1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

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


    User Avatar
    Staff Emeritus
    Science Advisor

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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    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:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Curve Fitting