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I have measurements of some function $f(l)$ at many values of $l$. However, $f(l_i)$ is covariate with surrounding values of $l$, a relationship which is described by a gaussian peak of some non-constant width $\sigma(l)$. I'd like to use this knowledge to generate a covariance matrix $K_{l,l^\prime}$ that describes possible measurements $f^\prime(l)$ of $f(l)$.

Is there a mathematical way to describe the relationship between $\sigma(l)$ and $K_{l,l^\prime}$?

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