- #1

- 106

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$$

\delta(x - \mu) = lim_{\sigma -> 0} \frac{1}{\sqrt{2\pi \sigma^2}} e^{\frac{-(x - \mu)^2}{2\sigma^2}}

$$

Is it possible to also say the reverse with a weighted sum of Dirac Deltas to construct a Gaussian spectrum?

$$

\frac{1}{\sqrt{2\pi \sigma^2}} e^{\frac{-(x - mu)^2}{2\sigma^2}} = \sum_{i} w_i \delta(x - i)

$$

Where, somehow the weights ##w_i## constitute how it is distributed (##\sigma##). If yes, how do we decide these weights?