Summary: The frequency analysis of a bistable binary oscillator triggered by a stationary random signal is performed by analyzing the expression for the power spectrum of its output. The oscillator state changes when the input noise exceeds a fixed threshold \(\theta\), which occurs in correspondence of the events produced by an ordinary renewal process. After each state change, a fixed refractory time \(T\) is to be passed before the output performs a new transition. A theoretical study shows that a coherence resonance effect appears in the output square wave if the threshold \(\theta\) is lower than a positive real value \(\underline{\theta}\). When the overcoming of the input threshold occurs according to a Poisson process with exponential parameter \(\alpha\), the regularity is present at the output only if the product \(\alpha T\) exceeds \(\sqrt 2 - 1\). The value of the characteristic frequency increases rapidly with \(\alpha T\) towards its asymptotic value 1/(\(2T\)). The same probabilistic approach is then adopted to perform the spectral analysis of a set of uncoupled binary oscillators, sharing the same refractory time \(T\) and the same input random signal. Under mild assumptions the whole system behaves as a single oscillator, whose output is amplified proportionally to the number of elements involved.