A digital processing device for a modulated signal, arranged at the input of a radio frequency receiver chain, suited in particular to a transmission system a direct sequence spread spectrum operation, comprising an analog-to-digital converter performing undersampling of the signal received, leading to an overlapping of the frequency range of the undersampled wanted signal by the frequency range of an interfering signal, demodulation means connected at the output of the analog-to-digital converter 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, and an additional filtering unit arranged between the low pass filter and the matched filter, for implementing a stochastic matched filtering operation to improve the signal-to-noise ratio at the input of the matched filter.