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| + | [[Category:Formulas]] | ||
| + | |||
| + | <center><font size= 4> | ||
| + | '''[[Collective_Table_of_Formulas|Collective Table of Formulas]]''' | ||
| + | </font size> | ||
| + | |||
| + | '''Basic Signals and Functions''' | ||
| + | |||
| + | (used in [[ECE301]] and [[ECE438]]) | ||
| + | |||
| + | </center> | ||
| + | |||
| + | ---- | ||
| + | |||
{| | {| | ||
|- | |- | ||
! colspan="2" style="background: #e4bc7e; font-size: 110%;" | Basic Signals and Functions in one variable | ! colspan="2" style="background: #e4bc7e; font-size: 110%;" | Basic Signals and Functions in one variable | ||
|- | |- | ||
| − | ! colspan="2" style="background: #eee;" | Continuous-time signals | + | ! colspan="2" style="background: #eee;" | Continuous-time signals. |
|- | |- | ||
| − | | align="right" style="padding-right: 1em;" | sinc function || <math>sinc(t )=\frac{sin(\pi t )}{\pi | + | | align="right" style="padding-right: 1em;" | sinc function || <math>sinc(t )=\frac{sin(\pi t )}{\pi t}, \text{ where }t\in {\mathbb R}</math> |
|- | |- | ||
| − | | align="right" style="padding-right: 1em;" | rect function || <math>rect (t) = \left\{ \begin{array}{ll}1, & |t|\leq \frac{1}{2} \\ 0, & \text{ else}\end{array}\right., \text{ | + | | align="right" style="padding-right: 1em;" | rect function || <math>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}</math> |
|- | |- | ||
| − | | align="right" style="padding-right: 1em;" | CT unit step function || <math> u(t)=\left\{ \begin{array}{ll}1, & t\geq 0 \\ 0, & \text{ else}\end{array}\right., \text{ | + | | align="right" style="padding-right: 1em;" | CT unit step function || <math> u(t)=\left\{ \begin{array}{ll}1, & \text{ for } t\geq 0 \\ 0, & \text{ else}\end{array}\right., \text{ where }t\in {\mathbb R}</math> |
|- | |- | ||
! colspan="2" style="background: #eee;" | Discrete-time signals | ! colspan="2" style="background: #eee;" | Discrete-time signals | ||
|- | |- | ||
| − | | align="right" style="padding-right: 1em;" | DT | + | | align="right" style="padding-right: 1em;" | DT delta function || <math>\delta[n]=\left\{ \begin{array}{ll}1, & \text{ for } n=1 \\ 0, & \text{ else}\end{array}\right., \text{ where }n\in {\mathbb Z} </math> |
| − | |- | + | |- |
| − | | align="right" style="padding-right: 1em;" | | + | | align="right" style="padding-right: 1em;" | DT unit step function || <math>u[n]=\left\{ \begin{array}{ll}1, & \text{ for } n\geq 0 \\ 0, & \text{ else}\end{array}\right., \text{ where }n\in {\mathbb Z} </math> |
|- | |- | ||
! colspan="2" style="background: #e4bc7e; font-size: 110%;" | Basic Signals and Functions in two variables | ! colspan="2" style="background: #e4bc7e; font-size: 110%;" | Basic Signals and Functions in two variables | ||
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|- | |- | ||
| align="right" style="padding-right: 1em;" | | | align="right" style="padding-right: 1em;" | | ||
| − | + | 2D Dirac delta | |
| − | | <math>\delta(x,y)=\delta(x) \delta(y)</math> | + | | <math>\delta(x,y)=\delta(x) \delta(y), \text{ where }x,y\in {\mathbb R}</math> |
|- | |- | ||
| align="right" style="padding-right: 1em;" | | | align="right" style="padding-right: 1em;" | | ||
| − | + | 2D sinc function | |
| − | | <math>sinc(x,y)=\frac{sin(\pi x)sin(\pi y)}{ | + | | <math>sinc(x,y)=\frac{sin(\pi x)sin(\pi y)}{\pi^2 x y }, \text{ where }x,y\in {\mathbb R}</math> |
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | | ||
| + | ([[2D_rect|info]]) 2D rect function | ||
| + | | <math>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}</math> | ||
|} | |} | ||
----- | ----- | ||
| − | [[Collective_Table_of_Formulas|Back to Collective Table | + | [[Collective_Table_of_Formulas|Back to Collective Table]] |
| − | + | ||
Latest revision as of 10:11, 18 September 2015
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} $ |
