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I'm working on an algorithmus that sould need the inverse of the SI function.

since this last once isn't oviouse to calculate, I'm trying to get only the parobla part from the SI function, to be clair , say I have this figure : enter image description here

I'm only interessted in the part from the max of each curve tell the point of intersection with the following one. So my question what is the fomula for the "parabola part " in si function.

the ploted function are all : si(3pi X /4)

thanks for any help.

Engine
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1 Answers1

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There are two problems, I think: fitting a parabola to the higher part, and moving the parabola to the next part of the sequence. This will address fitting the parabola.

I'd just use a least squares technique to find the $a$, $b$, and $c$ parameters.

This shows the part of the paper of interest:

enter image description here

Peter K.
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  • @ Peter thanks for your answer, but is too complicated for what I want to do since I know the MAx and Zero point ? – Engine May 12 '15 at 11:01
  • @user2007919 It depends on how accurate you want / need it to be. You only really need 3 points to find $a$, $b$, and $c$. If matching those points exactly (and not necessarily any others) is good enough, then go with that. The answer will be the same, except that $n=3$ in your case. – Peter K. May 12 '15 at 11:19
  • thanks a lot for your help, you're right it's not enough, the issue that I have is how to get the 2nd order Regression, if ou had a small example it would be great. thanks in advance – Engine May 12 '15 at 12:25