Referencia: Lathi Tabla 4.1 p334. Oppenheim Tabla 9.2 p692. Hsu Tabla 3-1 p115
| No. | x(t) | X(s) | ROC |
|---|---|---|---|
| 1a | δ(t) | 1 | Toda s |
| 1b | δ(t-T) | e-sT | Toda s |
| 2a | μ(t) | \frac{1}{s} | Re{s}>0 |
| 2b | -μ(-t) | \frac{1}{s} | Re{s}<0 |
| 3 | tμ(t) | \frac{1}{s^2} | Re{s}>0 |
| 4a | tnμ(t) | \frac{n!}{s^{n+1}} | Re{s}>0 |
| 4b | \frac{t^{n-1}}{(n-1)!} \mu (t) | \frac{1}{s^n} | Re{s}>0 |
| 4c | -\frac{t^{n-1}}{(n-1)!} \mu (-t) | \frac{1}{s^n} | Re{s}<0 |
| 5 | eλtμ(t) | \frac{1}{s-\lambda} | Re{s}>0 |
| 6 | teλtμ(t) | \frac{1}{(s-\lambda)^2} | Re{s}>0 |
| 7 | tneλtμ(t) | \frac{n!}{(s-\lambda)^{n+1}} | |
| 8a | cos (bt) μ(t) | \frac{s}{s^2+b^2} | Re{s}>0 |
| 8b | sin (bt) μ(t) | \frac{b}{s^2+b^2} | Re{s}>0 |
| 9a | e-atcos (bt) μ(t) | \frac{s+a}{(s+a)^2+b^2} | Re{s}>-a |
| 9b | e-atsin (bt) μ(t) | \frac{b}{(s+a)^2+b^2} | Re{s}>-a |
| 10 | \mu_n (t) = \frac{\delta ^n}{\delta t^n} \delta (t) | sn | Toda s |
| 11 | \mu_{-n} (t) = \mu (t) \circledast \text{...} \circledast \mu (t)
n veces |
\frac{1}{s^n} | Re{s}>0 |
| 12a | re-atcos (bt+θ) μ(t) | \frac{(r\cos (\theta)s + (ar \cos (\theta) - br \sin (\theta))}{s^2+2as+(a^2+b^2)} | |
| 12b | re-atcos (bt+θ) μ(t) | \frac{0.5 re^{j \theta}}{s+a-jb} + \frac{0.5 re^{-j \theta}}{s+a+jb} | |
| 12c | re-atcos (bt+θ) μ(t) | \frac{As+B}{s^2+2as+c} | |
| r = \sqrt{\frac{A^2 c +B^2 -2ABa}{c-a^2}} | \theta = \tan ^{-1} \Big( \frac{Aa-B}{A\sqrt{c-a^2}}\Big)
b = \sqrt{c-a^2} |
||
| 12d | e^{-at}\Bigg[A \cos (bt) + \frac{B-Aa}{b} \sin (bt) \Bigg] \mu (t) | \frac{As+B}{s^2 + 2as+c} | |
| b = \sqrt{c-a^2} | |||