The characteristic function (c.f.) of a random variable, $X$, is defined as:
$$ \varphi_X(t) = \mathbb{E}[e^{i\langle t,x \rangle}] $$
For example, the c.f. of a Poisson random variable, $X$ is:
$$ \varphi_X(t) = e^{-\lambda(1-e^{it})} $$
I know c.f.'s are an extension of moment-generating functions, and can therefore be used to compute moments. And it is also easy to find the c.f. of the sum of independent random variables (take the product of the individual c.f.'s).
My question is: how do we interpret the argument/input ($t$) of a c.f. ?
There is a similar question here.
However, I do not understand the answer that says it is a "'sensor setting' chosen to investigate whether the given PDF has some inbuilt periodicity at $t$".