مستخدم:Uwe a/latex

تعويض عن صورة غير مرخصة

$f(x)={{1 \over {2\pi j}}\int _{c+j\infty }^{c-j\infty }F(s)e^{st}ds}$	$F(s)=\int _{0}^{\infty }f(t)e^{-st}dt$
$\delta (t)$	$1$
$h(t)$	$1 \over s$
$t^{n},n=1,2,3$	$n! \over s^{n+1}$
$t^{n}e^{-at}$	$n! \over {(s+a)^{n+1}}$
$\cos w_{0}t$	$s \over {s^{2}+w_{0}^{2}}$
$\sin w_{0}t$	$w_{0} \over {s^{2}+w_{0}^{2}}$
$e^{-at}\cos w_{0}t$	$s+a \over {(s+a)^{2}+w_{0}^{2}}$
$e^{-at}\sin w_{0}t$	$w_{0} \over {(s+a)^{2}+w_{0}^{2}}$
$t\cos w_{0}t$	$s^{2}-w_{0}^{2} \over {(s^{2}+w_{0}^{2})^{2}}$
$t\sin w_{0}t$	$2w_{0}s \over {(s^{2}+w_{0}^{2})^{2}}$

Nr.	$f(x)={{1 \over {2\pi j}}\int _{+j\infty }^{-j\infty }F(w)e^{jwt}dw}$	$F(w)=\int _{-\infty }^{\infty }f(t)e^{-jwt}dt$
1	$\delta (t)$	$1$
2	$h(t)$	${1 \over {jw}}+\pi \delta (w)$
3	$\sin(t)$	$2 \over 2w$
4	$1$	$2\pi \delta (w)$
5	$\cos w_{0}t$	$\pi \{\delta (w-w_{0})-\delta (w+w_{0})\}$
6	$\sin w_{0}t$	${\pi \over j}\{\delta (w-w_{0})-\delta (w+w_{0})\}$
7	$h(t)\cos w_{0}t$	${\pi \over 2}\{\delta (w-w_{0})+\delta (w+w_{0})\}+{jw \over {w_{0}^{2}+(jw)^{2}}}$
8	$h(t)\cos w_{0}t$	${\pi \over 2j}\{\delta (w-w_{0})+\delta (w+w_{0})\}+{w_{0} \over {w_{0}^{2}+(jw)^{2}}}$
9	${p_{\alpha }(t)},{\sin \alpha t \over {\pi t}}$	${2\sin w\alpha \over w},{p_{\alpha }(t)}$
10	$e^{-a|t|}$	$2a \over {a^{2}+w^{2}}$
11	$1 \over {a^{2}+t^{2}}$	${\pi \over a}e^{-a|w|}$