We explore the possibility of a signal-to-noise ratio (SNR) gain both in a single neuron and a neuronal network. In the presence of a weak sinusoidal or pulse signal and Gaussian noise, the output SNR can exceed the input SNR over a wide range of noise intensities. The high output SNR and SNR gain can be acquired coincidentally at optimal noise levels. The results further verify that noise can play a constructive role in sensory processing in neuronal systems.