Compressed sensing enhanced random equivalent sampling

The feasibility of compressed sensing (CS) based waveform-reconstruction for data sampled from random equivalent sampling (RES) method is investigated. A novel measurement matrix motivated by the Whittaker-Shannon interpolation formula is proposed for this purpose. Experiments indicate that, for spectrally-sparse signal, the CS reconstructed waveform exhibits significantly higher signal-to-noise ratio (SNR) than that using the traditional time alignment method. A prototype realization of this proposed CS-RES method has been developed using off-the-shelf components. It is able to capture analog waveform at an equivalent sampling rate of 25 GHz while sampled at 100 MHz physically.