  Man-made communications signals are typically modelled as continuous-time
(CT) wide-sense cyclostationary (WSCS) processes. As modern processing is
digital, it operates on sampled versions of the CT signals. When sampling is
applied to a CT WSCS process, the statistics of the resulting discrete-time
(DT) process depends on the relationship between the sampling interval and the
period of the statistics of the CT process: When these two parameters have a
common integer factor, then the DT process is WSCS. This situation is referred
to as synchronous sampling. When this is not the case, which is referred to as
asynchronous sampling, the resulting DT process is wide-sense almost
cyclostationary (WSACS). In this work, we study the fundamental tradeoff of
sources codes applied to sampled CT WSCS processes, namely, their
rate-distortion function (RDF). We note that RDF characterization for the case
of synchronous sampling directly follows from classic information-theoretic
tools utilizing ergodicity and the law of large numbers; however, when sampling
is asynchronous, the resulting process is not information stable. In such
cases, commonly used information-theoretic tools are inapplicable to RDF
analysis, which poses a major challenge. Using the information spectrum
framework, we show that the RDF for asynchronous sampling in the low distortion
regime can be expressed as the limit superior of a sequence of RDFs in which
each element corresponds to the RDF of a synchronously sampled WSCS process
(but their limit is not guaranteed to exist). The resulting characterization
allows us to introduce novel insights on the relationship between sampling
synchronization and RDF. For example, we demonstrate that, differently from
stationary processes, small differences in the sampling rate and the sampling
time offset can notably affect the RDF of sampled CT WSCS processes.
