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Fourier series/ Gibb's phenomena/ accuracy of approximations watch

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    I am approximating a sinusoidal signal modulated by a gaussian envelope defined over the interval x=[-L/2,L/2]. However my question is more general:

    If you have a function which is continuous across the boundary at x=-L/2 and x=L/2, what other reasons, apart from discontinuity of the function across the boundary, would you have for the approximation (i.e. when you rebuild the function from the calculated fourier co-efficients, but only using a finite number of them) becoming less good at the boundaries.

    I'm aware I probably haven't described my problem very well.... to put in simple terms, if you look at my graph i've attached, I want to know why the yellow line gets big at the edges, even though the function is continuous everywhere (in the zeroth derivative).

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    I'm not sure what you want to know, but basically there are bound to be problems when approximating a discontinuous function with a continuous one...
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