 |
BUILT-IN MATHEMATICA SYMBOL
WaveletFilterCoefficients
WaveletFilterCoefficients[wave, filt]
gives the filter coefficients for the symbolic wavelet wave of type filt.
Details and Options
- WaveletFilterCoefficients[wave, filt] gives a list of the form
, where n is the index and 
the corresponding filter coefficient. - For orthogonal wavelets possible filters filt include:
and 
. - 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:
, 
, 
, and 
. - 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.
New in 8
