ELEC1010 Homework 2 [20] Deadline: 10pm Oct 12 (Fri)
Please submit ONE soft copy (pdf only) of your assignment to Canvas (Assignments)
before the deadline. NO LATE Submission! (Zero mark!)
1. [10] The baseband signals S1 and S2 are shown below:
S1 Amplitude S2
Amplitude
f/kHz 2 3 f/kHz
2 3
We need to transmit these two baseband signals S1 and S2 using amplitude modulation on
different frequency bands centered at 10 MHz, and 12 MHz, respectively.
1) Draw the resulting frequency spectrum containing the Two modulated signals in
ONE graph. Clearly label all the frequency.
2) What is the bandwidth of each modulated signal?
3) If we want to capture signal S2 (the carrier is 12 MHz) only, what kind of filter we
can apply? Clearly write down the characteristic of the filter. (Assume an ideal
filter is considered!)
4) After filtering in part 3), what will be all the additional processes in order to
recover the baseband signal S2? Clearly describe all the processes.
5) Draw the frequency spectrum/spectra for all the additional processes in part 4).
Clearly label all the frequency.
Solution:
1) The spectrum of the two modulated signals:
Carrier/center: 10 MHz 12 MHz
9.997 9.998 10.002 10.003 11.997 11.998 12.002 12.003 MHz
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2) The bandwidth for each modulated signal is 6 kHz.
3) We can apply a bandpass filter with low cutoff frequency at 11.997 MHz and
the high cutoff frequency at 12.003 MHz
4) Process 1: Mix the filtered signal with the same carrier (12 MHz) again.
Process 2: Apply a lowpass filter with the cutoff frequency at 3 kHz to recover
the original baseband signals.
5) Process 1:
24 MHz
0.002 0.003 23.997 23.998 24.002 24.003 MHz
Process 2:
Lowpass filter with cutoff frequency at 3 kHz
24 MHz
0.002 0.003 23.997 23.998 24.002 24.003 MHz
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2. [4] Suppose we want to transmit some binary sequence: 0111100011 using 1 volt to
represent bit 1 and -1 volt to represent bit 0. We will send 1 bit per second as the voltage
waveform in the time-domain using analog signal. During the transmission, the following
additive noise is presented as shown:
Noise
2
1.6
1.2
0.8
Voltage Level
0.4
-0.4
-0.8
-1.2
-1.6
-2
0 1 2 3 4 5 6 7 8 9 10
time(s)
1) Assume that the noise is additive, draw the waveform of the output signal (received
signal).
2) 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?
3) How many bits are in error?
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Solution:
1)
2) 1111000010
3) 0111100011 (original bit sequence)
3 bits are in error.
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3. [3] Given the following truth table with inputs A, B & C and output Y:
A B C Y
0 0 0 1
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 0
1) Write the mathematical formula.
Solution:
𝑌 𝐴 𝐵 𝐶 𝐴 𝐵 𝐶 𝐴 𝐵
Note: There are many other answers. As long as Y complies with the truth table, the
answer will be considered correct.
2) Draw the logic diagram using “logic gates”.
A
B
C Y
A
B
C
Or:
A Y
B
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4. [3] Answer the followings:
1) What is the biggest binary number (decimal value) you can write with 6 bits?
Solution: 63
2) What is the biggest binary number (decimal value and in terms of n) you can write
with n bits?
Solution: 2 1
3) If you want to represent the decimal numbers from 0 – 12, what is the minimum
number of bits you will need?
Solution: 4 bits
4) Convert the decimal number 438 to binary number.
Solution (short division or look-up table):
Look up table: 438=256+128+32+16+4+2
1 2 1 2 0 2 1 2 1 2 0 2 1 2 1 2 0 2
𝟏𝟏𝟎𝟏𝟏𝟎𝟏𝟏𝟎
Short division:
2 438 0
2 219 1
2 109 1
2 54 0
2 27 1
2 13 1
2 6 0
2 3 1
2 1
= 110110110
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