Method of compressed sensing and reconstruction of a spectrally-sparse signal

Abstract

A method is provided for performing compressed sensing of a spectrally-sparse signal within a given spectral band. The received signal being mixed 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 by low-pass filtering and sampled 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, using 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.

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