| \[f\left(t\right)\] | \[\textbf{F}\left(s\right)\] |
|---|---|
| \[\delta\left(t\right)\] | \[1\] |
| \[u\left(t\right)\] | \[\frac{1}{\textbf{s}}\] |
| \[e^{-at}\,u(t)\] | \[\frac{1}{\textbf{s}+a}\] |
| \[t^{n}\,u(t)\] | \[\frac{n!}{\textbf{s}^{n+1}}\] |
| \[t^{n}e^{-at}\,u(t)\] | \[\frac{n!}{\left ( \textbf{s} + a \right )^{n + 1}}\] |
| \[\cos\left(\omega t\right)\,u(t)\] | \[\frac{\textbf{s}}{\textbf{s}^{2} + \omega^{2}}\] |
| \[\sin\left(\omega t\right)\,u(t)\] | \[\frac{\omega}{\textbf{s}^{2} + \omega^{2}}\] |
| \[\cos\left(\omega t+\phi\right)\,u(t)\] | \[\frac{\textbf{s}\cos{\phi}-\omega\sin{\phi}}{\textbf{s}^{2} + \omega^{2}}\] |
| \[\sin\left(\omega t+\phi\right)\,u(t)\] | \[\frac{\textbf{s}\sin{\phi}+\omega\cos{\phi}}{\textbf{s}^{2} + \omega^{2}}\] |
| \[e^{-at}\cos\left(\omega t\right)\,u(t)\] | \[\frac{\textbf{s} + a}{\left ( \textbf{s} + a \right )^{2} + \omega^{2}}\] |
| \[e^{-at}\sin\left(\omega t\right)\,u(t)\] | \[\frac{\omega}{\left(\textbf{s}+a\right)^{2}+\omega^{2}}\] |
| \[e^{-at}\cos\left(\omega t+\phi\right)\,u(t)\] | \[\frac{(\textbf{s} + a)\cos{\phi}-\omega\sin{\phi}}{\left ( \textbf{s} + a \right )^{2} + \omega^{2}}\] |
| \[e^{-at}\sin\left(\omega t+\phi\right)\,u(t)\] | \[\frac{(\textbf{s}+a)\sin{\phi}+\omega\cos{\phi}}{\left(\textbf{s}+a\right)^{2}+\omega^{2}}\] |
| \[2\left|\,\textbf{k}\,\right|e^{-\alpha t}\cos\left(\beta t+\theta\right)\,u(t)\] | \[\frac{\left|\,\textbf{k}\,\right|\angle\theta}{\textbf{s}+\alpha-j\beta} +\frac{\left|\,\textbf{k}\,\right|\angle-\theta}{\textbf{s}+\alpha+j\beta}\] |