Impedance Equation fit to Complex Data

• To: mathgroup at smc.vnet.net
• Subject: [mg86482] Impedance Equation fit to Complex Data
• From: AgustusBenjamin at gmail.com
• Date: Wed, 12 Mar 2008 00:13:46 -0500 (EST)

```Dear Group,

I'm trying to fit an equation to data using FindFit.  When I type
in the equation and data and then FindFit, I get this:

Z := [Omega]^(-(2 ArcTan[H/G])/[Pi]) (G - i H) + R

Data := {{1.`, 2.658637`- 8.389573` i}, {1.5`,
1.784396`- 6.214955` i}, {2.5`,
1.656569`- 3.97147` i}, {3.5`,
1.633799`- 2.878841` i}, {5.5`,
1.357069`- 1.776964` i}, {6.5`,
1.259121`- 1.848249` i}, {8.5`,
1.105417`- 1.344566` i}, {9.5`,
1.119456`- 1.148945` i}, {11.5`,
1.082122`- 1.064767` i}, {14.5`,
1.015714`- 0.8684088` i}, {15.5`,
1.055329`- 0.664562` i}, {18.5`,
0.8675349`- 0.5107938` i}, {20.5`,
0.8968949`- 0.4148388` i}}

FindFit[Data, Z, {R, G, H}, \[Omega]]

FindFit::nrlnum: The function value {-0.658637+7.38957 \
\[ImaginaryI],0.0321006+5.39846 \[ImaginaryI],-0.0241135+3.33901 \
\[ImaginaryI],<<5>>,0.212762+0.769883 \[ImaginaryI],0.246899+0.605796
\
\[ImaginaryI],<<3>>} is not a list of real numbers with dimensions \
{13} at {R,G,H} = {1.,1.,1.}. >>

Why?!?!?  Why can't FindFit handle this?  What's wrong with it not
being a list of real numbers?  I'm pulling my hair out.  I've looked
at others' suggestions for similar problems and they don't work for
this problem.  Am I out of my mind?  Does anyone have a suggeston?

Regards,

Benji

```

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