V2EX heaviside function

Heaviside Function

定义 Definition

Heaviside function(也常称 Heaviside step function)赫维赛德阶跃函数/单位阶跃函数,一种分段函数,通常记作 H(t) 或 **u(t)**。它在自变量小于 0 时取 0,大于 0 时取 1;在 t = 0 处的取值在不同教材/领域可能规定为 0、1 或 1/2(取决于约定与应用场景)。

发音 Pronunciation (IPA)

/hvsad fkn/

例句 Examples

The Heaviside function jumps from 0 to 1 at \(t=0\).
赫维赛德函数在 \(t=0\) 处从 0 跳变到 1。

In signal processing, we use the Heaviside function to model a system that turns on at a specific time, which makes Laplace-transform calculations easier.
在信号处理里,我们用赫维赛德函数来描述某个时刻“开启”的系统,这会让拉普拉斯变换的计算更方便。

词源 Etymology

Heaviside”来自英国工程师与数学家 Oliver Heaviside(奥利弗赫维赛德)的姓氏;这种“阶跃”形式的函数在工程与运算微积分、拉普拉斯变换等领域非常常见,因此以他的名字命名。“function”意为“函数”。

相关词 Related Words

文学与经典著作 Literary Works

  • Operational Mathematics(Mikusinski 等“运算数学/运算演算”经典教材中常用单位阶跃函数)
  • The Fourier Transform and Its Applications(Ronald N. Bracewell,讨论阶跃与相关变换)
  • Mathematical Methods for Physicists(Arfken & Weber,物理数学方法中常出现阶跃函数与狄拉克 δ)
  • Advanced Engineering Mathematics(Erwin Kreyszig,工程数学教材中用于微分方程与拉普拉斯变换建模)
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