Signal Digital Signal Discrete Time Signal Visual of Discrete Time Signal with Examples Representation of Discrete Time Signal Classification of Discrete Time Signal Manipulation of Discrete Time Signal System Block Diagram Delay Elements Recursive System Static and Dynamic System Convolution Correlation

1. Digital Signal Processing
Signal and System (Digital)

2. Presenter
Mohammad Yeasin Newaj Khan
BSc. In EEE

3. Contents
Signal
• Digital Signal
• Discrete Time Signal
• Visual of Discrete Time Signal with
Examples
• Representation of Discrete Time Signal
• Classification of Discrete Time Signal
• Manipulation of Discrete Time Signal
System
• Block Diagram
• Delay Elements
• Recursive System
• Static and Dynamic System
• Convolution
• Correlation

4. SIGNAL
01

5. Digital Signal
A digital signal is a signal that is
being used to represent data as a
sequence of discrete values; at
any given time it can only take on,
at most, one of a finite number of
values.
What is Digital Signal?

6. Discrete Time Signal
Discreet-Time signals are
represented mathematically as sequences of numbers
The sequence is denoted 𝑥[Discreet-Time signals are
represented mathematically as sequences of numbers
The sequence is denoted 𝑥[𝑛
], and it is written formally as
𝑥 = 𝑥 𝑛 ; −∞ < 𝑛 < ∞
where n is an integer number
In practice sequences arises from the periodic sam
pling of an analog signal
], and it is written formally as
𝑥 = 𝑥 𝑛 ; −∞ < 𝑛 < ∞
where n is an integer number
In practice sequences arises from the periodic sam
pling of an analog signal

7. Visual Representation of Discrete Time Signal
Example - 1

8. Visual Representation of Discrete Time Signal
Example - 2

9. Types of Representation of Discrete Time Signal
There are four types of representation in discrete time signal.
These are:

10. Types of Representation of Discrete Time Signal

11. Classification of Discrete time signal

12. Classification
Discrete time signals can be classified as follows:
• Even and odd signals
• Periodic and non-periodic signals
• Deterministic and random signals
• Energy signals and power signals
• Multichannel and multidimensional signals

13. Periodic and Non-Periodic Signal

14. Periodic Signal
A signal is considered to be periodic signal if it completes a pattern within a
measurable time frame, called a period and repeats that pattern over
identical subsequent periods.
A period is defined as the amount of time (expressed in seconds) required
to complete one full cycle. Sinusoidal wave, cosine wave, triangle wave and
square wave are example of periodic signal.
Periodic signals are more commonly identified by their frequency (f) rather
than their period. The frequency of a signal is the inverse of the period.
Mathematically, this means that:
F=1/T
The frequency of a signal tells us how many times the signal repeats itself
during one second. Units of frequency are in cycles per second or Hertz (Hz).
Therefore, a signal with a frequency of 100Hz goes through 100 cycles
(Periods) in one second (the period of the signal is 0.01 seconds.

15. Aperiodic Signal
○ Aperiodic signal is a signal which does not repeat itself after a specific interval of
time.
○ Example of aperiodic signal is signal created by microphone or telephone when
one or two words are pronounced. Also, signal propagated by AM radio station or
FM radio stations are all aperiodic signal.
Aperiodic Signal

16. Symmetric and Asymmetric Signal

17. Symmetric and Asymmetric signal
Signal is said to be even or symmetric if the
time reversed signal is equal to the signal
itself.
Signal is an odd or anti-symmetric when the
time reversed signal is equal to negation of
signal. When signal does not satisfy the above
two, it is non-Symmetric in nature.

18. Manupulation of Discrete time signal

19. Manipulation

20. Manipulation

21. SYSTEM
02

22. Block Diagram

23. What is a Block Diagram in a System?
A block diagram is used to represent a control system in diagram
form. In other words, the practical representation of a control system
is its block diagram. Each element of the control system is
represented with a block and the block is the symbolic
representation of the transfer function of that element.

24. Delay Elements

25. Delay Elements

26. Recursive System

27. Recursive System

28. Static and Dynamic System

29. Static and Dynamic System
• A static system is a system in which output at any
instant of time depends on the input sample at the
same time. In other words, the system in which
output depends only on the present input at any
constant of time then this is known as the static
system.
• A static system is a system in which output at any
instant of time depends on the input sample at the
same time as well at other times. In other words, the
system in which output depends only on the past
and/or the future input at any constant of time then
this is known as the dynamic system. Dynamic
system possesses memory.

30. Convolution

31. Convolution

32. Convolution
Figure below shows the notation when convolution is used with linear systems. An
input signal, x[n], enters a linear system with an impulse response, h[n], resulting in
an output signal, y[n]. In equation form: x[n] t h[n] ' y[n]. Expressed in words, the input
signal convolved with the impulse response is equal to the output signal. Just as
addition is represented by the plus, +, and multiplication by the cross, ×, convolution
is represented by the star, t. It is unfortunate that most programming languages also
use the star to indicate multiplication. A star in a computer program means
multiplication, while a star in an equation means convolution.

33. Correlation

34. Correlation

35. Autocorrelation
&
Cross-correlation.

36. Autocorrelation

37. Cross-correlation.

38. THANK YOU