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Lattice Functions for the Analysis of Analog-to-Digital Conversion

机译：用于模数转换分析的格函数

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摘要

Analog-to-digital (A/D) converters are the common interface between analog signals and the domain of digital discrete-time signal processing. In essence, this domain simultaneously incorporates quantization both in amplitude and time, i. e. amplitude quantization and uniform time sampling. Thus, we view A/D conversion as a sampling process in both the time and amplitude domains based on the observation that the underlying continuous-time signals representing digital sequences can be sampled in a lattice-i.e. at points restricted to lie on a uniform grid both in time and amplitude. We refer to them as lattice functions. This is in contrast with the traditional approach based on the classical sampling theorem and quantization error analysis. The latter has been mainly addressed with the help of probabilistic models, or deterministic ones either confined to very particular scenarios or considering worst-case assumptions. In this paper, we provide a deterministic theoretical analysis and framework for the functions involved in digital discrete-time processing. We show that lattice functions possess a rich analytic structure in the context of integral-valued entire functions of exponential type. We derive set and spectral properties of this class of functions. This allows us to prove in a deterministic way and for general bandlimited functions a fundamental lower bound on the maximum frequency component introduced by quantization that is independent of the resolution of the quantizer.
机译：模数（A / D）转换器是模拟信号与数字离散时间信号处理领域之间的通用接口。本质上，该域同时包含幅度和时间的量化，即。 e。幅度量化和均匀时间采样。因此，基于观察到表示数字序列的基础连续时间信号可以在点阵中进行采样的观察，我们将A / D转换视为时域和幅度域中的采样过程。在时间和幅度上都限制在同一网格上的点。我们称它们为晶格函数。这与基于经典采样定理和量化误差分析的传统方法形成对比。后者主要是通过概率模型来解决的，或者是确定性模型，要么局限于非常特殊的情况，要么考虑最坏情况的假设。在本文中，我们为数字离散时间处理中涉及的功能提供了确定性的理论分析和框架。我们表明，在指数型整数值整体函数的上下文中，格函数具有丰富的解析结构。我们推导出此类函数的集合和频谱性质。这使我们能够确定性地证明，对于一般的带宽限制函数，量化所引入的最大频率分量的基本下限与量化器的分辨率无关。

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