It gives the flow to understand the signals and systems with their definitions, examples and properties.

1. QUICK
POINTERS
TO
SIGNALS AND
SYSTEMS Dr Mrs Minakshi Pradeep Atre, PVGCOET, Pune

2. Introduction to Signals & Systems
Objectives & Outcomes:
Signals
Systems
Transforms
RV and
Probability
Objectives
Outcomes
Mathematical
representatio
n
Classification
System
classification
Identification,
classification &
basic signal
operations

3. Fundamentals
 Signals: Introduction, Graphical, Functional, Tabular and Sequence representation of
Continuous and Discrete time signals. Basics of Elementary signals: Unit step, Unit
ramp, Unit parabolic, Impulse, Sinusoidal, Real exponential, Complex exponential,
Rectangular pulse, Triangular, Signum, Sinc and Gaussian function.
 Operations on signals: time shifting, time reversal, time scaling, amplitude scaling,
signal addition, subtraction, signal multiplication. Communication, control system
and Signal processing examples.
 Classification of signals: Deterministic, Random, periodic , Non periodic, Energy ,
Power, Causal , Non- Causal, Even and odd signal.
 Systems: Introduction, Classification of Systems: Lumped Parameter and Distributed
Parameter System, static and dynamic systems, causal and non-causal systems,
Linear and Non- linear systems, time variant and time invariant systems, stable and
unstable systems, invertible and non- invertible systems.

4. Flow of the Presentation
Part 1:
Discussion of the
fundamentals of
signals and
systems
Part 2:
Sample code
implementation
using MATLAB

5. Part 1:
Discussion of the
methodology of
Fundamentals of
Signals and
Systems

6. Components of SS
Signals
Operations
Classifications
Systems
Classification
Courtesy: google

7. Signals
 Unit step
 Unit ramp
 Unit Impulse
 Sinusoidal
 Real exponential and Complex exponential
 Rectangular pulse
 Triangular
 Signum
 Sinc
 Gaussian function
 Unit parabolic

8. Signals
 Why Signals?
 Definition
 Mathematical expression
 Tabular form
 CT and DT form
 Graphical form
 Properties
Signals are Patterns!
They help us build the
mathematical models for the
nature of the real system
responses!

9. Example of Signal : Impulse/ Delta function
 Definition
 Mathematical expression
 Tabular form
 CT and DT form
 Graphical representation
 Properties
 Definition: Area under the curve is 1
 Mathematical expression:
 Graphical representation
 Properties:
 Equivalence property
 Sampling property &
 Scaling property

10. How signals look?

11. We are discrete signals and follow Nyquist
Courtesy: researchgate.net

12. Operation Real life examples
Amplitude scaling Audio Amplifier
Amplitude/ signal
addition/ subtraction
Audio Mixer
Amplitude/ signal
Multiplication
Modulation
Time reflection Radar (coming back to
station)
Time scaling Sound of siren
Time shifting Radar
Signal
Operations
Time
Shifting
Scaling
Reflection/
reversal
Amplitude
Scaling
Addition
Multiplication

13. Step1 : mathematical
expression is given for that
operation
Step 2: Prepare the table for
amplitude and time index
Step 3: Develop the
graphical representation of
the final signal
Flow of carrying out the signal operation

14. Classification of Signals
 Deterministic, Random
 Periodic , Non periodic
 Energy , Power
 Causal , Non- Causal
 Even and odd signal
class condition examples
Periodic
x(t) =
x(T+t)
Sine/
cosine
Energy Rect
signal
Causal
Response
occurs only
when input is
applied
All real time
signals,
music signal
Even/
odd
x( t ) = -
x(-t)
Cosine is
odd
Random and deterministic signals :
Noise and Music Signal

15. Systems
 Definition
 Introduction
 Classification of Systems:
 Lumped Parameter and Distributed Parameter System,
 Static and dynamic systems,
 Causal and non-causal systems,
 Linear and Non- linear systems,
 Time variant and time invariant systems,
 Stable and unstable systems,
 Invertible and non- invertible systems

16. System Classification
Class/ Type Definition/ Description Condition Mathematical
Examples
Real life examples
Lumped Parameter
& Distributed
parameters
A lumped system:
function of time alone
A distributed system : all
dependent variables are
functions of
time and one or more
spatial variables
Represented by
ordinary differential
equations (ODEs)
Represented by
partial differential
equations (PDEs)
Ex. Transmission
lines are distributed
systems
Ex. RLC filters/
systems are
lumped parameter
systems
Static & dynamic
systems
Depends only on present
input for an output
{ Static: Memoryless }
{ Dynamic: with memory
}
y(n) = x(n)
y(n) = x(n) + x(n -1)
Multiplexers
Flip-flops

17. System Classification
Class/ Type Definition/
Description
Condition Mathematical
Examples
Real life
examples
Causal & non-
causal systems
Output occurs
only if input is
applied
Non-causal
systems are
hypothetical
x(t) = 0 for t<0 y(t) = x(t) + x(t - 1)
y(t) = x(t+3) + x(2t)
Speech signals
---
Linear & Non-
linear systems
Superposition
theorem
(homogeneity
and additivity)
F[a1x1(t) + a2x2(t)]
= a1y1(t) + a2y2(t)
y(t) = t.x(t)
Y(t) = x(t). X(t-1)
Typical RLC
circuit

18. System Classification
Class/ Type Definition/
Description
Condition Mathematical
Examples
Real life examples
Time variant &
time invariant
systems
Input shifted,
output is also
shifted by the
same amount
x(t-to) = x(t, to) y(t) = x(2.t) RC circuits: if C value
changes with time,
then time-varying
system,
Else if R,C are
constant then time
varying system
Stable & unstable
systems
BIBO condition Absolute
summability
y(t) = a.x(t) Mass-damper system
is stable but
integrator ckt is
unstable
Invertible & non-
invertible systems
Y(t) = T{x(t)} and
when we take z(t)
= T^-1{y(t), we get
z(t) = y(t) then it’s
y(t) = 10 +
x(t)
y(t) = x^2(t)
V = I.R

19. Signals and Systems
Image
2D signal
EEG
Multidimensional
signal
ECG
1D signal
HUMAN BODY
SYSTEM

20. Part 2:
Sample code
implementation
using MATLAB

24. THANK YOU