Electromechanical resonators are a key element in radio-frequency telecommunication devices and thus new resonator concepts from nanotechnology can readily find important industrial opportunities. Here, the successful experimental realization of AM, FM, and digital demodulation with suspended single-walled carbon-nanotube resonators in a field-effect transistor configuration is reported. The crucial role played by the electromechanical resonance in demodulation is clearly demonstrated. The FM technique is shown to lead to the suppression of unwanted background signals and the reduction of noise for a better detection of the mechanical motion of nanotubes. The digital data-transfer rate of standard cell-phone technology is within the reach of these devices.