This document provides an introduction to signals and their classification. It discusses continuous-time signals, discrete-time signals, periodic signals, non-periodic signals, even and odd signals, and signal energy and power. Continuous-time signals have a value for all points in time, while discrete-time signals have values for specific points in time formed by sampling. Signals can be classified as deterministic or non-deterministic, periodic or non-periodic, even or odd. The document also covers operations on signals like time shifting and scaling, and defines energy and power for discrete-time signals. Textbooks and references on digital signal processing are listed.

1. IT6502-DIGITAL SIGNAL
PROCESSING
VI Semester B.E. CSE
Classification of Signals
Mrs.S.Jeeva, AP/ECE
Ramco Institute of Technology
Rajapalayam.
Academic Year (2018-2019 Even)

2. Introduction to Signals
• A Signal is the function of one or more independent
variables that carries some information to represent a
physical phenomenon.
e.g. ECG, EEG
• Two Types of Signals
1. Continuous-time signals
2. Discrete-time signals

3. 3
1. Continuous-Time Signals
• Signal that has a value for all points in time
• Function of time
– Written as x(t) because the signal “x” is a function of time
• Commonly found in the physical world
– ex. Human speech
• Displayed graphically as a line
x(t)
t

4. 4
2. Discrete-Time Signals
• Signal that has a value for only specific points in time
• Typically formed by “sampling” a continuous-time signal
– Taking the value of the original waveform at specific intervals in time
• Function of the sample value, n
– Write as x[n]
– Often called a sequence
• Commonly found in the digital world
– ex. wav file or mp3
• Displayed graphically as individual values
– Called a “stem” plot
x[n]
n1 2 3 4 5 6 7 8 9 10
Sample number

5. 5
Examples: CT vs. DT Signals
( )x t [ ]x n
nt

6. 6
• Discrete-time signals are often obtained by
sampling continuous-time signals
Sampling
( )x t [ ] ( ) ( )t nTx n x t x nT== =. .

7. Discrete-Time Signals
• Sampling is the acquisition of the values of a
continuous-time signal at discrete points in time
• x(t) is a continuous-time signal, x[n] is a discrete-
time signal
[ ] ( )x x where is the time between sampless sn nT T=

8. Discrete Time Exponential and
Sinusoidal Signals
• DT signals can be defined in a manner analogous to their
continuous-time counter part
x[n] = A sin (2Пn/No+θ)
= A sin (2ПFon+ θ)
x[n] = an
n = the discrete time
A = amplitude
θ = phase shifting radians,
No = Discrete Period of the wave
1/N0= Fo= Ωo/2 П = Discrete Frequency
Discrete Time Sinusoidal Signal
Discrete Time Exponential Signal

9. Discrete Time Sinusoidal Signals

10. Discrete Time Unit Step Function or
Unit Sequence Function
[ ]
1 , 0
u
0 , 0
n
n
n
≥
= 
<

11. Discrete Time Unit Ramp Function
[ ] [ ]
, 0
ramp u 1
0 , 0
n
m
n n
n m
n =−∞
≥ 
= = − 
< 
∑

12. Discrete Time Unit Impulse Function or
Unit Pulse Sequence
[ ]
1 , 0
0 , 0
n
n
n
δ
=
= 
≠
[ ] [ ] for any non-zero, finite integer .n an aδ δ=

13. Unit Pulse Sequence Contd.
• The discrete-time unit impulse is a function in the
ordinary sense in contrast with the continuous-
time unit impulse.
• It has a sampling property.
• It has no scaling property i.e.
δ[n]= δ[an] for any non-zero finite integer ‘a’

14. Operations of Signals
• Sometime a given mathematical function may
completely describe a signal .
• Different operations are required for different
purposes of arbitrary signals.
• The operations on signals can be
Time Shifting
Time Scaling
Time Inversion or Time Folding

15. 0 0, an integern n n n→ +Time shifting
Operations of Discrete Time
Functions

16. Operations of Discrete Functions Contd.
Scaling; Signal Compression
n Kn→ K an integer > 1

17. Classification of Signals
• Deterministic & Non Deterministic Signals
• Periodic & A periodic Signals
• Even & Odd Signals
• Energy & Power Signals

18. Deterministic & Non Deterministic Signals
Deterministic signals
• Behavior of these signals is predictable w.r.t time
• There is no uncertainty with respect to its value at any
time.
• These signals can be expressed mathematically.
For example x(t) = sin(3t) is deterministic signal.

