V2EX z transform

Z Transform

定义 Definition

Z 变换(Z-transform):一种用于分析离散时间信号与离散系统的数学变换方法,把离散序列从“时域/序列域”映射到以复变量 z 表示的“Z 域”,便于研究系统的稳定性、频率响应与差分方程求解等。(也常写作 Z-transform,属于数字信号处理与控制领域的基础工具。)

发音 Pronunciation (IPA)

/zi trnsfrm/

例句 Examples

The Z transform converts a sequence into a function of z.
Z 变换把一个序列转换为关于 z 的函数。

Using the Z transform, we can solve the difference equation and determine whether the discrete-time system is stable.
利用 Z 变换,我们可以求解差分方程,并判断该离散时间系统是否稳定。

词源 Etymology

“Z-transform”中的 Z 来自复分析里常用的复变量记号 z;“transform”表示“变换/映射”。该术语在离散系统与采样数据分析的发展中逐渐固定下来,用来强调它与连续时间常见的拉普拉斯变换(Laplace transform)在思想上的对应关系,但对象是离散序列。

相关词 Related Words

文学与经典著作中的用例 Literary Works

  • Discrete-Time Signal Processing(Alan V. Oppenheim, Ronald W. Schafer)
  • Digital Signal Processing: Principles, Algorithms, and Applications(John G. Proakis, Dimitris G. Manolakis)
  • Signals and Systems(Alan V. Oppenheim, Alan S. Willsky)
  • Theory and Application of Digital Signal Processing(Lawrence R. Rabiner, Bernard Gold)
  • Linear Systems and Signals(B. P. Lathi)
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