- A system for tracking the peak power of a telecommunication signal to be transmitted for an RF power amplification of said telecommunication signal to be transmitted, comprising: - an RF power amplifier having an RF input , a supply voltage input and an RF output , - a digital processing device , - a digital to RF converter , and - a DC-DC converter , the digital processing device having an input capable of receiving the telecommunication signal to be transmitted in the form of digital data, a first output connected to an input of the digital to RF converter and a second output connected to an input of the DC-DC converter , the digital to RF converter having an output connected to the RF input of the RF power amplifier , the DC-DC converter having an output connected to the supply voltage input of the RF power amplifier , characterized in that the output of the DC-DC converter is able to assume a discrete voltage value from among N discrete voltage values, N being an integer greater than or equal to 2, the digital processing device comprising, between its input and its first output , a delay element τ, and between its input and its second output , a processing chain comprising an envelope tracking control logic capable of creating an envelope tracking control signal with N discrete levels from digital data received at the input of the digital processing device , said envelope tracking control signal with N discrete levels being sampled at a predetermined sampling frequency, the processing chain further comprising, downstream from the envelope tracking control logic , a driver logic of the DC-DC converter comprising a device for calculating the peak value and a device for selecting the supply voltage , the device for calculating the peak value being capable of: - windowing the envelope tracking control signal with N discrete levels , using a sliding time window, the duration of which is defined by a predefined number of samples of the envelope tracking control signal with N discrete levels , the offset between time windows being equal to a sample of the envelope tracking control signal with N discrete levels , and - calculating the maximum value of the envelope tracking control signal with N discrete levels over each time window of the sliding time window, and the supply voltage selection device being capable of controlling the DC-DC converter in order to impose at all times, on the output of the latter, from among the N discrete voltage values, as a function of the maximum value of the envelope tracking control signal with N discrete levels over the current time window, of the value of the envelope tracking control signal with N discrete levels delayed by the duration of the sliding time window and of the current value of the output of the device for selecting the supply voltage , a discrete supply voltage value greater than or equal to the envelope tracking control signal with N discrete levels , said discrete supply voltage value being applied during a minimum duration equal to the duration of the sliding time window. - an RF power amplifier having an RF input , a supply voltage input and an RF output , - a digital processing device , - a digital to RF converter , and - a DC-DC converter , - windowing the envelope tracking control signal with N discrete levels , using a sliding time window, the duration of which is defined by a predefined number of samples of the envelope tracking control signal with N discrete levels , the offset between time windows being equal to a sample of the envelope tracking control signal with N discrete levels , and - calculating the maximum value of the envelope tracking control signal with N discrete levels over each time window of the sliding time window, <EOS>