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I am running a wavelet transform (cmor) to estimate damping and frequencies that exists in a signal.cmor has 2 parameters that I can change them to get more accurate results. center frequency(Fc) and bandwidth frequency(Fb). If I construct a signal with few freqs and damping then I can measure the error of my estimation(fig 2). but in actual case I have a signal and I don't know its freqs and dampings so I can't measure the error.so a friend in here suggested me to reconstruct the signal and find error by measuring the difference between the original and reconstructed signal e(t)=|x(t)−x^(t)|. so my question is:
Does anyone know a better function to find the error between reconstructed and original signal,rather than e(t)=|x(t)−x^(t)|.
can I use GA to search for Fb and Fc? or do you know a better search method?
Hope this picture shows what I mean, the actual case is last one. others are for explanationsenter image description here

Thanks in advance

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    $\begingroup$ I think GA is not a suitable optimization algorithm for this problem. GA is mostly used when parameters to be optimized are a lot and when the objective function varies in a way which is not able to be tracked. I suggest you to use Wavelets with high accuracy. $\endgroup$ – Mahdi Khosravi Sep 1 '13 at 19:18
  • $\begingroup$ @MahdiKhosravi hi, thanks for your answer. what is " Wavelets with high accuracy"? a new wavelet type or what? $\endgroup$ – Electricman Sep 1 '13 at 19:55
  • $\begingroup$ I mean use Wavelets with higher resolution to get results with more accuracy. $\endgroup$ – Mahdi Khosravi Sep 1 '13 at 20:35
  • $\begingroup$ @MahdiKhosravi I've done that already and the estimated parameters are accurate enough.But in this post I wanted to ask how can I optimize fc and fb(resolution) with another algorithm. $\endgroup$ – Electricman Sep 2 '13 at 7:28
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    $\begingroup$ $e(t) = |x(t) - \hat x(t)|$. I don't have any better idea. $\endgroup$ – Mahdi Khosravi Sep 2 '13 at 13:08
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You should be able to use GA or any other derivative-free optimization methods to solve your problem [1]. The correct parameter values can be determined using your application. If I'm trying to optimize for compression then I will look into the entropy of the resultant coefficients. Deciding on the actual values for your parameters will depend on how you plan to use them. The correct parameter values are simply the ones that work better.

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  • $\begingroup$ I don't know enough about GA and search methods. I've just edited my post to get sure that my question is clear, Look at my edit please , and help me to implement GA or another search method. Tnx $\endgroup$ – Electricman Sep 2 '13 at 20:30
  • $\begingroup$ How can I find the best wavelet parameters by entropy criterion? @hasan $\endgroup$ – Electricman Dec 6 '13 at 9:34

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