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Math Help - sampling a smooth function

  1. #1
    Newbie
    Joined
    May 2009
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    sampling a smooth function

    Hi everybody,

    First, I am sorry if it is not the right place to ask my question. Could someone please help me with the following question:

    After sampling a smooth function (or at least a continuously differentiable function) like f(.) with a small enough sampling time, is it a correct assumption to say that f(n+1) (sample at (n+1)th instant) is approximately equal to f(n) (sample at nth instant)? is there any theorem in this respect? Thank you very much for your kind help.
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  2. #2
    Senior Member
    Joined
    Apr 2009
    From
    Atlanta, GA
    Posts
    408

    Understanding

    Can we have an example please?

    I think what you are asking is given a function f that it differentiable at x=a and a maximum discrepancy \delta>0, find a corresponding \epsilon>0 such that |f(a+\epsilon)-f(a)|<\delta, and yes, this will always be the case, but it will be different for each function and \delta.
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