- 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,