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Curve Fitting

  1. Aug 25, 2004 #1
    I face the following problem.
    I need to find the best values of the parameters [itex]a,b,c[/itex]
    of the complex function [itex]f(x)=a+\frac{b-a}{1+j x c}[/itex] of the real
    variable [itex]x[/itex] where ([itex]j^2=-1[/itex])
    such that
    [itex]f(2 \pi 10^6)=2.33-j 1.165 10^{-3}[/itex] and
    [itex]f(2 \pi 10^{10})=2.347-j 3.7552 10^{-3}[/itex].

    It seems to be a curve fitting problem but the function [itex]f(x)[/itex] is complex!
  2. jcsd
  3. Aug 25, 2004 #2


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    True enough; you have three constants to optimize to 4 restraints.
    What's your problem?
  4. Aug 25, 2004 #3


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    Oh, those engineers and their jmaginary numbers!
  5. Aug 26, 2004 #4


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    To get you started:
    1. Define:
    Ask yourself:
    Why have you been given so huge arguments?
    In particular, can I use that fact to my advantage later on?

    3. Requirements of curve fitting:
    4. Define:
    5. Define:

    6. Construct:

    Clearly, S>=0, and S=0 if and only if the curve fitting is exact.
    We are interested in the choice of (a,b,c) such that a minimum of S is found.
    Hence, we should consider the system of 3 equations:

    This system can (theoretically, at least!) be solved for minimizing values
    To find a simple, approximate solution to the system of equations, I suggest that you utilize your knowledge that [tex](x_{0},x_{1})[/tex] are huge numbers.
    Good luck!
    This is just one of many techniques to derive curve-fitting coefficients.
    It is by no means clear that this technique provides the simplest system to solve for coefficients (a,b,c). Look up in a numerical analysis book (or something like that) to get other ideas..
    Last edited: Aug 26, 2004
  6. Aug 26, 2004 #5

    Hahaha :rofl:
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