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Calculating Shannon-like entropy function of a 1D signal with random noise

You're a bit missing the point here: when you use the formula $ H = - \sum_i x_i \log(x_i)$ instead of $ H(P) = - \sum_i p_i \log(p_i)$ for anything where $P(x_i) \ne x_i$, then that's where your ...
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