论文标题
连续和离散的LTI系统
Continuous and Discrete LTI Systems
论文作者
论文摘要
本章回顾了具有单个输入单个输出（SISO）的连续和离散线性时间不变（LTI）系统的基础。我们从信号和系统的一般概念开始，信号表示问题以及相关的正交基础以离散和连续形式的形式。然后，我们转到LTI系统的关键属性，并讨论其本征函数，时间域和频域中的输入输出关系，连接连续和离散公式的共形映射以及通过差分方程和差异方程式进行建模。最后，我们关闭了两个重要的应用程序：（线性）时间序列分析和预测和（线性）数字过滤器的模型，用于多分辨率分析。本章包含七个练习，该练习的解决方案在书的网页中提供了。
This chapter reviews the fundamentals of continuous and discrete Linear Time-Invariant (LTI) systems with Single Input-Single Output (SISO). We start from the general notions of signals and systems, the signal representation problem and the related orthogonal bases in discrete and continuous forms. We then move to the key properties of LTI systems and discuss their eigenfunctions, the input-output relations in the time and frequency domains, the conformal mapping linking the continuous and the discrete formulations, and the modeling via differential and difference equations. Finally, we close with two important applications: (linear) models for time series analysis and forecasting and (linear) digital filters for multi-resolution analysis. This chapter contains seven exercises, the solution of which is provided in the book's webpage.
