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Based on a paper in here, they have proposed a method to optimize morlet function parameter. I have tried to implement their technique, but I can't get rational results. any idea?
In here you can see what they have done briefly: Imagine you have a signal with following frequency and damping pairs :
$(f_i ,\zeta_i), (f_{i+1},\zeta_{i+1})$ and $f_i,f_{i+1} $ are two closely spaced frequency i.e. $1.01Hz,1,09 Hz$
now we define $f_{i,i+1}=\frac{f_i+f_{i+1}}{2}$ and $\Delta f_{i,i+1}=f_{i+1}-f_i$
based on Heisenberg uncertainty principle the $f_c\sqrt{f_b}$ must be in range of :
$2\alpha\frac{f_{i,i+1}}{2\pi\Delta f_{i,i+1}}\leqslant f_c\sqrt{f_b}\leqslant \frac{2\gamma}{\beta}Tf_i;[1_a] $
for another reason $f_c \geq \frac{5}{2\pi};[1_b]$
which demonstrates that $f_c\sqrt{f_b}$should be chosen within an interval so that a compromise could be made between frequency and time resolutions, Another consideration is that because $f_c\sqrt{f_b}$ is within an interval, there exist numerous pairs of $f_b$and $f_c$. Practically, it is necessary to introduce some other criteria to select optimum values of $f_b$ and $f_c$, the minimum Shannon entropy is used for criteria :
$E=-\sum_{i=1}^{M}d_i log(d_i)[2]$, where $d_i$ is: $d_i=\frac{|W(a_i,t)|}{\sum_{j=1}^{M}W(a_j,t)}$ $,M$ is number of scales
so we must minimize $E$ from equation[2] in range of [$1_a,1_b$].
I have used fmincon matlab function to solve this non linear unequality constrain in matlab
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  • $\begingroup$ I can't read the paper as it is paywalled, so can't help you. Not that I would likely be able to understand your question even if I could. $\endgroup$ – mathreadler Jan 3 '16 at 22:58
  • $\begingroup$ Ah wait maybe I would be able to understand it after all I was just a bit tired when I read the question. But I'm a poor hobby researcher so sadly I can't afford to pay by the copy. $\endgroup$ – mathreadler Jan 3 '16 at 23:07
  • $\begingroup$ @mathreadler Thanks for your attention. I solved the paper 2 years ago and published the paper on that. :) $\endgroup$ – Electricman Jan 4 '16 at 21:06
  • $\begingroup$ Ah great, is it possible to read it somewhere? I think I maybe would find it interesting. $\endgroup$ – mathreadler Jan 4 '16 at 21:50
  • $\begingroup$ Sure please write down your email. @mathreadler $\endgroup$ – Electricman Jan 6 '16 at 21:10

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