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CDFWavelet

represents a Cohen–Daubechies–Feauveau wavelet of type "9/7".

CDFWavelet["type"]

represents a Cohen–Daubechies–Feauveau wavelet of type "type".

Details

CDFWavelet defines a set of biorthogonal wavelets.
The following "type" 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.
CDFWavelet can be used with such functions as DiscreteWaveletTransform, WaveletPhi, etc.

Examples

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Basic Examples (3)

Scaling function:

Wavelet function:

Filter coefficients:

Scope (16)

Basic Uses (10)

Compute primal lowpass filter coefficients:

Dual lowpass filter coefficients:

Primal highpass filter coefficients:

Dual highpass 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:

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 (1)

Multivariate scaling and wavelet functions are products of univariate ones:

Properties & Relations (16)

Lowpass filter coefficients sum to unity; :

Highpass filter coefficients sum to zero; :

Dual lowpass 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; :

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:

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