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.