Recovery of Undersampled Signals Based on Compressed Sensing

The conventional recovery algorithm of multi-frequency signals based on compressed sensing (CS) requires that the sampling rate of the original signal still satisfies the Nyquist sampling theorem. Undersampling only means extracting a part of the original sampling points as the measurement, which does not reduce the sampling rate of the analog to digital converter (ADC). In this paper, we extend the CS further by proposing a new approach for the recovery of signals at several sub-Nyquist sampling rates. Furthermore, the effectiveness of the proposed algorithm in frequency estimation has been validated by simulations compared with that based on Chinese remainder theorem (CRT).

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