It is shown that, in spite of claims put forward in the literature, the stochastic resonance (SR) appears even in linear systemsboth overdamped and inertial driven by Gaussian white noise, and even after averaging the asymptotics over the initial phase of the input signal. This supports recent suggestions that SR is a universal effect present in every stochastic process modulated by external signals. It is also shown that the noise may sustain the output signal which otherwise would vanish exponentially in the course of time