Signal

1. 1
Signal Analysis & Definition of
modulation
Lecture 1-2
University of Mustansiriyah College of Engineering
Department of Computer Engineering Second Class/ First Semester
Analogue Communication
Dr. Haider Tarish Haider
 Email: haiderth@uomustansiriyah.edu.iq
 2019-218

2. 2
Lecture 1-2
Periodic and Non periodic (Aperiodic): which can be repeated itself after a fixed length
of time (i.e. f(t)=f(t+T), for -∞< t< ∞).
Signal Analysis
The signals can be classified into the following types:
Deterministic and Random: which can be expressed mathematically as a function of time
(f(t)=t2 ) other signals is random or noise signals.
Periodic function Non periodic function

3. 3
Lecture 1-2
𝛿 𝑡 =
∞ , 𝑡 = 0
0 , 𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒
Prosperities:
 −∞
∞
𝛿 𝑡 𝑑𝑡 = 1
 −∞
∞
𝑓 𝑡 𝛿 𝑡 𝑑𝑡 = 𝑓(0)
 −∞
∞
𝑓 𝑡 𝛿 𝑡 − 𝑡0 𝑑𝑡 = 𝑓(𝑡0)
Examples of Signals
1- Impules (Dirac):
2-Unite Step:
u t =
1, 𝑡 ≥ 0
0, 𝑡 < 0

4. 4
Lecture 1-2
3-Signum function
sgn t =
−1, 𝑡 < 0
0, 𝑡 = 0
−1, 𝑡 > 0
Signal Spectrum
The spectrum is the frequency domain description of a signal. Fourier series and transform is
one of the fundamental methods the represent the signals in frequency domain.
𝐹 𝑤 = −∞
∞
𝑓 𝑡 𝑒−𝑖𝜔𝑡𝑑𝑡 Forward transform
𝑓 𝑡 =
1
2𝜋 −∞
∞
𝐹 𝑤 𝑒𝑖𝜔𝑡
𝑑𝑤 inverse transform

5. 5
Lecture 1-2
Spectrum of sinusoidal signal.
f(t)=A cos(w0t+), we can write
cos 𝑥 =
𝑒𝑗𝑥
+ 𝑒−𝑗𝑥
2
, sin 𝑥 =
𝑒𝑗𝑥
+ 𝑒−𝑗𝑥
2𝑗
)
(
2
)
( jWct
jWct
e
e
A
t
f 


Single side spectrum
-Two side spectrum

6. 6
Lecture 1-2
Example: find the spectrum (single and double sided) of the signal
𝒇 𝒕 = 𝟕 − 𝟏𝟎𝒄𝒐𝒔 𝟒𝟎𝝅𝒕 − 𝟔𝟎° + 𝟒𝒔𝒊𝒏(𝟏𝟐𝟎𝝅𝒕)
Solution: we can rewrite f(t) in cosin form
𝒇 𝒕 = 𝟕𝒄𝒐𝒔𝟐𝝅𝟎𝒕 + 𝟏𝟎𝒄𝒐𝒔 𝟐𝝅𝟐𝟎𝒕 − 𝟏𝟐𝟎° + 𝟒𝒔𝒊𝒏(𝟐𝝅𝟔𝟎𝒕 − 𝟗𝟎)
A Method of Translation:
A signal may be translated to a new spectral range be multiplying the signal with an
auxiliary sinusoidal wave form.
Let the signal be a sinusoidal waveform

7. 7
Lecture 1-2
)
(
2
cos
)
( jWmt
jWmt
m
m
m
m e
e
A
t
w
A
t
v 


 , Am = constant amplitude, freq
w
fm m



2
m
f
1
Am/2
-fm fm
f/Hz
fm
f/Hz
Am
Two-side spectrum
Single-Side spectrum

8. 8
Lecture 1-2
Consider the auxiliary signal. )
(
2
cos jWct
jWct
c
c
c
c e
e
A
t
w
A
v 



Ac = constant amplitude
fc= frequency
Multiplication of vm(t) and vc(t) will result invm(t) vc(t)= (Am coswmt) (Ac coswct)
]
)
cos(
)
[cos(
2
t
w
w
t
w
w
AmAc
m
c
m
c 



The amplitude spectrum of the product is
-(fc+fm) -fc -(fc-fm) fc-fm fc fc+fm
 
t
wm
wc
j
t
wm
wc
j
t
wm
wc
j
t
wm
wc
j
c
m
e
e
e
e
A
A )
(
)
(
)
(
)
(
4











9. 9
Lecture 1-2
Note: It may be seen that the original spectral lines have been translated both in the positive
and negative frequency direction by the amount fc.
The message signal of finite energy and non- periodic, it may be represented in freq. domain
by its Fourier Transform.
Let the signal m(t) be band limited to the freq. range zero to wm its Fourier Transform M(w)
is as shown.
The spectrum resulting when m(t) is multiplied by t
wc
cos (Ac=1)
wm
-wm
0
)
(w
M
Bw=wm
Is F(m(t) cos wct)= dt
e
t
w
t
m jwt
c





