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A question about ''Wavelet''
 
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Ming-Haw Yaou
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PostPosted: Wed Jul 15, 1992 5:18 pm    
Subject: A question about ''Wavelet''
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A question about "Wavelet"

Hello everyone !!

I have a question about the binary orthonormal wavelets.

Let P(x) be the scaling function and Q(x) be the wavelet,
Pmn(x):=2^(-m/2)P(2^(-m)x-n) and Qmn(x):=2^(-m/2)Q(2^(-m)x-n) be
the bases for multiresolution wavelet signal approximation.
In the orthonormal case, both Pmn(x) and Qmn(x) are orthonormal bases,
also P(x) and Q(x) are mutually orthogonal.

My question is :

Is it possible to find a pair of functions P(x) and Q(x) such that the
following two properties can be satisfied:

(a) Both Pmn(x) and Qmn(x) are orthonormal bases, P(x) and Q(x)
are mutually orthogonal. That is, P(x) and Q(x)
can construct a binary orthonormal wavelet analysis.
(b) The second derivatives of P(x) and Q(x), denoted as P"(x) and Q"(x),
are mutually orthogonal too.

I will very appreciate if any answer or advice is sent from you.
Please e-mail to : u7811837@cc.nctu.edu.tw

Thank in advance

Ming-Haw Yaou.
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