“数字信号处理”课程的几何视角

“数字信号处理”的经典课程体系以“系统”为中心,以离散时间傅立叶变换、z变换和离散傅立叶变换为分析工具,以滤波器设计为目的,注重定理和公式推导及其性质分析,很难让学生建立一个形象的、完整统一的知识体系框架。本文从几何视角将 “系统”化和“代数”化的经典课程体系重构为面向“信号”的“几何”知识体系,从而提升学生对本质问题的“洞察力”,帮助学生建立系统的知识体系。

Digital Signal Processing Course from a Geometric Perspective

Targeting at filter design, the classical curriculum framework of Digital Signal Processing is centered on the system, with discrete-time Fourier transform, z-transform and discrete Fourier transform as analysis tools. It emphasizes the derivation of theorems and formulas and the analysis of their properties, which is complicated for students to establish a comprehensive knowledge framework. From the perspective of geometry, this paper reconstructs the classical curriculum system that is "system" and "algebraic"-oriented into a "geometric" knowledge system oriented to "signals", thereby enhancing students'' "insight" on essential issues and establishing a systematic knowledge framework.