# Maxium value of discrete convolution

I'm trying to calculate the maximum possible short-term energy $E[n]$ of a sampled signal $s$ in terms of $N$ and $\text{bitdepth}$.

$$E[n] =\sum_{m=-\infty}^{\infty} s^2[n]w[n-m]$$

where

$$w(n) = 0.54 - 0.46\; \cos \left ( \frac{2\pi n}{N-1} \right) \quad \text{(Hamming window)}$$

and $$-2^{bitdepth} \le s[n] \le 2^{bitdepth}$$ hope this makes sense

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