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WaveletFilterCoefficients

WaveletFilterCoefficients
gives the filter coefficients for the symbolic wavelet wave of type filt.
MORE INFORMATION
  • For orthogonal wavelets possible filters filt include: and .
  • The primal high-pass filter coefficients satisfy , where are primal low-pass 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: , , , and .
  • The primal high-pass filter coefficients satisfy , where are dual low-pass filter coefficients. Dual high-pass filter coefficients satisfy , where are primal low-pass 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
EXAMPLESCLOSE ALL
Basic Examples   (4)
Primal low-pass filter coefficients:
Primal high-pass filter coefficients:
Dual low-pass filter coefficients:
Dual high-pass filter coefficients:
Primal low-pass filter coefficients:
In[1]:=
Click for copyable input
Out[1]=
 
Primal high-pass filter coefficients:
In[1]:=
Click for copyable input
Out[1]=
 
Dual low-pass filter coefficients:
In[1]:=
Click for copyable input
Out[1]=
 
Dual high-pass filter coefficients:
In[1]:=
Click for copyable input
Out[1]=
Scope   (5)
Compute primal low-pass filter coefficients:
Primal high-pass filter coefficients:
Dual low-pass filter coefficients:
Dual high-pass filter coefficients:
gives a list of available properties:
Options   (2)
By default WorkingPrecision->MachinePrecision is used:
Use higher-precision filter computation:
Properties & Relations   (3)
Low-pass filter coefficients sum to unity; :
High-pass filter coefficients sum to zero; :
The low-pass and high-pass filter coefficients are orthogonal; :
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