Basic Signals and Functions

(used in ECE301 and ECE438)

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

$rect(x,y)= \left\{ \begin{array}{ll}1, & \text{ for } |x|\leq \frac{1}{2} \text{ and } |y|\leq \frac{1}{2} \\ 0, & \text{ else}\end{array}\right., \text{ where }x,y\in {\mathbb R}$

## Alumni Liaison

Sees the importance of signal filtering in medical imaging

Dhruv Lamba, BSEE2010