Thread: Wavelet transform of a signal - Problem

1. Wavelet transform of a signal

Basically I have a signal distributed over [0,1] like this:

and want to transform it with complex Gabor mother function.

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

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

(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:

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

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.

2. 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.