While playing around, I came across the following function
$$f(x)=\lceil\{|x|\}\rceil$$
Its $0$ at integers, $1$ otherwise.(The mod is to extend it to $x<0$)
So I made $$g(x)=\frac1{f(x)}-1$$
which blows up for ints and $0$ otherwise. It looks like a Dirac comb but I have a feeling it isn't. Is $g$ a Dirac Comb?