Obtaining digital representations of multivariate continuous-time (CT) signals is a challenge encountered in many signal processing systems. In practice, these signals are often acquired to extract some underlying information, i.e., for a specific task. Employing conventional task-agnostic analog-to-digital converters (ADCs), typically designed to minimize the mean squared error (MSE) in reconstructing the CT input signal, can be costly and energy-inefficient in such cases. In this work, we study task-based ADCs, which are designed to obtain a digital representation of a multivariate CT input process with the goal of recovering an underlying statistically related parameter vector, referred to as \emph{the task}. The proposed system employs analog filtering, uniform sampling, and scalar uniform quantization of the input process before recovering the task vector using a linear digital recovery filter. We optimize the analog and digital filters and derive closed-form expressions for the achievable MSE in recovering the task vector from a set of analog signals when utilizing ADCs with a fixed sampling rate and amplitude resolution. Based on our derivation, we provide guidelines for designing practical acquisition systems subject to a constraint on the bit rate. Our analysis proves that the intuitive approaches of either recovering the task vector solely in digital or designing the analog filter to estimate the task vector are inferior to the proposed joint design. We then consider the recovery of a set of matched filter outputs under a rate budget. We numerically verify our theoretical observations and demonstrate that task-based ADCs substantially outperform analog matched filtering as well as applying the matched filter solely in the digital domain. [...]
翻译:在许多信号处理系统中,获取多变连续时间(CT)信号的数字表示是一项挑战。在实践中,这些信号往往被获取,以提取某些基本信息,即特定任务所需的某些基本信息。使用常规任务-不可知模拟数字转换器(ADCs),通常设计在重建CT输入信号时尽量减少平均平方错误(MSE),在这类情况下成本高且能源效率低。在这项工作中,我们研究基于任务的筛选器(ADCs),旨在获取多变连续时间(CCT)输入进程的数字表示,目的是恢复与统计相关的直径参数矢量。在利用ADCs(固定采样率和粘贴度)观测器时,为恢复任务矢量而从一组模拟信号获得数字表达,目的是要恢复与统计相关的直线数字转换器相关的直线性数据。在实际的校正分析中,我们提供了一种对数据转换结果的模拟方法,在实际的排序分析中,我们提供了一种对数字转换任务定义的精确度,我们提供了一种对数字分析的精确度。