We consider the processing of narrowband signals that modulate carrier waveforms in sensory systems. The tuning of sensory neurons to the carrier frequency results in a high sensitivity to the amplitude modulations of the carrier. Recent work has revealed how specialized circuitry can extract the lower-frequency modulation associated with the slow envelope of a narrowband signal, and send it to higher brain along with the full signal. This paper first summarizes the experimental evidence for this processing in the context of electroreception, where the narrowband signals arise in the context of social communication between the animals. It then examines the mechanism of this extraction by single neurons and neural populations, using intracellular recordings and new modeling results contrasting envelope extraction and stochastic resonance. Low noise and peri-threshold stimulation are necessary to obtain a firing pattern that shows high coherence with the envelope of the input. Further, the output must be fed through a slow synapse. Averaging networks are then considered for their ability to detect, using additional noise, signals with power in the envelope bandwidth. The circuitry that does support envelope extraction beyond the primary receptors is available in many areas of the brain including cortex. The mechanism of envelope extraction and its gating by noise and bias currents is thus accessible to non-carrier-based coding as well, as long as the input to the circuit is a narrowband signal. Novel results are also presented on a more biophysical model of the receptor population, showing that it can encode a narrowband signal, but not its envelope, as observed experimentally. The model is modified from previous models by stimulus reducing contrast in order to make it sufficiently linear to agree with the experimental data.