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Man-made communications signals are typically modelled as continuous-time(CT) wide-sense cyclostationary (WSCS) processes. As modern processing isdigital, it operates on sampled versions of the CT signals. When sampling isapplied to a CT WSCS process, the statistics of the resulting discrete-time(DT) process depends on the relationship between the sampling interval and theperiod of the statistics of the CT process: When these two parameters have acommon integer factor, then the DT process is WSCS. This situation is referredto as synchronous sampling. When this is not the case, which is referred to asasynchronous sampling, the resulting DT process is wide-sense almostcyclostationary (WSACS). In this work, we study the fundamental tradeoff ofsources codes applied to sampled CT WSCS processes, namely, theirrate-distortion function (RDF). We note that RDF characterization for the caseof synchronous sampling directly follows from classic information-theoretictools utilizing ergodicity and the law of large numbers; however, when samplingis asynchronous, the resulting process is not information stable. In suchcases, commonly used information-theoretic tools are inapplicable to RDFanalysis, which poses a major challenge. Using the information spectrumframework, we show that the RDF for asynchronous sampling in the low distortionregime can be expressed as the limit superior of a sequence of RDFs in whicheach element corresponds to the RDF of a synchronously sampled WSCS process(but their limit is not guaranteed to exist). The resulting characterizationallows us to introduce novel insights on the relationship between samplingsynchronization and RDF. For example, we demonstrate that, differently fromstationary processes, small differences in the sampling rate and the samplingtime offset can notably affect the RDF of sampled CT WSCS processes.

The Rate Distortion Function of Asynchronously Sampled Memoryless Cyclostationary Gaussian Processes