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Mathematical curve

DJF
16-Pearl
16-Pearl

Mathematical curve

Anyone happen to know a mathematical equation that would represent data like this (an s-curve in a log-log plot)?  Excel attached.

Thanks!

 

2019-07-17_13-09-22.png

1 ACCEPTED SOLUTION

Accepted Solutions
LouP
11-Garnet
(To:DJF)

This looks like a linear system frequency response, with complex frequency s = jx. Real poles at s=0 and s~2, real zero at s~0.2. the attached shows a simple rational approximation (one zero, two poles) that fits reasonably well. The attached pdf shows a minerr optimization of the form.

 

Is the data in fact a linear system frequency response?

 

Lou

 

 

View solution in original post

7 REPLIES 7
ValeryOchkov
24-Ruby IV
(To:DJF)

One way

loglogplot.png

Werner_E
24-Ruby V
(To:DJF)


@DJF wrote:

Anyone happen to know a mathematical equation that would represent data like this (an s-curve in a log-log plot)?  Excel attached.

Thanks!

 

 


I would say that depends what you would need the equation for. In most cases, you know the function type for this process, and then it's all about finding the appropriate parameters using the measurement data.

If you doesn't know anything, then usually a simple interpolation (linear or spline) is all thats needed.

 

Here is a similar approach than Valery's (polynomial fit of the logarithmized data) but done on the original data.

B.png

DJF
16-Pearl
16-Pearl
(To:Werner_E)

Thanks WE and Valery.  I was hoping for something besides a polynomial or spline that passes through everything.  Guess I should have stated that.  I'm looking for a fundamental curve that has that shape.  (I never found one myself).   (You'd think someone would have compiled master lists of equations and their shapes, but I guess that's too much to ask.  Maybe when I retire....)

DJF
16-Pearl
16-Pearl
(To:DJF)

Hold on, this isn't too bad.  Even pretty good without the d and e exponents.2019-07-17_19-17-36.png

Solution without animation is not solution!

osc.gif


@ValeryOchkov wrote:

Solution without animation is not solution!

 


... or its not a solution at all

LouP
11-Garnet
(To:DJF)

This looks like a linear system frequency response, with complex frequency s = jx. Real poles at s=0 and s~2, real zero at s~0.2. the attached shows a simple rational approximation (one zero, two poles) that fits reasonably well. The attached pdf shows a minerr optimization of the form.

 

Is the data in fact a linear system frequency response?

 

Lou

 

 

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