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> Volume 1, Issue 1
A question about ''Wavelet''

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MingHaw Yaou Guest

Posted: Wed Jul 15, 1992 5:18 pm Subject: A question about ''Wavelet''




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)xn) and Qmn(x):=2^(m/2)Q(2^(m)xn) 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 email to : u7811837@cc.nctu.edu.tw
Thank in advance
MingHaw Yaou. 





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