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