Basic Signals and Functions
| Basic Signals and Functions in one variable | |
|---|---|
| Continuous-time signals. | |
| sinc function | $ sinc(t )=\frac{sin(\pi t )}{\pi t}, \text{ where }t\in {\mathbb R} $ |
| rect function | $ rect (t) = \left\{ \begin{array}{ll}1, & \text{ for } |t|\leq \frac{1}{2} \\ 0, & \text{ else}\end{array}\right., \text{ where }t\in {\mathbb R} $ |
| CT unit step function | $ u(t)=\left\{ \begin{array}{ll}1, & \text{ for } t\geq 0 \\ 0, & \text{ else}\end{array}\right., \text{ where }t\in {\mathbb R} $ |
| Discrete-time signals | |
| DT delta function | $ \delta[n]=\left\{ \begin{array}{ll}1, & \text{ for } n=1 \\ 0, & \text{ else}\end{array}\right., \text{ where }n\in {\mathbb Z} $ |
| DT unit step function | $ u[n]=\left\{ \begin{array}{ll}1, & \text{ for } n\geq 0 \\ 0, & \text{ else}\end{array}\right., \text{ where }n\in {\mathbb Z} $ |
| Basic Signals and Functions in two variables | |
| Continuous-time | |
|
2D Dirac delta |
$ \delta(x,y)=\delta(x) \delta(y), \text{ where }x,y\in {\mathbb R} $ |
|
2D sinc function |
$ sinc(x,y)=\frac{sin(\pi x)sin(\pi y)}{\pi^2 x y }, \text{ where }x,y\in {\mathbb R} $ |
|
(info) 2D rect function |
$ rect(x,y)= \left\{ \begin{array}{ll}1, & \text{ for } |x|\leq \frac{1}{2} \text{ and } |y|\leq \frac{1}{2} \\ 0, & \text{ else}\end{array}\right., \text{ where }x,y\in {\mathbb R} $ |