19. Deterministic & Non Deterministic Signals
Contd.
Non Deterministic or Random signals
• Behavior of these signals is random i.e. not predictable
w.r.t time.
• There is an uncertainty with respect to its value at any
time.
• These signals can’t be expressed mathematically.
• For example Thermal Noise generated is non
deterministic signal.

20. Periodic and Non-periodic Signals
• Given x(t) is a continuous-time signal
• x (t) is periodic iff x(t) = x(t+Tₒ) for any T and any integer n
• Example
– x(t) = A cos(ωt)
– x(t+Tₒ) = A cos[ω(t+Tₒ)] = A cos(ωt+ωTₒ)= A cos(ωt+2π)
= A cos(ωt)
– Note: Tₒ =1/fₒ ; ω=2πfₒ

21. Periodic and Non-periodic Signals
Contd.
• For non-periodic signals
x(t) ≠ x(t+Tₒ)
• A non-periodic signal is assumed to have a
period T = ∞
• Example of non periodic signal is an
exponential signal

22. Important Condition of Periodicity for
Discrete Time Signals
• A discrete time signal is periodic if
x(n) = x(n+N)
• For satisfying the above condition the
frequency of the discrete time signal should
be ratio of two integers
i.e. fₒ = k/N

23. Even and Odd Signals
Even Functions Odd Functions
gt()=g−t() gt()=−g−t()

24. Even and Odd Parts of Functions
( )
( ) ( )g g
The of a function is g
2
e
t t
t
+ −
=even part
( )
( ) ( )g g
The of a function is g
2
o
t t
t
− −
=odd part
A function whose even part is zero, is odd and a function
whose odd part is zero, is even.

25. Discrete Time Even and Odd Signals
[ ]
[ ] [ ]g g
g
2
e
n n
n
+ −
= [ ]
[ ] [ ]g g
g
2
o
n n
n
− −
=
[ ] [ ]g gn n= − [ ] [ ]g gn n= − −

26. Signal Energy and Power for DT
Signal
•The signal energy of a for a discrete time signal x[n] is
[ ]
2
x x
n
E n
∞
=−∞
= ∑
•A discrtet time signal with finite energy and zero
power is called Energy Signal i.e.for energy signal
0<E<∞ and P =0

27. Signal Energy and Power for DT
Signal Contd.
The average signal power of a discrete time power signal
x[n] is
[ ]
1
2
x
1
lim x
2
N
N
n N
P n
N
−
→∞
=−
= ∑
[ ]
2
x
1
x
n N
P n
N =
= ∑
For a periodic signal x[n] the average signal power is
The notation means the sum over any set of
consecutive 's exactly in length.
n N
n N
=
 
 ÷
 ÷
 
∑

29. • TEXT BOOK:
1. John G. Proakis & Dimitris G.Manolakis, “Digital Signal
Processing – Principles, Algorithms & Applications”,
Fourth Edition, Pearson Education / Prentice Hall, 2007.
• REFERENCES:
1. Emmanuel C..Ifeachor, & Barrie.W.Jervis, “Digital Signal
Processing”, Second Edition, Pearson Education / Prentice
Hall, 2002.
2. Sanjit K. Mitra, “Digital Signal Processing – A Computer
Based Approach”, Tata Mc Graw Hill, 2007.
3. A.V.Oppenheim, R.W. Schafer and J.R. Buck, “Discrete-
Time Signal Processing”, 8th Indian Reprint, Pearson,
2004.
4. Andreas Antoniou, “Digital Signal Processing”, Tata Mc
Graw Hill, 2006.

30. THANKYOU