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wave2lp

Laurent polynomials associated with wavelet

Syntax

[Hs,Gs,Ha,Ga] = wave2lp(W)

Description

[Hs,Gs,Ha,Ga] = wave2lp(W) returns the four Laurent polynomials associated with the wavelet W (see liftwave).

The pairs (Hs,Gs) and (Ha,Ga) are the synthesis and the analysis pair respectively.

The H-polynomials (G-polynomials) are low-pass (high-pass) polynomials.

For an orthogonal wavelet, Hs = Ha and Gs = Ga.

Examples

% Get Laurent polynomials associated to the "lazy" wavelet.
[Hs,Gs,Ha,Ga] = wave2lp('lazy')
 
Hs(z) = 1
 
Gs(z) = z^(-1)
 
Ha(z) = 1
 
Ga(z) = z^(-1)

% Get Laurent polynomials associated to the db1 wavelet.
[Hs,Gs,Ha,Ga] = wave2lp('db1')
 
Hs(z) = + 0.7071 + 0.7071*z^(-1)
 
Gs(z) = - 0.7071 + 0.7071*z^(-1)
 
Ha(z) = + 0.7071 + 0.7071*z^(-1)
 
Ga(z) = - 0.7071 + 0.7071*z^(-1)

% Get Laurent polynomials associated to the bior1.3 wavelet.
[Hs,Gs,Ha,Ga] = wave2lp('bior1.3')
 
Hs(z) = + 0.7071 + 0.7071*z^(-1)
 
Gs(z) = ...                                                                         
    + 0.08839*z^(+2) + 0.08839*z^(+1) - 0.7071 + 0.7071*z^(-1) - 
0.08839*z^(-2)  ...
    - 0.08839*z^(-3)                                                                
 
Ha(z) = ...                                                                         
    - 0.08839*z^(+2) + 0.08839*z^(+1) + 0.7071 + 0.7071*z^(-1) + 
0.08839*z^(-2)  ...
    - 0.08839*z^(-3)                                                                
 
Ga(z) = - 0.7071 + 0.7071*z^(-1)

See Also

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