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As technology grows, higher frequency signals are required to be processed invarious applications. In order to digitize such signals, conventional analog todigital convertors are facing implementation challenges due to the highersampling rates. Hence, lower sampling rates (i.e., sub-Nyquist) are consideredto be cost efficient. A well-known approach is to consider sparse signals thathave fewer nonzero frequency components compared to the highest frequencycomponent. For the prior knowledge of the sparse positions, well-establishedmethods already exist. However, there are applications where such informationis not available. For such cases, a number of approaches have recently beenproposed. In this paper, we propose several random sampling recovery algorithmswhich do not require any anti-aliasing filter. Moreover, we offer certainconditions under which these recovery techniques converge to the signal.Finally, we also confirm the performance of the above methods through extensivesimulations.

Reconstruction of Sub-Nyquist Random Sampling for Sparse and Multi-Band Signals