  A renowned information-theoretic formula by Shannon expresses the mutual
information rate of a white Gaussian channel with a stationary Gaussian input
as an integral of a simple function of the power spectral density of the
channel input. We give in this paper a rigorous yet elementary proof of this
classical formula. As opposed to all the conventional approaches, which either
rely on heavy mathematical machineries or have to resort to some "external"
results, our proof, which hinges on a recently proven sampling theorem, is
elementary and self-contained, only using some well-known facts from basic
calculus and matrix theory.
