V2EX unit step

Unit Step

释义 Definition

“单位阶跃(函数)”:信号与系统/数学中常用的阶跃函数,通常记作 \(u(t)\) 或 \(H(t)\)。一般定义为:当 \(t<0\) 时为 0,当 \(t\ge 0\) 时为 1,用来表示“从某一时刻开始突然开启”的输入。(在不同学科里,常见约定也可能取 \(H(0)=1/2\)。)

发音 Pronunciation (IPA)

/junt stp/

例句 Examples

The unit step turns on at \(t=0\).
单位阶跃在 \(t=0\) 时刻“开启”。

In control theory, multiplying a signal by the unit step enforces causality by making it zero for \(t<0\).
在控制理论中,把信号与单位阶跃相乘可以强制因果性,使其在 \(t<0\) 时为零。

词源 Etymology

“unit”表示“单位的、为 1 的”,强调函数开启后取值为 1;“step”表示“台阶/阶跃”,形容图像像台阶一样从 0 突然跳到 1。该函数也常被称为“Heaviside step function(海维赛德阶跃函数)”,源于英国科学家 Oliver Heaviside 的相关研究与记号传统。

相关词 Related Words

文学与名著用例 Notable Works

  • Oliver Heaviside, Electromagnetic Theory(常见为 Heaviside step function 的来源与命名背景)
  • Alan V. Oppenheim & Alan S. Willsky, Signals and Systems(用 \(u(t)\) 表示单位阶跃并讨论系统响应)
  • Ronald N. Bracewell, The Fourier Transform and Its Applications(在傅里叶分析中常以单位阶跃作为典型信号)
  • Athanasios Papoulis, The Fourier Integral and Its Applications(涉及阶跃函数与频域分析的经典处理)
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