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Laurent polynomials associated with wavelet
Syntax
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
laurpoly
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