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I have some data to fit that looks like the blue curve, would anyone know what is it called or just the equation for it?

Some extra info: I`m trying to fit some data from an electronics experiment dealing with impedance (in alternating current, frequency dependent) and phase difference of inductors and capacitors.

Much Thanks

enter image description here

Lyu
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  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Mar 18 '23 at 13:34
  • There are infinitely many functions that fit those points. Are you expecting it to have any useful properties like smoothness or continuity? Are you expecting the curve comes from a certain family? – CyclotomicField Mar 18 '23 at 13:35
  • No, any would do. Though since I'm dealing with physical systems i guess continuity and differentiability are a must. – Lyu Mar 18 '23 at 13:36
  • Typically you decide on the form of a function either based on the problem or on the look of the data. That form has some parameters that you can adjust to minimize the error. Polynomials and sums of sine waves are common choices when you don't know anything better. – Ross Millikan Mar 18 '23 at 13:51
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    Polynomial regression will give you a good fit. – CyclotomicField Mar 18 '23 at 13:51
  • Well roughly speaking a logistic-like curve captures the increasing-then-settling-into-saturation aspect, then you have some sort of activity kicking in once you hit the plateau. – A rural reader Mar 18 '23 at 15:23
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    On this site you're getting general-purpose curve-fitting advice. On physics.stackexchsnge.com you might get an actual mathematical model for your electronics experiment. – Karl Mar 18 '23 at 16:17
  • Got it, thank you. – Lyu Mar 20 '23 at 15:19

1 Answers1

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Too long for a comment.

The curve fit you want depends on what you want to do with it.

Without some underlying physical model, there is probably no nice looking expression that matches these data.

Your data covers a very large range of frequencies. That suggests that you don't plan to extrapolate to larger or smaller inputs. If what you want are interpolated values, there are several good possibilities. The data points are pretty dense, so linear interpolation might do. If you really need smoothness, consider splines.

Ethan Bolker
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