What is signal and systems? Image result for intro to signal and system Signals and Systems is an introduction to analog and digital signal processing, a topic that forms an integral part of engineering systems in many diverse areas, including seismic data processing,

1. INTRODUCTIONTO
SIGNALSANDSYSTEMS
Lecture1

2. Thereading material
 Thetext book
Signalsand Systems
 Alan V
. Oppenheim
 Alan S. Willsky
 S. HamidNawab
 2nd Edition
 Web based demos

3. Thereading material
 Anauxiliarybook
Signalsand Linear
SystemsAnalysiswith
Matlab
 Gordon E.Carlson
 Second Ed.

4. T
ests
 Two tests
5 marks each
Thebest score
Nonobjective type
 No MCQ, No Blanks,No True/false
Subjectivetype tests only
 Definitions,Descriptions,Mathematical Evidences
 Arguments,Comparisons,Interpretations,Calculations,
and Conclusions etc.

5. Chapter 1
S.
No.
Topic
No. of
Lectures
1 Basic concepts of Signals and Systems 1
2 Signal representationand models 1
3
Classification of signals and Basic operations on
signals
1
4
System characteristics,linear time-invariant (LTI)
systems
1
5
System response, system equations and impulse
response, system order,Causality and Stability
1
Total 5

6. Definitions
 Signal
 Signal Processing
 System
 Carrier of information
Signal transmitted
from antenna
a radio
 Manipulating, Modifying,
transforming
Amplification/attenuation, Rectification,
Modulation, Filtering, Mixing
 A setup / set of components that
processesthesignals
Man
Robot

7. Classification of Signals
 Electrical and non-electrical
 Continuous-time/ Discrete-time
 Periodic/ Aperiodic
 Time-limited / time-unlimited
 Right/Left handed
 Deterministic/ Random
 Even/ Odd

8. Classification of Signals
 Electrical and non-electrical
 Continuous-time/ Discrete-time
 Periodic/ Aperiodic
 Time-limited / time-unlimited
 Right/Left handed
 Deterministic/ Random
 Even/ Odd
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
-1
.5
0
.5
1
xt
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
1
.5
0
.5
-1
xnT

9. Classification of Signals
 Electrical and non-electrical
 Continuous-time/ Discrete-time
 Periodic/ Aperiodic
 Time-limited / time-unlimited
 Right/Left handed
 Deterministic/ Random
 Even/ Odd

10. Classification of Signals
 Electrical and non-electrical
 Continuous-time/ Discrete-time
 Periodic/ Aperiodic
 Time-limited / time-unlimited
 Right/Left handed
 Deterministic/ Random
 Even/ Odd
xt T xt
xn NT xnT

11. Classification of Signals
 Electrical / Non-electrical
 Continuous-time/ Discrete-time
 Periodic/ Aperiodic
 Time-limited / time-unlimited
 Right/Left handed
 Deterministic/ Random
 Even/ Odd
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
0.5
1
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
1
0.5
0
-0.5
-1
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
-1
0
1
Time-unlimited Signals
-2 -1.5 -1 -0.5 0
Time-limited Signals
0.5 1 1.5 2
1
0.8
0.6
0.4
0.2

12. Classification of Signals
 Electrical / Non-electrical
 Continuous-time/ Discrete-time
 Periodic/ Aperiodic
 Time-limited / time-unlimited
 Right/Left handed
 Deterministic/ Random
 Even/ Odd

13. Classification of Signals
 Electrical / Non-electrical
 Continuous-time/ Discrete-time
 Periodic/ Aperiodic
 Time-limited / time-unlimited
 Right/Left handed
 Deterministic/ Random
 Even/ Odd
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
1
0
-1
Time-unlimited Signals
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
1
0.8
0.6
0.4
0.2

14. Classification of Signals
 Electrical / Non-electrical
 Continuous-time/ Discrete-time
 Periodic/ Aperiodic
 Time-limited / time-unlimited
 Right/Left handed
 Deterministic/ Random
 Even/ Odd

15. Classification of Signals
 Electrical / Non-electrical
 Continuous-time/ Discrete-time
 Periodic/ Aperiodic
 Time-limited / time-unlimited
 Deterministic/ Random
 Right/Left handed
 Even/ Odd

16. Classification of Signals
 Electrical and non-electrical
 Periodic/ Aperiodic
 Continuous-time/ Discrete-time
 Time-limited / time-unlimited
 Deterministic/ Random
 Right/Left handed
 Even/ Odd
 Even Signal
x t  xt
xn xn
 Odd Signal
xt xt
xnxn

17. Classification of Signals
 Electrical and non-electrical
 Periodic/ Aperiodic
 Continuous-time/ Discrete-time
 Time-limited / time-unlimited
 Deterministic/ Random
 Right/Left handed
 Even/ Odd
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
-1
0
1
Time-unlimited Signals
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
1
0
-1

