Sure. A "system" (which is an incredibly broad term; in practice a circuit composed of resistors, capacitors, and inductors can model any linear system so we stick with that) takes the signal x(t) and maps it to something else, f(x(t)). The autocorrelation function r(t) defines the bias of the coin (r(t) is generally given in the problem, or in real life found empirically). All of these functions are difficult to work with directly.

However, their Laplace transforms are much easier: X(s) and R(s), and because of how Laplace transforms work, F(s)X(s) (convolution becomes multiplication after a Laplace transform). So if F(s) is 1 / R(s), F(s)X(s) = X(s) / R(s), which means all of the correlation in X(s) is divided out, and you're left with an uncorrelated function, or fair coin in this case.