1) The document introduces various types of signals including continuous time signals, discrete time signals, standard signals like step signals, ramp signals, impulse signals, sinusoidal signals, and exponential signals. 2) Continuous time signals are defined for every instant in time while discrete time signals are defined for discrete instants in time. Common standard signals include unit step, ramp, parabolic, pulse, sinusoidal, and exponential signals. 3) Examples of applications of the standard signals are mentioned such as step signals being used for switching devices on and off, and sinusoidal signals being used to represent any sound signal.

1. Introduction of Signals
&
Standard Signals
Dr.K.G.SHANTHI
Professor/ECE
shanthiece@rmkcet.ac.in
1
RMK College of Engineering and Technology

2. Introduction of
Signals
Types of Signals
Basic Standard
signals
Applications
2
Contents

3. Introduction
of signals

4. Signal
A function of one or more variables that convey
information on the nature of a physical
phenomenon.
Signals are represented mathematically as
functions of one or more independent variables.
The independent variable: time (speech),space
(images).
Eg. A speech signal can be represented
mathematically by acoustic pressure as a
function of time
4

5. Signals
• Signal is denoted by x(t), where the variable t is
called independent variable and the value x(t)
is dependent variable.
• Dependent variable = voltage
• Independent variable = time

6. Signal Classification :Based on
Dimension
 1 Dimensional - Varies with respect to one independent variable
(time or space or distance) e.g. Speech, daily
maximum temperature, annual rainfall at a place
 2 Dimensional - Varies with respect to more than one independent
variable e.g. Image
 3 Dimensional - Varies with respect to more than two independent
variables (space ,distance and depth) e.g. Video
I Dimensional
3 Dimensional
2 Dimensional

7. Basic types of signals
• Continuous Time Signal (CT)
• Discrete Time Signal (DT)
(CT) (DT)

8. Continuous Time Signal (CT)
The independent variable is continuous, and thus these signals are
defined for a continuum of values of the independent variable.
 A signal that is defined for every instants of time is known as
continuous time signal. Continuous time signals are continuous in
amplitude and continuous in time.
A speech signal as a function of time and atmospheric pressure as a
function of altitude are examples of continuous-time signals.
 It is denoted by x(t)
8

9. Discrete Time Signal (DT)
9
 A signal that is defined for discrete instants of time is known
as discrete time signal. Eg:stock market index
 Discrete time signals are continuous in amplitude and discrete
in time.
 It is also obtained by sampling a continuous time signal.
 It is denoted by x[n]

10. Sampling
> Discrete-time signals are often obtained by
sampling continuous-time signals
10
Where, T = Time between
samples

11. Basic standard
signals

12. Basic (Elementary or Standard) signals
• Step Signal
• Ramp signal
• Impulse signal
• Parabolic Signal
• Sinusoidal and exponential signal
• Sinc signal
• Rectangular signal
• Signum signal
• Triangular signal
12
CT and DT
Test Signals
Input Signals
for process

13. 13
Unit Step Signal
STEP SIGNAL
• Represented by u(t) and u(n)
• Heaviside function
Application:
• DC Generator(Switching on and off of a device)
• Communication applications
x(t)=A for t≥0
x(t)=0 for t<0
x(n)=A for n≥0
x(n)=0 for n<0
DT Signal
CT Signal

14. 14
RAMPSIGNAL
• Represented by r(t)
and r(n)
Application:
Current and Voltage
relation circuits
DT Signal
CT Signal

15. 15
parabolic SIGNAL
•Acceleration function
•Represented as p(t)
and p(n)
Application:
The Bike responds to
acceleration
x(t)=At
2
/2;t≥0
x(t)=0 for t<0
DT Signal
CT Signal

16. RelationbetweenUnitStepsignal, Unitrampsignaland UnitParabolicsignal:
•Unit ramp signal is obtained by integrating unit step signal
∫u(t)dt=∫1dt=t=r(t)
•Unit Parabolic signal is obtained by integrating unit ramp signal
∫r(t)dt=∫tdt=t2/2=p(t)
•Unit step signal is obtained by differentiating unit ramp signal
d/dt r(t)=d/dt (t)=1=u(t)
• Unit ramp signal is obtained by differentiating unit Parabolic signal
d/dt p(t)=d/dt (t2/2)=t=r(t)
16

17. Pulse signal (Rectangular pulse function)
•Pi Function, Gate function
•Represented by rect(t)
17
x(t)=A;t1≤t≤t2 and
x(t)=0 elsewhere
Unit Pulse signal
π(t)=1;|t|≤1/2 and π(t)=0;elsewhere
x(n)=A;n1≤n≤n2 and
x(n)=0 elsewhere
DT Signal
CT Signal

18. 18
IMPULSE SIGNAL
• Delta function
• CT - Dirac delta function
• DT- Kronecker delta
function
• Unit Area signal
Application
• Thunderbolt
• ECG function
DT Signal
CT Signal

19. 19
SINUSOIDALSIGNAL
Cosinusoidal signal-CT
• Ω=2πf=2π/T and Ω is
angular frequency in
rad/sec
• f is frequency in cycles/sec
or Hertz
• A is amplitude
• T is time period in seconds
• 𝛷 is phase angle in
radians
Application
•Any sound signal
•The light signal
Sinusoidal signal-CT
Sinusoidal signal-CT
Cosinusoidal signal-DT

