1. Signals and Systems
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Chapter (1)

2. Lecture Contents What does a signal mean? Classifications of Signals
Continuous-Time and Discrete-Time Signals
Analog and Digital Signals
Even and Odd Signals
Periodic and Non-periodic signals
Sinusoidal Signals
Signals and Systems Analysis

3. 1.1 What does a signal mean ?
A signal is a function representing a physical quantity or variable, typically is contains information about the behavior or nature of the phenomenon.
A system is viewed as transformation (mapping) of 𝑥 into 𝑦, to process input signals to produce output signals.
Types of Signals in our lives and some examples:
Electrical Signals:
(e.g. voltage and current)
Electromagnetic Signals:
(e.g. radio, waves and light)
Sound Signals:
(e.g. human sounds and music)
System
Input signal
𝑥(𝑡)
Output signal
𝑦(𝑡)
Signals and Systems Analysis

4. 1.1 What does a signal mean ? Data : Signals : Signaling :
entities that convey information
Signals :
electric or electromagnetic representations of data
Signaling :
physically propagates along a medium
Transmission :
communication of data by propagation and processing of signals
7-Dec-18
Networks and Communication Department

5. 1.2 Classifications of Signals
Continuous-Time and Discrete-Time Signals (Basic types of Signals)
Continuous-Time Signals:
A signal 𝑥(𝑡) is continuous-time signal if the independent variable t is continuous.
Discrete-Time Signals:
A signal 𝑥(𝑡) is defined at discrete times, a discrete-time signal is often identified as a sequence of numbers, denoted by 𝑥 𝑛 .
A very important class of discrete-time signals 𝑥 𝑛 is obtained by sampling a continuous-time signal 𝑥 𝑡 .
Signals and Systems Analysis

6. Continuous-time Signals:
A continuous-time signal is a signal that can be defined at every instant of time. A continuous-time signal contains values for all real numbers along the X-axis. It is denoted by x(t).
Analog signals is a continuous-time signals.
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7. Discrete-time Signals:
Signals that can be defined at discrete instant of time is called discrete time signal. Basically discrete time signals can be obtained by sampling a continuous-time signal. It is denoted as x[n]
Digital signals is Discrete-time signals.
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8. 1.2 Classifications of Signals (Cont.)
Analog and Digital Signals
Signals and Systems Analysis

9. 1.2 Classifications of Signals (Cont.)
Analog and Digital Signals
Analog signals:
If a continuous-time signal 𝑥(𝑡) can take on any value in the continuous interval (𝑎, b), where 𝑎 may be - and b may be +, then the continuous-time signal 𝑥(𝑡) is called an analog signal.
Digital signals:
It is a discrete or non-continuous 𝑥 𝑛 waveform, that could take only a finite number of values; with examples such as computer 1s and 0s.
Signals and Systems Analysis

10. Analog and Digital data :
Audio
Video
Text and Numbers.
IRA (ASCII).
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11. Analog Signals : Audio Signals
Frequency range of typical speech is 100Hz-7kHz
Easily converted into electromagnetic signals
Varying volume converted to varying voltage
Can limit frequency range for voice channel to Hz
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12. Analog Signals : Audio Signals 7-Dec-18
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13. Analog Signals : Video Signals
To produce a video signal a TV camera is used
USA standard is 483 lines per frame, at a rate of 30 complete frames per second
Actual standard is 525 lines but 42 lost during vertical retrace
Horizontal scanning frequency is 525 lines x 30 scans = lines per second
Max frequency if line alternates black and white
Max frequency of 4.2MHz
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14. Analog Signals : Video Signals 7-Dec-18
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15. Analog signals :
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16. Digital Signals:
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17. Digital Signals : cheaper less susceptible to noise interference
Advantages
Disadvantages
cheaper
less susceptible to noise interference
suffer more from attenuation
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18. Digital Signals :
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19. 1.2 Classifications of Signals (Cont.)
E. Even and Odd Signals
A signal 𝑥(𝑡) or 𝑥 𝑛 is referred to as an even signal if
𝒙(−𝒕) = 𝒙(𝒕)
𝐱 −𝒏 = 𝐱 𝒏
Signals and Systems Analysis

20. 1.2 Classifications of Signals (Cont.)
E. Even and Odd Signals (Cont.)
A signal 𝑥(𝑡) or 𝑥 𝑛 is referred to as an odd signal if
𝒙(−𝒕) = −𝒙(𝒕)
𝐱 −𝒏 = −𝐱 𝒏
Signals and Systems Analysis

21. Even and Odd signals: Even Odd
An even signal is any signal 'x' such that x(t) = x(-t)
Even signals are symmetric around vertical axis
an odd signal is a signal 'x' for which x(t) = - x(-t)
Odd signals are symmetric about origin
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22. 1.2 Classifications of Signals (Cont.)
Periodic and Non-periodic signals: Periodic signal: Pattern repeated over time. Non-periodic signal(Aperiodic): Pattern not repeated over time.

23. 1.2 Classifications of Signals (Cont.)
Periodic and Non-periodic Signals:
A continuous-time signal 𝒙(𝒕) is said to be periodic with period T if there is a positive nonzero value of T for which
𝒙(t + T) = 𝒙(𝒕) for all t
In other words, a periodic signal has the property that it is unchanged by a time shift of T (called period T).
An example of such a signal is shown below
Signals and Systems Analysis

24. 1.2 Classifications of Signals (Cont.)
Periodic and Non-periodic Signals (Cont.):
From this equation
𝒙(t + T) = 𝒙(𝒕)
it follows that
𝒙(t + mT) = 𝒙(𝒕)
for all t and any integer m.
Note that this definition does not work for a constant signal 𝒙(𝒕).
Any continuous-time signal which is not periodic is called a non- periodic (or aperiodic ) signal.
Signals and Systems Analysis

25. 1.2 Classifications of Signals (Cont.)
Periodic and Non-periodic Signals (Cont.):
Signals and Systems Analysis

26. 1.2 Classifications of Signals (Cont.)
Periodic and Non-periodic Signals (Cont.):
Signals and Systems Analysis

27. Periodic and Aperiodic signals
A signal is said to be periodic if it repeats itself after some amount of time x(t+T)=x(t), for some value of T. The period of the signal is the minimum value of time for which it exactly repeats itself.
Signal which does not repeat itself after a certain period of time is called aperiodic signal.
7-Dec-18
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28. Types of Signals and its Properties:
Summary
This module describes just some of the many ways in which signals can be classified. They can be continuous time or discrete time, analog or digital, periodic or aperiodic, odd or even.
7-Dec-18
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