Envelope gating and noise shaping in populations of noisy neurons.

Narrowband signals have fast and slow time scales. The transmission of narrowband signal features on both times cales, by spiking neurons, is demonstrated experimentally and theoretically. The interaction of the narrowband input and the threshold nonlinearity may create out-of-band interference, hindering the transmission of signals in a low-frequency range. The resultant out-of-band signal is the "envelope," or time-varying modulation of the narrowband signal. The levels of noise and nonlinearity intrinsic to the neuron gate transmission on the slow "envelope" time scale. When a narrowband and a distinct slow signal drive the neuron, the slow signal may be poorly transmitted. Increasing intrinsic noise in an averaging network removes the envelope in favor of the slow signal, paradoxically increasing the signal-to-noise ratio. These gating effects are generic for threshold and excitable systems.