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ELEC1010 Homework Guide

The document provides instructions for homework assignment 2 in ELEC1010. It includes 3 questions to be answered. Question 1 involves amplitude modulation of 3 baseband signals using different carrier frequencies. Question 2 analyzes the effect of noise on signal transmission using threshold detection. Question 3 completes a truth table and derives a mathematical formula for a given symbol diagram. The deadline to submit the assignment is October 16th at 10pm as a single PDF file through Canvas. No late submissions will be accepted.

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Yuen Hei Max Lee
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2K views4 pages

ELEC1010 Homework Guide

The document provides instructions for homework assignment 2 in ELEC1010. It includes 3 questions to be answered. Question 1 involves amplitude modulation of 3 baseband signals using different carrier frequencies. Question 2 analyzes the effect of noise on signal transmission using threshold detection. Question 3 completes a truth table and derives a mathematical formula for a given symbol diagram. The deadline to submit the assignment is October 16th at 10pm as a single PDF file through Canvas. No late submissions will be accepted.

Uploaded by

Yuen Hei Max Lee
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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ELEC1010 Homework 2 [20] Deadline: 10pm Oct 16 (Fri)

Please submit ONE soft copy (pdf only) of your assignment to Canvas (Assignments)
before the deadline. NO LATE Submission! (Zero mark!)

1. [10] We have three different baseband signals, S1, S2 and S3.


S1 = 2sin(3200𝜋t), S2 = 3sin(4800𝜋𝑡) and S3 = 4sin(5600𝜋𝑡)
We would like to send all three signals at the same time by using amplitude modulation.

a) [1] How can this be done? Please explain clearly.


b) [1.5] What is the bandwidth of each baseband signal?
c) [3] Assume that the carriers used by S1, S2 and S3 are sine waves with frequency 10,
20 and 30 kHz, respectively. All the carriers have amplitude = 1. Draw the frequency
spectrum of the transmitted signal. Clearly label all the frequencies.
d) [4.5] Now I want to select and recover the baseband signal S1. What will be the
processes involved? Clearly describe all the processes. Draw the frequency spectrum
for each of the processes involved. Clearly label all the frequencies.

Solution:

a) Use different carriers / carrier frequencies to send the signals (data/baseband


signals).

b) 𝑆1: 𝟏. 𝟔𝒌𝑯𝒛 𝑆2: 𝟐. 𝟒𝒌𝑯𝒛 𝑆3: 𝟐. 𝟖𝒌𝑯𝒛

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c)

8.4 11.6 17.6 22.4 27.2 32.8 kHz

d)

Process 1: Apply a bandpass filter, centered at 10 kHz, with bandwidth 3.2 kHz.

8.4 11.6 kHz

Process 2: Multiply the modulated signal by the carrier at frequency 10 kHz.

0 1.6 18.4 21.6 kHz

Process 3: Apply a lowpass filter with cutoff frequency of 1.6 kHz.

0 1.6 kHz

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2. [6] Suppose the input bit sequence: 0011011110110011 uses 1 volt to represent “bit 1”
and -1 volt to represent “bit 0”. The signal is transmitted at 1 bit per second. During the
transmission, additive noise is presented and added to the transmitted signal. The received
signal is as shown:
voltage

a) Assume that threshold detection is used at the receiver, what is the binary output of
the received signal if the threshold is set to be 0 volt?
b) How many bits of the signal in part a) are in error?
c) If the threshold is set to be -1 volt, what is the binary output of the received signal?
d) How many bits of the signal in part c) are in error?

Solution:

Original 0 0 1 1 0 1 1 1 1 0 1 1 0 0 1 1
Part a) 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 0
Part c) 0 1 0 1 1 1 0 1 1 1 1 0 1 1 0 0

b) 9 bits in error

d) 10 bits in error

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3. [4] Given the symbol diagram with inputs A, B & C and output Y:

i. Complete the truth table:


A B C Y
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 0
1 1 1 0

ii. Write the mathematical formula.

Solution:

𝑌 = 𝐴 ∙ 𝐵 ∙ 𝐶̅ ∙ +𝐴 ∙ 𝐵 ∙ 𝐶

(There are many possible answers!)

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