# Transfer function from a fourth order polynomial?

1. Apr 16, 2016

### Secold

1. The problem statement, all variables and given/known data
Excel data for an assignment I'm doing has spit out a curve from some experimental data as shown here:

http://i.imgur.com/KcJyEEj.png

I'm wondering if there's a nice way to put this as a transfer function in the form of Y/X or something similar

2. Relevant equations

3. The attempt at a solution
Simply using algebra seemed to not work to be able to get y/x, unless I'm missing something obvious.
I figured maybe if I used laplace transforms I could get a situation where Y/X would appear. Not sure how to go about this as it's pretty different from the differential equations laplace is normally used on.

Any idea?

2. Apr 17, 2016

### Staff: Mentor

The polynomial is probably the only way to express it, though you could factorize it if you consider that would look neater.

Maybe a quartic is too unwieldy for you? I'd expect your real life process will be limited to a restricted range of x values, so you could try approximating your quartic over that useful range with a cubic or even a binomial. You might find you can get a good fit.

The usual "transfer function" involves both magnitude and phase, each smoothly changing with frequency. You have no phase term here, apart from maybe a couple of abrupt sign reversals as the graph crosses the x-axis.

3. Apr 20, 2016

### rude man

No, since the relationship is nonlinear. A transfer function needs to be linear, by definition. You can approximate nonlinear relationships by describing functions, but this is not a true transfer function.

Some people might take your expression and call it a transfer function. Not common usage but OK IMO.

https://en.wikipedia.org/wiki/Transfer_function