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CDFWavelet

CDFWavelet
represents a Cohen-Daubechies-Feauveau wavelet of type .
CDFWavelet
represents a Cohen-Daubechies-Feauveau wavelet of type .
  • CDFWavelet defines a set of biorthogonal wavelets.
  • The following forms can be used:
"5/3"used in lossless JPEG2000 compression
"9/7"used in lossy JPEG2000 compression
  • The scaling function () and wavelet function () have compact support. The functions are symmetric.
Scaling function:
Wavelet function:
Filter coefficients:
Scaling function:
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Wavelet function:
In[1]:=
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Filter coefficients:
In[1]:=
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Out[1]=
Compute primal low-pass filter coefficients:
Dual low-pass filter coefficients:
Primal high-pass filter coefficients:
Dual high-pass filter coefficients:
Lifting filter coefficients:
Generate 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 scaling function using different levels of recursion:
View the tree of wavelet coefficients:
Get the dimensions of wavelet coefficients:
Plot the wavelet coefficients:
View the tree of wavelet coefficients:
Get the dimensions of wavelet coefficients:
Plot the wavelet coefficients:
View the tree of wavelet coefficients:
Get the dimensions of wavelet coefficients:
Plot the wavelet coefficients:
View the tree of wavelet coefficients:
Get the dimensions of wavelet coefficients:
Plot the wavelet coefficients:
View the tree of wavelet coefficients:
Get the dimensions of wavelet coefficients:
Plot the wavelet coefficients:
Multivariate scaling and wavelet functions are products of univariate ones:
Low-pass filter coefficients sum to unity; :
High-pass filter coefficients sum to zero; :
Dual low-pass filter coefficients sum to unity; :
Dual high-pass 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; :
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 low-pass filter:
Fourier transform of is given by :
Frequency response for is given by :
The filter is a dual low-pass filter:
Fourier transform of is given by :
Frequency response for is given by :
The filter is a low-pass filter:
Fourier transform of is given by :
Frequency response for is given by :
The filter is a low-pass filter:
Fourier transform of is given by :
Plot translates and dilations of scaling function:
Plot translates and dilations of wavelet function:
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