18. Evenor Odd ?
Even
Odd
-2 -1.5 -1 -0.5 0 0
.5 1 1
.5 2
0
1
2
-2 -1.5 -1 -0.5 0 0
.5 1 1
.5 2
-1
0
1
-2 -1.5 -1 -0.5 0 0
.5 1 1
.5 2
0
1
2
Neither Even
Nor Odd

19. Signal Representation
 Simple definition
Continuousthroughout
the domain from -∞ to ∞
 Piecewise definition
Continuousin the
subdomainsand
discontinuities at the
junctions
t
f t e


f t  
0
et
t  0
t  0
for all t

20. BasicTime-Operations onSignals
 Time-Shifting
Time advance
Time delay
 Time-Scaling
Compression
Expansion
 Time-Reversal
yt xat
a 1
a 1
yt xt
yt xt  
  0
  0
a 0

21. Time Shifting
 Time-Shifting
Time advance
Time delay
-2 -1.5 -1 -0.5 0.5 1 1.5 2
0
time
1
0.5
0
x(t+tau)
-2 -1.5 -1 -0.5 0.5 1 1.5 2
1
0.5
0
0
time
x(t)
yt xt  
  0
  0
Time Shifting

22. Time Shifting
 Time-Shifting
Time advance
Time delay
yt xt  
  0
  0
Time Shifting
-2 -1.5 -1 -0.5 0.5 1 1.5 2
1
0.5
0
0
time
x(t+tau)
-2 -1.5 -1 -0.5 0.5 1 1.5 2
0
time
1
0.5
0
x(t)

23. Time Scaling
 Time-Scaling
Compression
Expansion
a 0
-3 -2 -1 0 1 2 3
1
0.5
0
yt xat
a 1
a 1
Time Scaling
x(2t)
-3 -2 -1 0 1 2 3
1
0.5
0
x(0.5t)
-3 -2 -1 0 1 2 3
1
0.5
0
x(t)

24. Time Reversal
 Time-Reversal
-3 -2 -1 1 2 3
0
time
yt xt
Time Reversal
1
0.5
0
x(-t)
-3 -2 -1 1 2 3
1
0.5
0
0
time
x(t)

25. Evenor Odd ?
Even
Odd
-2 -1.5 -1 -0.5 0 0
.5 1 1
.5 2
0
1
2
-2 -1.5 -1 -0.5 0 0
.5 1 1
.5 2
-1
0
1
-2 -1.5 -1 -0.5 0 0
.5 1 1
.5 2
0
1
2
Neither Even
Nor Odd

26. x(t) = xe(t) + xo(t)
Even Signal Odd Signal
xt xe t xo t
xt xe t xo t
xt xe t xo t
xt xt 2xe t
x t
1
xt xt
e
2
xt xt 2xo t
x t
1
xt xt
o
2
+

27. x(t) = xe(t) + xo(t)
Even Signal Odd Signal
xt xe t xo t
xt xe t xo t
xt xe t xo t
xt xt 2xe t
e
2
x t
1
xt xt
xt xt 2xo t
x t
1
xt xt
o
2
+

28. x(t) = xe(t) + xo(t)
Even Signal Odd Signal
xt xe t xo t
xt xe t xo t
xt xe t xo t
xt xt 2xe t
e
2
x t
1
xt xt
xt xt 2xo t
x t
1
xt xt
o
2
+ -

29. x(t) = xe(t) + xo(t)
Even Signal Odd Signal
xt xe t xo t
xt xe t xo t
xt xe t xo t
xt xt 2xe t
e
2
x t
1
xt xt
xt xt 2xo t
o
2
x t
1
xt xt
+ -

30. x(t) = xe(t) + xo(t)
Even Signal Odd Signal
xe t
xt xt
2
xt xt
2

o
x t
2
2
o
x t
e
x t 
 t xt xt
xt x
 
2
2
2
xt xt
xt xt
o
x t
e
x t   

2
xt
2

xt
  xt
o
x t
e
x t
2

31. Break into Evenand Odd parts
-2 -1.5 -1 -0.5 0.5 1 1.5 2
2
1.5
1
0.5
0
0
time (seconds)
x(t)

32. Break into Evenand Odd parts
-2 -1.5 -1 -0.5 0.5 1 1.5 2
2
1.5
1
0.5
0
0
time (seconds)
x(t)




xt 
2(t 1) 1 t  0
2 0  t 1
0 elsewhere
xt ?

