1. Digital processing device for a modulated signal, arranged at the input of a radio frequency receiver chain, suited in particular to a transmission system using binary carrier phase modulation by means of a binary message on which a direct sequence spread spectrum operation has been carried out, this device comprising analog-to-digital conversion means performing undersampling of the signal received, leading to an at least partial overlapping of the frequency range of the undersampled wanted signal by the frequency range of a first interfering signal corresponding to the noise of the transmission channel, and further comprising demodulation means connected at the output of the analog-to-digital conversion means in order to bring the undersampled wanted signal back to baseband, a low pass filter connected at the output of the demodulation means and a filter matched to the spreading code used, wherein the analog-to-digital conversion means include a comparator capable of comparing the amplitude of the undersampled signal to a reference value, in order to carry out a 1-bit quantizing of the undersampled signal, said comparator causing the creation of a second interfering signal corresponding to the quantizing noise, and in that it includes an additional filtering unit arranged between the low pass filter and the matched filter, said filtering unit implementing a multi-noise, stochastic matched filtering operation making it possible to improve the overall signal-to-noise ratio, at the input of the filter matched to a spreading code, taking into account the signal-to-noise ratio of the transmission channel, on the one hand, and the signal-to-quantizing noise ratio, on the other hand.