet function () have compact support. The functions are symmetric.
- ReverseBiorthogonalSplineWavelet can be used with such functions as DiscreteWaveletTransform and WaveletPhi , etc.
Examples
open all close allBasic Examples (6)
Primal scaling function:
Primal wavelet function:
Dual scaling function:
Dual wavelet function:
Primal filter coefficients:
Dual filter coefficients:
Scope (17)
Basic Uses (10)
Compute primal lowpass filter coefficients:
Dual lowpass filter coefficients:
Primal highpass filter coefficients:
Dual highpass filter coefficients:
Lifting filter coefficients:
Generate a function to compute lifting wavelet transform:
Primal scaling function:
Dual scaling function:
Plot scaling function using different levels of recursion:
Primal wavelet function:
Dual wavelet function:
Plot wavelet function at different refinement scales:
Wavelet Transforms (5)
Compute a DiscreteWaveletTransform :
View the tree of wavelet coefficients:
Get the dimensions of wavelet coefficients:
Plot the wavelet coefficients:
Compute a DiscreteWaveletPacketTransform :
View the tree of wavelet coefficients:
Get the dimensions of wavelet coefficients:
Plot the wavelet coefficients:
Compute a StationaryWaveletTransform :
View the tree of wavelet coefficients:
Get the dimensions of wavelet coefficients:
Plot the wavelet coefficients:
Compute a StationaryWaveletPacketTransform :
View the tree of wavelet coefficients:
Get the dimensions of wavelet coefficients:
Plot the wavelet coefficients:
Compute a LiftingWaveletTransform :
View the tree of wavelet coefficients:
Get the dimensions of wavelet coefficients:
Plot the wavelet coefficients:
Higher Dimensions (2)
Multivariate scaling and wavelet functions are products of univariate ones:
Multivariate dual scaling and wavelet functions are products of univariate ones:
Properties & Relations (19)
ReverseBiorthogonalSplineWavelet [1,1] is equivalent to HaarWavelet :
ReverseBiorthogonalSplineWavelet is equivalent to BiorthogonalSplineWavelet :
ReverseBiorthogonalSplineWavelet is equivalent to BiorthogonalSplineWavelet :
ReverseBiorthogonalSplineWavelet is equivalent to BiorthogonalSplineWavelet :
ReverseBiorthogonalSplineWavelet is equivalent to BiorthogonalSplineWavelet :
Lowpass filter coefficients sum to unity; :
Highpass filter coefficients sum to zero; :
Dual filter coefficients sum to unity; :
Dual highpass filter coefficients sum to zero; :
Scaling function integrates to unity; :
Dual scaling function integrates to unity; :
Wavelet function integrates to zero; :
Dual wavelet function integrates to zero; :
Scaling function has compact support {n1,n2}:
Dual scaling function has compact support {nd1,nd2}:
Corresponding wavelet function has support {(n1– nd2+1)/2, (n2– nd1+1)/2}:
Dual wavelet function has support {(nd1– n2+1)/2, (nd2– n1+1)/2}:
satisfies the recursion equation :
Plot the components and the sum of the recursion:
satisfies the recursion equation :
Plot the components and the sum of the recursion:
satisfies the recursion equation :
Plot the components and the sum of the recursion:
satisfies the recursion equation :
Plot the components and the sum of the recursion:
Frequency response for is given by :
The filter is a lowpass filter:
Fourier transform of is given by :
Frequency response for is given by :
The filter is a dual lowpass filter:
Fourier transform of is given by :
Frequency response for is given by :
The filter is a lowpass filter:
Fourier transform of is given by :
Frequency response for is given by :
The filter is a lowpass filter:
Fourier transform of is given by :
Neat Examples (2)
Plot translates and dilations of scaling function:
Plot translates and dilations of wavelet function:
Tech Notes
Related Guides
History
Text
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.
APA
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-January-2026]}
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-January-2026]}