ETM2046 Analog & Digital Communications
Tutorial 1: Principles of Communications and Spectral Analysis
(Solutions)
Principles of Communications
1.
Information
Source Transmitter
Channel
Information
Sink Receiver
2. Frequency = c / wavelength = 3E8 m/s / 550E-9 m = 5.45E14Hz or 0.545 PHz
3. Wavelength = c / frequency = 3E8 m/s / 3E19 Hz = 10pm (1 pm = 1E-12 m)
4. Infrared.
5. Gamma Rays - Killing Cancer Cells
X-Rays - Medical Uses (X-Raying People)
Ultra Violet - Sterilising and sun tanning
Visible Light - Light we see, photography is a use.
Infra-Red Light - Night Vision, short distance communication and heating.
Microwaves - Cooking, communication.
Radio Waves - Include radio and TV broadcast, communications.
Audio Waves – Sound we hear, music, communications.
6.
Radio FM Radio wave Receiver
Radio AM Radio wave Receiver
GPS Microwave Receiver
Remote control Radio wave Receiver
Reverse sensor Microwave Receiver / Transmitter
Bluetooth Microwave Receiver / Transmitter
Head Light Visible wave Receiver
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ETM2046 Analog & Digital Communications
Spectral Analysis (Fourier Series)
2.
Trigonometric Fourier series of x(t):
Since is an even function signal,
3.
f(x)
x
-3 - 0 3
(a) For the trigonometric form,
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ETM2046 Analog & Digital Communications
Since this is an odd function,
(b) For exponential form,
To find
For
(c) DC value is
4. is periodic with period,
Let
Then,
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ETM2046 Analog & Digital Communications
Spectral Analysis (Fourier Transform)
5. (a)
From Frequency Shifting Property,
From Time Shifting Property,
(b)
From Scaling Property,
(c)
From Differentiation Property,
6.
g(t)
f(t) 1.5
-1 0 t 0 2 t
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ETM2046 Analog & Digital Communications
can be obtained in three steps:
I: Time expanding
II: Delaying by 2 seconds
III: Multiplying by 1.5
Step I:
Step II:
Step III:
7. The signal is given in the figure below
v (t )
1
2
0 t
1
2
Using Differentiation Property,
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ETM2046 Analog & Digital Communications
8.
- - +
Spectral Analysis (Signal Spectrum)
9. Given that
Hence,
10.
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ETM2046 Analog & Digital Communications
(a) Draw the graph of versus
(b) Draw the graph of versus
(c) Using the Differentiation Property,
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ETM2046 Analog & Digital Communications
