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## Mathematical curve  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! 1 ACCEPTED SOLUTION

Accepted Solutions  10-Marble
(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

7 REPLIES 7  24-Ruby III
(To:DJF)

One way   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.   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....)  16-Pearl
(To:DJF)

Hold on, this isn't too bad.  Even pretty good without the d and e exponents.   24-Ruby III
(To:Werner_E)

Solution without animation is not solution!   24-Ruby V
(To:ValeryOchkov)

@ValeryOchkov wrote:

Solution without animation is not solution!

... or its not a solution at all  10-Marble
(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 