V2EX z-transform

Z-transform

Definition / 定义

Z-transform(Z变换):一种把离散时间序列表示为复变量 z 的函数的数学工具,常用于数字信号处理离散控制系统中,便于分析系统的稳定性、频率响应与差分方程。

Pronunciation / 发音

/zd trnsfrm/(英式)
/zi trnsfrm/(美式)

Examples / 例句

The Z-transform helps us analyze discrete-time signals more easily.
Z 变换帮助我们更容易地分析离散时间信号。

Using the Z-transform, the engineer derived the system’s transfer function and checked whether the poles lay inside the unit circle.
借助 Z 变换,工程师推导出了系统的传递函数,并检查极点是否位于单位圆内。

Etymology / 词源

“Z-transform”由 Z(表示复平面中的变量 z)与 transform(“变换”)组成。之所以用 z,与复分析中常用字母表示复变量的传统有关;该方法在离散系统理论发展中逐渐成为标准记号,用来与连续时间的 Laplace transform(拉普拉斯变换)相对应。

Related Words / 相关词

Literary Works / 文学作品

  • Alan V. Oppenheim & Ronald W. Schafer, Discrete-Time Signal Processing(《离散时间信号处理》)
  • Katsuhiko Ogata, Discrete-Time Control Systems(《离散时间控制系统》)
  • John G. Proakis & Dimitris G. Manolakis, Digital Signal Processing: Principles, Algorithms, and Applications(《数字信号处理》)
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