20. 20
DT Signal
SignumSIGNAL
• Represented by sgn(t)
Used in
•Communication
CT Signal

21. 21
DT Signal
Triangular SIGNAL
• Represented by tri(t)
Application
• Analog to Digital
conversion circuits
CT Signal

22. 22
DT Signal
SincSIGNAL
• Sine Cardinal function
• Represented by sinc(t)
Used in
•Digital Signal Processing
•Information Theory
, t = 0
1 , t = 0
CT Signal

23. 23
Exponential SIGNAL
Applying Euler’s Identity
𝑥(𝑡) =𝐴𝑒𝑠𝑡 =𝐴𝑒(𝜎+𝑗Ω 𝑡)=𝐴𝑒𝜎𝑡 𝑒𝑗Ω𝑡
Complex exponential signal is defined as
𝑥(𝑡) =𝐴𝑒𝑠𝑡
where 𝐴 is amplitude,
s is complex variable
𝑠=𝜎+𝑗Ω
𝑥(𝑡) =𝐴𝑒𝜎𝑡 (𝑐𝑜𝑠Ω𝑡+𝑗𝑠𝑖𝑛Ω𝑡)

24. 24
ComplexExponential SIGNAL
Where
Then 𝑥 (𝑡)=𝐴𝑒𝜎𝑡(𝑐𝑜𝑠Ω𝑡+𝑗𝑠𝑖𝑛Ω𝑡),
When , 𝜎 = +ve
𝑥𝑟(𝑡) =𝐴𝑒𝜎𝑡𝑐𝑜𝑠Ω𝑡 𝑎𝑛𝑑
𝑥i(𝑡) =𝐴𝑒𝜎𝑡𝑠𝑖𝑛Ω𝑡
Exponentially growing
sinusoidal signal
Exponentially growing
cosinusoidal signal Exponentially decaying
cosinusoidal signal
Exponentially decaying
sinusoidal signal
Where
Then 𝑥 (𝑡)=𝐴𝑒-𝜎𝑡(𝑐𝑜𝑠Ω𝑡+𝑗𝑠𝑖𝑛Ω𝑡),
When , 𝜎 = -ve
𝑥𝑟(𝑡) = 𝐴𝑒-𝜎𝑡 𝑐𝑜𝑠Ω𝑡 𝑎𝑛𝑑
𝑥i(𝑡) =𝐴𝑒-𝜎𝑡 𝑠𝑖𝑛Ω𝑡

25. Real ExponentialSIGNAL
25
 Real Exponential signal is defined as 𝑥(𝑡) =𝐴𝑒 𝜎𝑡 where A is
amplitude. It is obtained when Ω=0.
 Depending on the value of ‘𝜎’ we get dc signal or growing
exponential signal or decaying exponential signal

26. 26
Consider 𝜎 =1 (𝜎 >0)
x(t) = e𝜎𝑡= e𝑡
t= 0, e0 = 1
t= 1, e1 = 2.7
t= 2, e2 = 7.3
Consider 𝜎 =-1 (𝜎 <0)
x(t) = e𝜎t= e-t
t= 0, e0 = 1
t= 1, e-1 = 0.36
t= 2, e-2 = 0.13
Rising
Falling

27. Real Exponential signal is defined as
27
Exponential SIGNAL- DT
x(n) = an for all n
0<a<1 = Sequence decays exponentially
a>1 = Sequence grows exponentially
a<0 = Discrete time exponential signal
takes alternating signs
Decreasing exponential
signal
Increasing
exponential signal
Increasing exponential
signal with alternating signs
Decreasing exponential
signal with alternating signs

28. 28
Exponential SIGNAL
Consider a= ½ (0<a<1)
n= 0, (½)0 = 1
n= 1, (½)1 = ½ = 0.5
n= 2, (½)2 = ¼ = 0.25
Consider a= 2 (a>1)
n= 0, 20 = 1
n= 1, 21 = 2
n= 2, 22 = 4

29. 29
Practise
a= -2
a= -½
Consider a= -½
n= -2, (-½)-2 = 4
n= -1, (-½)-1 = -2
n= 0, (-½)0 = 1
n= 1, (-½)1 = -½ = -0.5
n= 2, (-½)2 = ¼ = 0.25
Consider a = - 2
n= -2, (-2)-2 = 1/4
n= -1, (-2)-1 = -1/2
n= 0, (-2)0 = 1
n= 1, (-2)1 = -2
n= 2, (-2)2 = 4
n= 3, (-2)3 = -8
-2 -1 0 1 2 3
x(n)= (-2)n
1/4
-1/2
1
-2
4
-8
n
w.k.t X(n) = αn
-2 -1 0 1 2
x(n)= (-1/2)n
1/4
-1/2
1
-2
4
n

30. ComplexExponential SIGNAL-Dt
30
Complex Exponential signal is defined as
Where
Exponentially decreasing
Cosinusoidal signal
Exponentially decreasing
sinusoidal signal
Exponentially growing
Cosinusoidal signal
Exponentially growing
sinusoidal signal

31. 31
Thanks!