|
$x(t)$ |
$X(\omega)$ |
|
1 |
$e^{-a t}u(t), a>0$ |
$\frac{1}{a+j\omega}$ |
ref. |
2 |
$e^{a t} u(-t) , a>0$ |
$\frac{1}{a-j\omega}$ |
|
3 |
$e^{-a \vert t\vert}, a>0$ |
$\frac{2a}{a^2+\omega^2}$ |
|
4 |
$te^{-a t}u(t), a>0$ |
$\frac{1}{ (a+j\omega)^2}$ |
|
5 |
$t^ne^{-a t}u(t), a>0$ |
$\frac{n!}{ (a+j\omega)^{n+1}}$ |
|
6 |
$\delta(t)$ |
$1$ |
ref. |
7 |
$1$ |
$2\pi \delta(\omega)$ |
ref. |
8 |
$e^{j\omega_0t}$ |
$2\pi \delta (\omega-\omega_0) $ |
ref. |
9 |
$\text{sgn}(t)$ |
$\frac{2}{j\omega}$ |
ref. |
10 |
$u(t)$ |
$\pi \delta(\omega) +\frac{1}{j\omega}$ |
ref. |
11 |
$\cos \omega_0 t$ |
$\pi \left[ \delta(\omega+\omega_0) + \delta (\omega-\omega_0) \right]$ |
ref. |
12 |
$\sin \omega_0 t$ |
$j\pi \left[ \delta(\omega+\omega_0) - \delta (\omega-\omega_0) \right]$ |
ref. |
13 |
$\cos \omega_0 t u(t)$ |
$\frac{\pi}{2} \left[ \delta(\omega+\omega_0) + \delta (\omega-\omega_0) \right] +\frac{j\omega}{\omega_0^2-\omega^2}$ |
|
14 |
$\sin \omega_0 t u(t)$ |
$\frac{\pi}{2j} \left[ \delta(\omega+\omega_0) - \delta (\omega-\omega_0) \right] +\frac{\omega_0}{\omega_0^2-\omega^2}$ |
|
15 |
$e^{-at} \sin \omega_0t u(t), a>0$ |
$ \frac{\omega_0}{(a+j\omega)^2+\omega_0^2}$ |
|
16 |
$e^{-at} \cos \omega_0t u(t), a>0$ |
$ \frac{a+j\omega}{(a+j\omega)^2+\omega_0^2}$ |
|
17 |
$ \displaystyle \sum_{n=-\infty}^{\infty} \delta(t-nT_s)$ |
$ \displaystyle \omega_0 \sum_{n=-\infty}^{\infty} \delta(\omega-n\omega_0) , \omega_0=\frac{2\pi}{T_s}$ |
ref. |
18 |
$ \text{rect}_\tau (t)$, 너비가 $\tau$인 rectangle pulse |
$ \tau \text{sinc}\left ( \frac{\omega \tau}{2\pi}\right)$ |
ref. |
19 |
$ \frac{W}{2\pi} \text{sinc}\left ( \frac{W}{2\pi}t\right)$ |
$\text{rect}_W (\omega)$, 너비가 $W$인 rectangle pulse$ |
ref. |
20 |
$ \Delta \left ( \frac{t}{\tau}\right)$ 기울기가 $\frac{1}{\tau}$인 삼각파 |
$ \tau \text{sinc}^2 \left ( \frac{\omega \tau}{2\pi}\right)$ |
|
21 |
$ e^{-\frac{t^2}{2\sigma ^2}}$ |
$ \sigma \sqrt{\pi} e^{-\frac{\sigma^2\omega^2}{2}}$ |
|