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Let's have the discrete periodic function $f(t)$ which has only 5 non-zero values $f(t_0) = -10, f(t_1) = -5, f(t_2) = -10, f(t_3) = -15$ and $f(t_4) = -10$, all other points within the period $[t_0,t_4]$ being zero. The obvious interpolating function which recovers these values is $f(t) = 5sin(t) - 10$. Is this a unique interpolating function or you can propose other interpolating functions, such as polynomial functions with constraints? Any concrete examples, please?

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