An autonomous active medical implantable device, with a power supply and a wake-up circuit that responds to receipt of specific pulses transmitted through the interstitial tissues of the body. A transmitter device (40) generates trains of modulated pulses applied to electrodes (22, 24), and a receiver (50) processes (e.g., filter, amplify and demodulate) pulses collected on electrodes (22′, 24′). The receiver circuits (50) are selectively activated from a dormant (sleep) state in which they are not powered by a power source (34), to an operational (active) state in which they are powered and able to process (e.g., filter, amplify and demodulate) the collected pulses. A specific wake-up pulse train, configured in a predetermined characteristic pulse pattern, triggers passive wake-up circuits (66) in the receiver (50) to switch the receiver circuits from the sleep state to the operational state.