33. Break into Evenand Odd parts
Graphically Mathematically
 



x t  
1 t  0
0  t  1
elsewhere
2
0
 2(t 1)




xt 
2(1t) 0  t 1
2 1 t  0
0 elsewhere
-2 -1.5 -1 -0.5 0.5 1 1.5 2
0
0.5
1
1.5
2
0
time (seconds)
x(-t)

34. Break into Evenand Odd parts
Graphically
-2 -1 0 1 2
0
1.5
1
0.5
2
x(t)
-2 -1 0 1 2
0
1.5
1
0.5
2
x(-t)
-2 -1 0 1 2
0
2
1.5
1
0.5
Even Part
-2 -1 0 1 2
-1
1
0.5
0
-0.5
Odd Part

35. Break into Evenand Odd parts
Mathematically




xt 
2(t 1) 1 t  0
2 0  t 1
0 elsewhere 



xt 
2(1t) 0  t 1
2 1 t  0
0 elsewhere



xt xt 
21 t
0 0
2(t 1) 2 1 t  0
0  t  1
elsewhere



xt xt 
1 t  0
3t 0  t 1
0 elsewhere
 2(t 2)



xt xt 
21 t
0 0
2(t 1) 2 1 t  0
0  t  1
elsewhere

36. System Characteristics
 Electrical/Non-Electrical
 Memory/memoryless
System order
 Causality
Causal/ Non-causal
 Stability
Stable/Non-stable
 Time-invariance
Time-variant/Time-invariant
 Linearity
Linear/Non-linear
 Invertibility
Invertible/Non-invertible

37. System Characteristics
 Electrical/Non-Electrical
 Memory/memoryless
System order
 Causality
Causal/ Non-causal
 Stability
Stable/Non-stable
 Time-invariance
Time-variant/Time-invariant
 Linearity
Linear/Non-linear
 Invertibility
Invertible/Non-invertible

38. System Characteristics
 Electrical/Non-Electrical
 Memory/memoryless
System order
 Causality
Causal/ Non-causal
 Stability
Stable/Non-stable
 Time-invariance
Time-variant/Time-invariant
 Linearity
Linear/Non-linear
 Invertibility
Invertible/Non-invertible

39. System Characteristics
 Electrical/Non-Electrical
 Memory/memoryless
System order
 Causality
Causal/ Non-causal
 Stability
Stable/Non-stable
 Time-invariance
Time-variant/Time-invariant
 Linearity
Linear/Non-linear
 Invertibility
Invertible/Non-invertible

40. System Characteristics
2
yt 2xt xt 1
1
xt  2
2
2
yn 2xn xn1
1
xn 2
2
yn 2xn xn1
1
xn 2
 Electrical/Non-Electrical
 Memory/memoryless
System order
 Causality
Causal/ Non-causal
 Stability
Stable/Non-stable
 Time-invariance
Time-variant/Time-invariant yt 2xt xt 1
1
xt  2
 Linearity
Linear/Non-linear
 Invertibility
Invertible/Non-invertible

41. System Characteristics
 BIBO stability
Boundedoutputfor
bounded input
 Electrical/Non-Electrical
 Memory/memoryless
System order
 Causality
Causal/ Non-causal
 Stability
Stable/Unstable
 Time-invariance
Time-variant/Time-invariant
 Linearity
Linear/Non-linear
 Invertibility
Invertible/Non-invertible

42. System Characteristics
 Electrical/Non-Electrical
 Memory/memoryless
System order
 Causality
Causal/ Non-causal
 Stability
Stable/Non-stable
 Time-invariance
Time-variant/Time-invariant
 Linearity
Linear/Non-linear
 Invertibility
Invertible/Non-invertible

43. System Characteristics
  
x t  y t
 Electrical/Non-Electrical
 Memory/memoryless
System order
 Causality
Causal/ Non-causal
 Stability
Stable/Non-stable
 Time-invariance
Time-variant/Time-invariant
 Linearity
Linear/Non-linear
 Invertibility
Invertible/Non-invertible
xt   yt  

44. System Characteristics
 Electrical/Non-Electrical
 Memory/memoryless
System order
 Causality
Causal/Non-causal
 Stability
Stable/Non-stable
 Time-invariance
Time-variant/Time-invariant
 Linearity
Linear/Non-linear
 Invertibility
Invertible/Non-invertible
1 1
x  y
x2  y2
Ax1  Bx2  Ay1  By2

45. System Characteristics
 Electrical/Non-Electrical
 Memory/memoryless
System order
 Causality
Causal/Non-causal
 Stability
Stable/Non-stable
 Time-invariance
Time-variant/Time-invariant
 Linearity
Linear/Non-linear
 Invertibility
Invertible/Non-invertible
-2 -1.5 -1 -0.5 0.5 1 1.5 2
-2
-1
0
1
2
0
x(t)
y(t)
-2 -1.5 -1 -0.5 0.5 1 1.5 2
-4
-2
0
2
4
0
x(t)
y(t)
- 2 - 1 . 5 - 1 - 0 . 5 0 . 5 1 1 . 5 2
0
0 . 5
1
1 . 5
2
2 . 5
3
3 . 5
4
0
x(t )
y(t
)

46. System Characteristics
 Electrical/Non-Electrical
 Memory/memoryless
System order
 Causality
Causal/Non-causal
 Stability
Stable/Non-stable
 Time-invariance
Time-variant/Time-invariant
 Linearity
Linear/Non-linear
 Invertibility
Invertible/Non-invertible

47. System Representation
Block Diagram System Component

48. System Representation
Block Diagram System Component