)
cos
)
(
(
dt
e
t
m
dt
e
t
m t
wc
w
j
t
wc
w
j












 )
(
)
(
)
(
2
1
)
(
2
1









 )
(
2
1
)
(
2
1
wc
w
M
wc
w
M

10. 10
Lecture 1-2
wc-wm wc wc+wm
-wc-wm -wc -wc+wm
F(m(t)coswct)
Bw=2wm
USB- upper side band Spectral components above the auxiliary signal (wc wc + wm)
LSB- lower sideband Spectral components below the auxiliary signal (wc- wm wc)

11. 11
Lecture 1-2
Elements of a Communication System
i/p message
i/p transducer Transmitter Communication
channel
Receiver O/P
transducer
Destination
i/p signal Transmitted
signal
Receive
signal
i/p signal i/p message
noise
Source
Source: information sources such as human voice, machine of message, TV, or data.
Transducer: The input transducer converts the message to (a signal) an electric
signal (voltage or current).
Similarly; the O/P transducer at the destination converts the O/P signal to the
appropriate message form.
Transmitter: The transmitter coupled i/p massage signal to the channel for effective
and efficient transformation. Several signal processing operation may be perform by
the transmitter such as amplification filtering and modulation.

12. 12
Lecture 1-2
Modulation: it's a process design to match the properties of the transmitted signal to the
channel.
Transmission channel: The channel provides the electrical connection between the
information source and the user (receiver). The channel may have different forms.
 Wires or cables: telephone lines, power lines,
 Space (wireless).
 Optical fiber.
 Water.
 Earth.
 Regard less of channel type; it degrades the transmitted signal in a number of
ways.
• Attenuation: reduction of signal strength with distance.
• Distortion: signal alteration due to imperfect channel response.
• Interference: contamination by extraneous signals of a form similar to the desired
of a form similar to the desired signal
• Noise: Random and unpredictable electric signal form natural causes both internal
and external to the system.

13. 13
Lecture 1-2
Receiver: The function of the receiver is to extract the desired signal from the
degraded version of the transmitted signal coming from the channel this is
performed through the process of demodulations.
Signal- to-Noise Ratio (SNR): The ratio of the signal power (S) to the noise power
(N).
𝑆𝑁𝑅 =
𝑆
𝑁
or 𝑆𝑁𝑅 𝑑𝐵 = 10log
𝑆
𝑁
Bandwidth (B): is the frequency range occupied by a modulated carrier signal
Types of Communication Systems:
Communication system can be divided in the three categories, based on the type of
modulation used and the nature of the information source:
 Analog communication systems.
 Digital communication systems.
 Hybrid communication systems.

14. 14
Lecture 1-2
Analog signal transmission:
For purpose of analysis analog signal transmission defines the transmission of:
arbitrary, finite energy low pass signals over a given channel.
In some cases, the signal will be a single sinusoidal tone or power signal.
f(t)= coswmt
Low- pass channel: baseband communication
Band pass channel: broad band comm Modulation
need
Note: The majority of practical channels have band pass characteristics and
modulation is necessary for translating the low pass signal spectrum to match the
band pass channel c/c.

15. 15
Lecture 1-2
Type of modulation: According to carrier wave:
1- Continuous Wave (CW) modulation: The carrier is a sinusoidal wave form at a
freq. much higher than any of the freq. components continue in the modulating signal
(the amplitude, frequency, phase or combination) is altered of the carrier in accordions
with the information to be transmitted.
 Amplitude modulation: AM, Double-Side Band (DSB), Single Side Band SSB, etc.
 Angle modulation: Frequency Modulation (FM), Phase Modulation (PM).
2- Pulse Modulation (PM):
a. Pulse amplitude mod.
b. Pulse duration (width) mod.
c. Pulse position mod.
Note: The carrier is a periodic trans. of pulses.

16. 16
Lecture 1-2
According to message:
1- Analog modulation.
2- Digital coded modulation. Pulse code modulation (PCM)
Note: Regardless type of modulation it must be a reversible process.
Reasons for modulation:
1- Modulation for ease of radiation:
Audio signal 100Hz  3000 Hz
For efficient radiation of the 100Hz component
Required antenna length
= 3*105 m = 300km, for direct radiation (impractical)
2- Modulation to reduce noise & interference.
3- Modulation for frequency assignment.
Digital signal
Analog signal
PCM
m
f
c 6
2
8
10
*
3
10
10
*
3




10


17. 17
Lecture 1-2
4- Modulation for multiplexing
- Long distance telephone.
- FM stereo
5- Modulation to overcome equipment limitation.

18. 18
Q & A
Thank You