
From:  lui 
Subject:  [Tftbhelp] 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((tt')/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(womega)] 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.
Cheers
Antony

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