标签：infty right frac 变换 lim sum quad 性质
| 名称 |
时域 \(f(k)\) |
Z域 \(F(z)\) |
| 线性 |
\(a_1 f_1(k) + a_2 f_2(k)\) |
\(a_1 F_1(z) + a_2 F_2(z)\) |
| 移序（移位）性 |
\(f(k+m) \quad (m > 0)\) |
\(z^m F(z) - \sum_{k=0}^{m-1} f(k) z^{m-k-1}\) |
|
\(f(k-m)u(k-m) \quad (m > 0)\) |
\(z^{-m} F(z)\) |
| 比例性（尺度变换） |
\(a^k f(k)\) |
\(F\left(\frac{z}{a}\right)\) |
| Z域微分 |
\(k f(k)\) |
\(-z \frac{dF(z)}{dz}\) |
| Z域积分 |
\(\frac{1}{k} f(k) \quad (a > 0)\) |
\(\int_{z}^{\infty} F(v) v^{-(a+1)} dv\) |
| 时域卷积 |
\(f_1(k) * f_2(k)\) |
\(F_1(z) F_2(z)\) |
| 时域相乘 |
\(f_1(k) \cdot f_2(k)\) |
\(\frac{1}{2\pi j} \oint_C F_1(v) F_2\left(\frac{z}{v}\right) \frac{dv}{v}\) |
| 序列求和 |
\(\sum_{n=0}^{\infty} f(n)\) |
\(\frac{z}{z-1} F(z)\) |
| 初值定理 |
\(f(0) = \lim_{z \to \infty} F(z)\) |
|
|
\(f(m) = \lim_{z \to \infty} z^m \left[ F(z) - \sum_{k=0}^{m-1} f(k) z^{-k} \right]\) |
|
| 终值定理 |
\(f(\infty) = \lim_{z \to 1} (z-1) F(z)\) |
|
标签：infty,
right,
frac,
变换,
lim,
sum,
quad,
性质
From： https://www.cnblogs.com/codersgl-blog/p/18652524