Here f(x) is an arbitrary differentiable function and dx is a small increment. I am also interested in the limit of this expression when both n -> Infinite and dx -> 0. I guess the absolute value of this expression is a sort of generalized derivative of f(x) or some how related to the derivatives of the function evaluated in x. I would also appreciate any reference to relevant texts or articles.
It looks to me like a discrete form of an integral. Otherwise, if f(x) is known, you might try to linearize f(x) in order to get simpler sums
It is the first frequency bin of the Discrete Fourier Transform of a sampled version of f(x).
Refer to http://en.wikipedia.org/wiki/Discrete_Fourier_transform
It is assumed that f(x) has a periodicity equal to n*dx.
Many thanks Piero Angeletti. That is then the lowest frequency Fourier component of the sampled function after the zero freq. component (mean value).
What could be said about its limit when both n -> Infinite and dx -> 0 ?
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