# vrf AW: Linearity

Question asked by VRFuser on Dec 14, 2003
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  diagrams to impress your boss...

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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