1.
ANJUMAN COLLAGE OF ENGINEERING
AND TECHNOLOGY
Subject :- Signal And System
STANDARD SIGNAL
Created By: Sultan Ali Javed Ali (02) Guided By: Mohsina Anjum
Group 1:- Roll.no.( 1 to 5)

2.
Introduction
 In time domain analysis the response of a dyna mic sytem to an input is
expressed as a function of time.
 It is possible to compute the time response of a system if the nature of
input and the mathematical model of the system ]are known.
 Usually, the input signals to controls system are not known fully ahead of
time.
 For example, in a radar tracking system , the position and the speed of the
target to be tracked may vary in a random fashion.

3.
STANDARD TEST SIGNAL
 The characteristics of actual input signals are a sudden shock, a
sudden change, a constant velocity and constant acceleration.
 The dynamic behavior of a system is therefore judged and
compared under application of standard text signals , an
impluse, a step, a constan velocity and constant acceleration.
 Another standard signal of great importance is a sinusoidal
signal.

4.
Some Types of Standard Signal :-
1. Unit Step function Signal
2. Unit Ramp function Signal
3. Unit Parabolic function Signal
4. Unit Impulse function Signal
5. Sinusoidal Signal
6. Exponential Signal

5.
• The unit step signal which is defined for every instant of time is known
as continuous-time unit step signal. The continuous-time unit step signal
is denoted by u(t).
• Mathematically, the continuous-time unit step signal u(t) is defined as
follows:
1). Unit Step function Signal :-
u(t)={ 1 for t≥0
{ 0 for t<0

6.
• The continuous-time unit ramp signal is that function which starts at 𝑡
= 0 and increases linearly with time. It is denoted by r(t).
• Mathematically, the continuous-time unit ramp signal is defined as
follows :
2). Unit Ramp function Signal :-
r(t)= { t for t≥0
{0 for t<0

7.
• The continuous-time unit parabolic signal is a unit parabolic signal
which is defined for every instant of positive time. It is denoted by p(t).
• Mathematically, the continuous-time unit parabolic signal is defined as
follows :
3). Unit Parabolic function Signal:-
p(t)= {

8.
• An ideal impulse signal is a signal that is zero everywhere but at the
origin (t = 0), it is infinitely high. Although, the area of the impulse is
finite. The unit impulse signal is the most widely used standard signal
used in the analysis of signals and systems.
• The continuous-time unit impulse signal is denoted by δ(t) and is defined
as:
4). Unit Impulse Signal :-

9.
• A sinusoidal signal which is defined for
every instant of time is called continuous-
time sinusoidal signal.
𝑥(𝑡) = 𝐴 sin(𝜔𝑡 + 𝜑)
• A sinusoidal signal which is defined only at
discrete instants of time is called discrete-
time sinusoidal signal
𝑥(n) = 𝐴 sin(𝜔n + 𝜑)
5). Sinusoidal Signal :-

10.
• A real exponential signal which is defined for every
instant of time is called continuous time real
exponential signal. A continuous time real exponential
signal is defined as follows:
𝑥(𝑡) = 𝐴𝑒𝛼𝑡
• A real exponential signal which is define at discrete
instants of time is called discrete-time real
exponential signal or sequence. A discrete-time real
exponential sequence is defined as :
𝑥(n) = 𝐴𝑒𝛼n
6). Exponential Signal :-

11.
Thanking You...