  The random equivalent sampling (RES) is a well-known sampling technique that
can be used to capture a high-speed repetitive waveform with low sampling rate.
In this paper, the feasibility of spectrum-blind multiband signal
reconstruction for data sampled from RES is investigated. We propose a RES
sampling pattern and its corresponding mathematical model that guarantees
well-conditioned reconstruction of multiband signal with unknown spectral
support. We give the minimum number of RES acquisitions that hold overwhelming
probability to successfully reconstruct original signal. We demonstrate that
for signal with specific spectral occupation, the number of RES acquisitions
and the minimum sampling rate could be approached. The signal reconstruction is
studied in the framework of compressive sampling (CS) theory. The
eigen-decomposition and minimum description length (MDL) criteria are adopted
to adaptively estimate the dimension of signal, and the number of unknowns of
reconstruction problem is reduced. Experimental results are reported to
indicate that, for a spectrum-blind sparse multiband signal, the proposed
reconstruction algorithm for RES is feasible and robust.
