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[Tftb-help] Urgent Help needed on wavelet

From: lui
Subject: [Tftb-help] Urgent Help needed on wavelet
Date: Mon, 3 Sep 2007 16:45:27 +1000

Dear friends,
Thanks for your reply regarding to my questions. Regarding to the wavelet transform question, I probably should have include the actual equations here.
Traditionally and in the TF toolbox, the wavelet transform of the sigal f(t) is being defined as
W(t,a;h) = (a^-0.5) x Integrate [f(t') x h((t-t')/a)]dt'    (1)
which the lower and upper limits of the integral are negative infinity and positive infinity, and h(t) is the mother wavelet.
Under Hao Ling's defintion, the wavelet transform is defined as
W(tau,omega) = (tau^0.5) Integrate [F(w) x H(tau(w-omega)] dw   (2)
or in terms of the signal in time domain, the wavelet transform can be given as
W(tau,omega) = (tau^-0.5) x Integrate [f(t) x h(t/tau) x exp(j*omega*tau)] dt    (3)
The 'a'  factor in equation (1) and 'tau' factor in equation (2) and (3) essentially the scaling factor in the wavelet transform, the "omega" is written as capital and it is different from 'w = 2 x pi x f.'  Noticed that there is an extra exponential compoent in (2).
It would be great if someone can give me some hints or solution to compute (2) and (3) based on the existing TF toolbox.
If you would like to have further info about the transform, email me and I will send you the papers.

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