  The application of nonlinear transformations to a cyclostationary signal for
the purpose of revealing hidden periodicities has proven to be useful for
applications requiring signal selectivity and noise tolerance. The fact that
the hidden periodicities, referred to as cyclic moments, are often compressible
in the Fourier domain motivates the use of compressive sensing (CS) as an
efficient acquisition protocol for capturing such signals. In this work, we
consider the class of Temporal Higher Order Cyclostationary Statistics (THOCS)
estimators when CS is used to acquire the cyclostationary signal assuming
compressible cyclic moments in the Fourier domain. We develop a theoretical
framework for estimating THOCS using the low-rate nonuniform sampling protocol
from CS and illustrate the performance of this framework using simulated data.
