用旋转矢量三维图理解拉普拉斯变换的物理意义

Understand the Physical Meaning of Laplace Transform with a 3D Map of Rotating Vectors

摘要: 拉普拉斯变换被广泛应用于不同的领域，但拉普拉斯变换的物理意义很少在信号和系统教科书中以图形方式描述。本文基于旋转矢量的三维图，提出拉普拉斯变换三维幅度谱和三维相位谱绘制方法。通过三维拉普拉斯变换谱描述拉普拉斯变换的本质上是将一个信号分解为无穷多广义非等幅振荡的正弦波线性组合。实验结果表明该方法能够直观揭示拉普拉斯变换复杂数学公式背后本质和物理含义。

Abstract: The Laplace transform is widely used in different fields, but the physical meaning of the Laplace transform is rarely graphically described in signal and systems textbooks. Three-dimensional amplitude spectrum and phase spectrum of the Laplace transform is proposed based on the three-dimensional graph of the rotation vector. The Laplace transform decomposes a signal into an infinite number of linear combinations of generalized variable amplitude sine waves. The experimental results show that the method intuitively reveals the essence and physical meaning behind the complex mathematical formula of Laplace transform.