Abstract: The present invention relates to a method of compressed sensing of a spectrally-sparse signal within a given spectral band, the received signal being mixed (820) over a sensing frame with a pulse train scrolling with a repetition frequency linearly modulated over time within this frame. The result of mixing is filtered (830) by means of a low-pass filtering and sampled (840) at a non-uniform rate equal to the repetition frequency, to result in complex samples representative of the received signal. The spectrum of the received signal can be estimated by weighting by means of the complex samples the spectral values of a pulse into a plurality of frequency equidistributed in the band, and by summing up these weighted values for each of these frequencies. An estimate of the received signal is thereby deduced by inverse Fourier transform. The spectral band can be scanned based on the spectrum thus estimated.