拉普拉斯变换的图形分析

Graphic Analysis of Laplace Transform

以单边指数函数为例 ,分析了拉普拉斯变换象函数 F (s)在其收敛域内随σ和ω的变化规律 ,通过 | F (s) |曲面图来观察这些规律 ,并解释了图中某些特定点及剖面的含义 ,以形象化的方式加深对拉普拉斯变换的认识。借助 MATL AB的绘图功能绘制出 F(s)的曲面图、剖面图及信号的频谱图 ,从中可以观察到频域与复频域的关系以及系统函数的零极点分布等。

In this paper, taking single side exponential function as an example, analyze Laplace transform F(s)' s variation rules with σ and ω within its region of convergence. These rules can be observed from the curved surface of the function | F(s) |. We can also explain the meanings of the cross sections and some of points in the diagram. Laplace transform may be comprehended further with the visual form. F(s) 's curved surface drawing, cross section drawing and frequency spectrum are drawn with MATLAB powerful drawing function. The relation between frequency domain and complex frequency domain and zero-pole may be observed from these drawings.