Signal | Laplace Transform | RoC | ... | |
1 | $u(t)$ | $\frac{1}{s}$ | $\text{Re}(s)>0$ | |
2 | $u(t)-u(t-a)$ | $\frac{1-e^{-as}}{s}$ | $\text{Re}(s)>0$ | |
3 | $\delta(t)$ | 1 | all complex plane | |
4 | $\delta(t-a)$ | $e^{-as}$ | all complex plane | |
5 | $e^{-at}u(t)$ | $\frac{1}{s+a}$ | $\text{Re}(s)>-a$ | |
6 | $\cos\Omega_0t u(t)$ | $\frac{s}{s+\Omega_0^2}$ | $\text{Re}(s)>0$ | |
7 | $\sin\Omega_0t u(t)$ | $\frac{\Omega_0}{s+\Omega_0^2}$ | $\text{Re}(s)>0$ | |
8 | $t^nu(t)$ | $\frac{n!}{s^{n+1}}$ | $\text{Re}(s)>0$ | |
9 | $t^ne^{-at}u(t)$ | $\frac{n!}{(s+a)^{n+1}}$ | $\text{Re}(s)>-a$ | |
10 | $e^{-at}\cos\Omega_0tu(t)$ | $\frac{s+a}{(s+a)^2+\Omega_0^2}$ | $\text{Re}(s)>-a$ | |
11 | $e^{-at}\sin\Omega_0tu(t)$ | $\frac{\Omega_0}{(s+a)^2+\Omega_0^2}$ | $\text{Re}(s)>-a$ | |
12 | $t\cos\Omega_0tu(t)$ | $\frac{s^2-\Omega_0^2}{(s^2+\Omega_0^2)^2}$ | $\text{Re}(s)>0$ | |
13 | $t\sin\Omega_0tu(t)$ | $\frac{2\Omega_0s}{(s^2+\Omega_0^2)^2}$ | $\text{Re}(s)>0$ | |
14 | $\cos^2\Omega_0 t u(t)$ | $\frac{s^2+2\Omega^2}{s(s^2+4\Omega_0^2)}$ | $\text{Re}(s)>0$ | 참고 |
15 | $\sin^2\Omega_0 t u(t)$ | $\frac{2\Omega^2}{s(s^2+4\Omega_0^2)}$ | $\text{Re}(s)>0$ | 참고 |
unilateral laplace transform이 기본인 점을 기억할 것.
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