# vrf AW: Linearity - solved

Question asked by VRFuser on Dec 15, 2003
Tell Mr. Design-Engineer, he ows us a pint - ALL of VRF....

-----Ursprngliche Nachricht-----
Von: William Drago [mailto:wdrago@suffolk.lib.ny.us]
Gesendet: Montag, 15. Dezember 2003 16:32
An: VRF
Betreff: [vrf] Re: Linearity - solved

All,

The second derivative is the first thing I tried. And as it turns out, it
does give the result I originally wanted. All I had to do was smooth the data
a little. The attached will show how the 2nd derivative increases in
magnitude as the curve tightens.

At any rate, that was all for naught. I had much better results by
interpolating the data to yield voltages that correspond to 0.1dB changes of
gain. Which is ultimately what the design engineer wanted anyway (I just wish

Bill

"Paulick, Stefan" <Stefan.Paulick.extern@brose.net> said:

> Hi Bill,
>
> having a look at your data, I would say that 'linearity' is no
> qualitiy
attribute for this function.
>
> You may
>
> a) use a transformation to a mathematical space (sorry, didn't know
> the
correct term) in which your function appears to be linear ( the suitable
mathematics is called in old Europe 'Jakobi- or Funktionaldeterminante').
>
> b) use a generic function which can be subtracted from your actual
> curve.
This may be a theoretical one or averages or whatever you expect to get.
>
> c) use a separation of the rising part (0.5 ..1V)and the plateau
(1.5V+...); and then apply linear methods.
>
> d) forget about linearity (;_)))and feed the stuff into a clever
> array-
algorithm which can be trained or trimmed to determine a 'good' from a 'poor'
curve. These things are usualy called 'fuzzy' or 'neuronal' or 'adaptive' and
do a brilliant job if you choose by accident the right one. Unfortunately,
there is - up to now - no mathematical theory known how to select a suitable
algorithm, so on this planet everyone does it 'try and error'.
>
> e) finally, a look at the theory of 'wavelets' may be helpfull, is is
> not
the generic way to deal with curves but I've heard rumours the they work fine
even with static signals. May be rubbish, but gives nice and colorful
>
> The suggested method with the circles gives from my point of view no
significant information, because you get both distance and angle of the
contact point, which is no good descriptive set of data - and if any noise is
included, you will see no details at all.
>
> The curve itself looks like a input pin from a semiconductor with
dynamically resistance amplification, so you may find loads of mathematical
theory under 'solid state semiconductor theory'.
>
>
> /Stefan
>
>
> -----Ursprngliche Nachricht-----
> Von: William Drago [mailto:wdrago@suffolk.lib.ny.us]
> Gesendet: Donnerstag, 11. Dezember 2003 18:52
> An: VRF
> Betreff: [vrf] Linearity
>
>
>
> All,
>
> I'm trying to calculate the relative non-linearity of a curve. I've
> come up
> with my own wacky way of doing it, but I'd like something mathematically
> cleaner. Ideally, I'd like a user function that returns the relative radius
> of every point on my curve. For all you math wizzes out there the data is
> attached.
>
> Thanx,
> Bill
>
> P.S. If this posts more than once it's because of a bug in the web
> based
> email software I'm using...
>
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