A sparse signal reconstruction approach for sequential equivalent time sampling

This paper presents a signal reconstruction algorithm for sequential equivalent time sampling (SETS). SETS has been incorporated in digital acquisition system to capture a repetitive waveform with a single analog to digital converter (ADC) clocked at a rate that is much lower than the signal's Nyquist rate. However, in order to achieve a high time resolution, a great number of acquisition runs need to be carried out. In this paper, the sparsity of underlying signal is exploited, and compressed sensing (CS) theory is employed to reconstruct signal from sub-Nyquist samples captured by SETS system. The CS measurement matrix is constructed in the context of SETS. Experimental results indicate that, the proposed CS-based reconstruction is feasible, and the sparse signal could be reconstructed from a small number of SETS samples. Compared to the traditional SETS signal reconstruction, the number used to signal reconstruction could be significantly reduced.