Notations to represent a smoothed function/variable

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I am writing an academic paper. In this paper, I already defined some discrete functions $f$, $g$ and variables $P$, $Q$. After that, some smoothed versions of them were derived. I was wondering what is the best notations to represent these smoothed functions & variables?

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Finally I choose to use $\tilde{f}$ to represent smoothed $f$, because in convex optimization $\tilde{f}$ is the extended-value extension which extends the domain of $f$ to $\mathbb{R}$.