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> Volume 6, Issue 12
Question: How to synthesize a function for samples.

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fardin akbaryan (fakbarya@acs.ucalgary.ca) Guest

Posted: Sat Nov 29, 1997 7:29 am Subject: Question: How to synthesize a function for samples.




#19 Question: How to synthesize a function for samples.
Dear Waveleters;
My research is on the generating a smooth function for a finite
number of samples. Wavelet Packet has been chosen. To get rid of the
boundary effects, I also assume the periodic boundary condition on the
signals.The WaveLab's functions are used for all the
computations. Here is the procedure.
1 f(x)=sin(x) is the prototype function and the number of samples
is taken as 128.
2 Packet tree has been constructed and the best packets are picked
by shannon entropy criteria.The best coefficients are shown as
Coeff(j,k,l).
3 For each of the selected packets, their basis functions are
computed.Basis function W(j,k,l) at jth scale,kth packet and lth
position can be constructed simply by putting value ONE at the
position(j,k,l), setting all the other packet tree to zero.Then the
function is synthesized by the reconstruction method. The support of
W(j,k,l) is [2^j*l 2^j*l+(2*N1)*2^j] where 2*N is the length of
filter.
4 The sin(x) can be expressed as SUM(W(j,k,l)*Coeff(j,k,l)).
I have tried Daubechies filters with different orders. But I can't
reproduce the original function,f(x)=sin(x). The results are completely
wrong. Do I miss something important here? Should I use other steps like
data preconditioning or postconditioning?
Is there anybody who can give me ideas how to get rid of this
problem? I'll really appreciate any idea and suggestion in this regard.
Regards
Fardin Akbaryan
Chem, & Petr. Eng. Dept., The university of Calgary
2500 University Drive NW, Calgary T2N 1N4, AB, Canada
Tel:(403)2207409 Fax:(403)2844852
email: fakbarya@acs.ucalgary.ca 





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