Detecting trough widths and locations in 1d signal
A wavelet analysis or wavelet transform will give you scale(frequency) vs time vs amplitude. I am not sure how that will help you with your problem. 
Here is an algorithm for wavelet transform :


Choose your wavelet : Haar , Molet etc ..say $ \psi (n) $ 
Choose Scale : the scale should be a multiple of smallest time interval dt. 
Calculate the FFT of wavelet - $\Psi_0 (s\omega _k)$
Normalise FFT of the Wavelet - $ \Psi (s\omega_k)=(2\pi s / \delta t)\Psi_0 (s\omega _k)$
Find FFT of time series x(t) = $ X_k = 1/N  \sum_{k=0}^{N-1} x(n) e^{-2\pi i k n/N } $
Then Wavelet transform is : 
  $ W(s)= \sum_{k=0}^{N-1} X_k\Psi^* (s\omega_k) e^ {i\omega_k n \delta t} $    ...where * is complex conjugate 
Generally the Fourier transform of the wavelet should be known analytically. 


Few good sources : 


http://paos.colorado.edu/research/wavelets/bams_79_01_0061.pdf
http://users.rowan.edu/~polikar/WAVELETS/WTpart1.html