bior 3.5 wavelet filter
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i want to know some detail about ( bior 3.5) ... filter and why it is named 3.5 ??
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Wayne King
le 24 Juin 2012
As Walter states those are the number of vanishing moments for the scaling and wavelet filters for both the reconstruction (synthesis) filters -- the first number (3 here) and the decomposition (analysis) filters -- the second number (5 here).
If you have the Signal Processing Toolbox in addition to the wavelet toolbox you can see this by looking at the zeros of the lowpass filters at pi (-1+j0)
[LO_D,HI_D,LO_R,HI_R] = wfilters('bior3.5');
zplane(LO_D); % 5 zeros at -1+j0
zplane(LO_R); % 3 zeros at -1+j0
A wavelet filter with N vanishing moments is orthogonal to polynomials of up to degree N-1. So using the bior3.5 filter will "kill" polynomials up to degree 4 in the decomposition. If the signal is approximated well locally by a polynomial up to order 4, then the wavelet coefficients obtained with the bior3.5 filter will be small.
On the other hand, the fewer vanishing moments used in the reconstruction will result a better result because it is smoother than the wavelet used in the decomposition.
This is a decided advantage of biorthogonal wavelets over orthogonal. In the biorthogonal case, you have the ability to use a wavelet with greater vanishing moments at the decomposition, and a smoother wavelet for the reconstruction (any errors introduced will be smooth errors).
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