  In this paper, a class of deterministic sensing matrices are constructed by
selecting rows from Fourier matrices. These matrices have better performance in
sparse recovery than random partial Fourier matrices. The coherence and
restricted isometry property of these matrices are given to evaluate their
capacity as compressive sensing matrices. In general, compressed sensing
requires random sampling in data acquisition, which is difficult to implement
in hardware. By using these sensing matrices in harmonic detection, a
deterministic sampling method is provided. The frequencies and amplitudes of
the harmonic components are estimated from under-sampled data. The simulations
show that this under-sampled method is feasible and valid in noisy
environments.
