# Wavelet transform of a signal - Problem

• Mar 26th 2013, 03:19 AM
BleuShut
Wavelet transform of a signal
Basically I have a signal distributed over [0,1] like this:

http://imagehost.pitestinet.ro/image...qhdexekvp5.jpg

and want to transform it with complex Gabor mother function.

http://imagehost.pitestinet.ro/image...yvx7y4pvel.jpg

Which should be scaled for measurement purposes here: (j: scale parameter which is an integer; k: translation/position index) (let's call this "1")

http://imagehost.pitestinet.ro/image...3fxckabk7w.png

Afterward wavelet coefficients can be calculated. It is defined as magnitude of: (we're calling this "2")

http://imagehost.pitestinet.ro/image...7630rmj96a.png
(psi "bar" indicates conjugate complex of scaled gabor function. S(beta) is the signal above.)

Back to signal; each change of slope like the one at @ 0.65 indicates a crack in the structure; and signal's wavelet transform graph should have a sudden peak at that position; peak value will be indicative of crack depth. Something like this:

http://imagehost.pitestinet.ro/image...kzbpol3ej4.jpg

...................................

Now as for the question; the result of "2" seems like a constant to me which obviously shouldn't be the case because you can't draw a meaningful graph with that. So I want to know:

1. whether I should integrate "2" over [0,x] for each point at [0,1]; resulting in separate wavelet coefficients for each point.

2. should I choose a variable translation index k in "2"? And if this is the case do you know how this "k" parameter is usually chosen?

3. Or is it something else entirely?

Thanks for taking the time to read.
• Mar 26th 2013, 05:41 AM
BleuShut
Re: Wavelet transform of a signal - Problem
If you have a MATLAB code that's simply about calculating wavelet transform of a signal that would be very appreciated too. Doesn't matter whatever function/signal it uses.