We study the rate-distortion function (RDF) for the lossy compression of discrete-time (DT) wide-sense almost cyclostationary (WSACS) Gaussian processes with memory, arising from sampling continuous-time (CT) wide-sense cyclostationary (WSCS) Gaussian source processes. The importance of this problem arises as such CT processes represent communications signals, and sampling must be applied to facilitate the DT processing associated with their compression. Moreover, the physical characteristics of oscillators imply that the sampling interval is incommensurate with the period of the autocorrelation function (AF) of the physical process, giving rise to the DT WSACS model considered. In addition, to reduce the loss, the sampling interval is generally shorter than the correlation length, and thus, the DT process is correlated as well. The difficulty in the RDF characterization follows from the information-instability of WSACS processes, which renders the traditional information-theoretic tools inapplicable. In this work we utilize the information-spectrum framework to characterize the RDF when a finite and bounded delay is allowed between processing of subsequent source sequences. This scenario extends our previous works which studied settings without processing delays or without memory. Numerical evaluations reveal the impact of scenario parameters on the RDF with asynchronous sampling.

翻译：本研究探讨了由连续时间宽平稳循环平稳高斯源过程采样产生的离散时间宽平稳近似循环平稳高斯过程（具有记忆特性）的有损压缩率失真函数。该问题的重要性在于此类连续时间过程代表了通信信号，而采样是实现与其压缩相关的离散时间处理所必需的。此外，振荡器的物理特性意味着采样间隔与物理过程自相关函数的周期不可公度，从而产生了本文所考虑的离散时间宽平稳近似循环平稳模型。为减少失真，采样间隔通常短于相关长度，因此离散时间过程同样具有相关性。率失真函数表征的困难源于宽平稳近似循环平稳过程的信息不稳定性，这使得传统的信息论工具无法适用。在本工作中，我们利用信息谱框架来表征当允许对连续源序列处理之间存在有限且有界延迟时的率失真函数。该场景扩展了我们先前研究无处理延迟或无记忆设置的工作。数值评估揭示了异步采样下场景参数对率失真函数的影响。