We study the effect of noisy oscillatory input on the signal discrimination by spontaneously firing neurons. Using analytically tractable model, we contrast signal detection in two situations: (i) when the neuron is driven by coherent oscillations and (ii) when the coherence of oscillations is destroyed. Analytical calculations revealed a region in the parameter space of the model where oscillations act to reduce the variability of neuronal firing and to enhance the discriminability of weak signals. These analytical results are employed to unveil a possible role of coherent oscillations in peripheral electrosensory system of paddlefish in improvement of detection of weak stimuli. The proposed mechanism may be relevant to a wide range of phenomena involving coherently driven oscillators.