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Transfer function from a fourth order polynomial?

  1. Apr 16, 2016 #1
    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:
    KcJyEEj.png

    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. jcsd
  3. Apr 17, 2016 #2

    NascentOxygen

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    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.
     
  4. Apr 20, 2016 #3

    rude man

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    Homework Helper
    Gold Member

    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
     
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