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ELEC8844 Semester Project
Version 2.0
Semester 1, 2022
Note: The instructions (indicated in Lecture 1) are to write a report of 2,000 words which is
approximately four A4 pages, typed in 12‐point font, using single line spacing or eight A4 pages,
using double line spacing. You are required to turn‐in your code, numerical results, graphical
results, and answers to questions. Your main report, excluding appendices, should include approach,
results (numerical and graphical), conclusion, answers to the questions including detailed
explanations, and references in standard IEEE format. In your approach, you may include block
diagrams and flow diagrams for your software. Any software taken from an external source (from
the engineering literature, past reports, past theses, or the internet) must be completely referenced.
The page limit does not include MATLAB code, or Simulink files. These items must be included as
appendices with clearly indicated titles and labels. The paper limit is an upper bound on the number
of pages in your main report. The numbers of pages in the appendices do not have limits.
The semester project must be turned‐in in the form of an Adobe Acrobat file. You must include your
name, student number, and date at the top of every page. This report must be your own work
and is not a group project. Marks will be deducted for cases in which reports from different
students are identical or have significant similarity. If you have not originated the computer
code or any part of the computer code, a reference must be given as a citation of the source
of the computer code. This includes code that has been published on the internet, books,
journals, reports, thesis documents or has been originated by other students.
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| I. | Sampling of Modulated Signals | ||||
| A message signal, , is defined as, m t |
|||||
| 3 2 3 1 1 cos 2 1. 10 cos 2 2.5 10 cos 2 3 10 m t x t x t x t |
|||||
| is time sampled to create a signal vector, 1 , for 1,2,…, s m t m k m k T k N |
|||||
| 2 |
3 |
||||
| The sampling frequency is |
1 | ||||
| | | | | | |
AssignmentTutorOnline
=25.6 kHz
1024
1
1. Mark What is the average power in ?
2
2. 1 Mark For =25.6 kHz and 1024, what is the average power in ?
How does this power compar
s
s
s
s
f
T
f N
m t
f N m n
| |
|
e to the average power in ?
1
3. Mark Generate a plot of ( ) as a function of t .
2
4. 1 Mark Generate a plot of the power spectral density of
in dBW/Hz as a func
m t
m t
m n
3
2 3 10
1
1
tion of frequency in Hertz.
5. 1 Mark Create the bandpass signal Re
and plot the power spectral density of .
Explain the result
j nTs
BP
BP
m n m n e
m n
3
1
2 11 10
2
2
ing power spectral density of .
6. 1 Mark Create the bandpass signal Re
and plot the power spectral density of
Explain t
s
BP
j nT
BP
BP
m n
m n m n e
m n
he resulting power spectral density of m n BP2 .
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| II. | Single Sideband Modulation | ||||
| A message signal, , is defined as, m t |
|||||
| 3 2 3 1 1 cos 2 1. 10 cos 2 2.5. 10 cos 2 3. 10 m t x t x t x t |
|||||
| is time sampled to create a signal vector, , for 0,1,2,…, 1 s m t m k m kT k N |
|||||
| 2 |
3 |
||||
| The sampling freque ncy is |
1 | ||||
| | | | | | |
=176.4 kHz
176,400
Use either MATLAB or Simulink to create a discrete‐time, complex envelope, upper‐sideband,
single sideband (USB‐SSB) signal using the phasing method.
This sign
s
s
s
USB
f
T
f N
m n
al has power for positive frequencies and no power for negative frequencies.
Note that the complex‐envelope is a complex, lowpass signal with 0.
1. 1 Mark Generate a plot of as a function of
c
USB
f
m n t
1
2. [1 Mark] Generate a plot of the power spectral density of and compute
the total power in the signal.
Comment on whether there is power only
s
USB
n T
m n
2
for positive frequency components of .
3. [1 Mark] Upconvert the complex envelope USB signal to a bandpass signal, [ ], where,
1
,
2
c s
USB
USB
j f nT
USB USB
m n
s n
s n real m n e 0,1,2,…, 1
=176.4 kH
1
50 kHz
and generate a plot of the power spectral density of the
s s
s
c
n N
f z
T
f
f
s
| n power spectral density of . m n |
n |
.
4. [1 Mark] Use Matlab or Simulink to demodulate and to output the demodulated signal
m . ˆ ˆ Compare the power spectral density of the demodulated signal m to the
USB
USB
n
s n
5. [1 Mark] Generate an audio signal file for 1,764,000 and =176.4 kH .
Write a MATLAB or Simulink program to USB‐SSB
s
N f z
modulate the audio signal to a carrier frequency of 50 KHz using a sampling
frequency of 176.4 KHz. Create an USB‐DSB demodulator and then down‐sample
by a factor of 4 the demodulated signal to a sampling frequency of 44.1 kHz.
Using the computer speaker, listen to the audio signal that was input
to the modulator.
Also, using the computer speaker, listen to the demodulated audio signal.
Describe how the original audio signal and demodulated audio signal compare.
Plot the signal at the modulator input as a function of time and plot the signal
at the demodulator output as a function of time.
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III. FM Transmission over an Additive Noise Channel
A message signal is cos 2 is sampled to create the
signal vector, where 1 kHz and
1 , for 1,2,…,
1
The sampling frequency is
=500 kHz
5,000,000
The discrete‐time complex enve
m
m
s
s
s
s
m t f t
f
m k m k T k N
f
T
f N
| 1 |
|
|
| The modulated FM real bandpass signal is, Re e , where is the carrier frequency. c s j f nT FM c s n e n f |
||
| The RF b | FM BP M FM B f f B |
M f f |
2
lope of the modulated FM signal is,
exp 2 , where 75 kHz and 1 volt.
n
s
k
e n A j f T m k f A
andwidth of the modulated FM signal is , 2 .
Therefore, the lowpass bandwidth of the complex envelope is
Additive channel noise is generated with the randn( ) function in MATLAB.
The v
2 2 2
ariance of the channel noise is
2
The channel noise sequence is,
2
where, and are two indepedent, Gaussian, zero mean random
sequences with standard
FM
N
s
FM
N
s
r i
r i
Bf
Bf
n n j n
n n
| |
|
2 2
2
2
deviation equal to 1.
This channel noise is then filtered with a low pass filter of bandwidth
with unity bandpass gain.
The signal to noise ratio in the FM signal bandwidth is,
SNR= =
2
FM
N FM
s
B
A A
Bf
| 2 |
M |
s |
2
2
2
2
Therefore,
2
s
FM
A
f f
f
A f
SNR B
| |
|
|
|
10
10
The signal to noise ration expressed in dB is 10log
and therefore, 10 .
dB
dB
SNR
SNR SNR
SNR
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As shown in Figure III‐1, the FM modulated complex envelope signal
plus channel noise is summed, lowpass filtered, and input
to the FM demodulator.
is put through a lowpass filter with bandwi
r n s n n
r n
dth
which results in the output .
is FM demodulated to obtain ˆ .
1. [2 Marks] Using MATLAB or Simulink Implement a FM modulator
and FM demodulator to demodula
FM
LP
LP
B
r n
r n m n
te .
2. [3 Marks] Plot the power spectral density of ˆ for
SNR 20 dB, 30 dB, 40 dB, and 120 dB and comment on the
effect of the channel n
LP
dB
r n
m n
oise on the demodulated signal.
Figure III‐1. Complex Envelope Channel and FM Demodulator.
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