信号与系统
说明
先开个坑（）
常用表格
Laplace变换表
| 时域信号 \(f(t)\) | 拉普拉斯变换 \(F(s)\) | 收敛域 (ROC) |
|---|---|---|
| \(\delta(t)\) | \(1\) | 全平面 |
| \(u(t)\) | \(\frac{1}{s}\) | \(\Re(s) > 0\) |
| \(e^{-at}u(t)\) | \(\frac{1}{s+a}\) | \(\Re(s) > -a\) |
| \(t \cdot u(t)\) | \(\frac{1}{s^2}\) | \(\Re(s) > 0\) |
| \(\frac{t^n}{n!} u(t)\) | \(\frac{1}{s^{n+1}}\) | \(\Re(s) > 0\) |
| \(\cos(\omega t)u(t)\) | \(\frac{s}{s^2 + \omega^2}\) | \(\Re(s) > 0\) |
| \(\sin(\omega t)u(t)\) | \(\frac{\omega}{s^2 + \omega^2}\) | \(\Re(s) > 0\) |
| \(e^{-at}\cos(\omega t)u(t)\) | \(\frac{s+a}{(s+a)^2 + \omega^2}\) | \(\Re(s) > -a\) |
| \(e^{-at}\sin(\omega t)u(t)\) | \(\frac{\omega}{(s+a)^2 + \omega^2}\) | \(\Re(s) > -a\) |
Z变换表
| 时域序列 \(x[n]\) | Z 变换 \(X(z)\) | 收敛域 (ROC) |
|---|---|---|
| \(\delta[n]\) | \(1\) | 全平面 |
| \(u[n]\) | \(\frac{1}{1 - z^{-1}}\) | \(\|z\| > 1\) |
| \(a^n u[n]\) | \(\frac{1}{1 - a z^{-1}}\) | \(\|z\| > \|a\|\) |
| \(n u[n]\) | \(\frac{z^{-1}}{(1 - z^{-1})^2}\) | \(\|z\| > 1\) |
| \(n a^n u[n]\) | \(\frac{a z^{-1}}{(1 - a z^{-1})^2}\) | \(\|z\| > \|a\|\) |
| \(\cos(\omega n)u[n]\) | \(\frac{1 - \cos\omega \, z^{-1}}{1 - 2\cos\omega \, z^{-1} + z^{-2}}\) | \(\|z\| > 1\) |
| \(\sin(\omega n)u[n]\) | \(\frac{\sin\omega \, z^{-1}}{1 - 2\cos\omega \, z^{-1} + z^{-2}}\) | \(\|z\| > 1\) |
| \(a^n \cos(\omega n)u[n]\) | \(\frac{1 - a\cos\omega \, z^{-1}}{1 - 2a\cos\omega \, z^{-1} + a^2 z^{-2}}\) | \(\|z\| > \|a\|\) |
| \(a^n \sin(\omega n)u[n]\) | \(\frac{a\sin\omega \, z^{-1}}{1 - 2a\cos\omega \, z^{-1} + a^2 z^{-2}}\) | \(\|z\| > \|a\|\) |