  As an alternative to the traditional sampling theory, compressed sensing
allows acquiring much smaller amount of data, still estimating the spectra of
frequency-sparse signals accurately. However, compressed sensing usually
requires random sampling in data acquisition, which is difficult to implement
in hardware. In this paper, we propose a deterministic and simple sampling
scheme, that is, sampling at three sub-Nyquist rates which have coprime
undersampled ratios. This sampling method turns out to be valid through
numerical experiments. A complex-valued multitask algorithm based on
variational Bayesian inference is proposed to estimate the spectra of
frequency-sparse signals after sampling. Simulations show that this method is
feasible and robust at quite low sampling rates.
