This is a practice environment. Please go to https://eassessment.monash.edu for your exams. – 1 year old
Examination Period
EXAM CODES: ECE2111 Signals and systems
TITLE OF PAPER: mock exam EXAM DURATION:
During an exam, you must not have in your possession any item/material that has not been authorised for your exam. This includes books, notes, paper, electronic device/s, mobile phone, smart watch/device, calculator, pencil case, or writing on any part of your body. Any authorised items are listed below. Items/materials on your desk, chair, in your clothing or otherwise on your person will be deemed to be in your possession.
You must not retain, copy, memorise or note down any exam content for personal use or to share with any other person by any means following your exam.
You must comply with any instructions given to you by an exam supervisor.
As a student, and under Monash University’s Student Academic Integrity procedure, you must undertake your in-semester tasks, and end-of-semester tasks, including exams, with honesty and integrity. In exams, you must not allow anyone else to do work for you and you must not do any work for others. You must not contact, or attempt to contact, another person in an attempt to gain unfair advantage during your exam session. Assessors may take reasonable steps to check that your work displays the expected standards of academic integrity.
Failure to comply with the above instructions, or attempting to cheat or cheating in an exam may constitute a breach of instructions under regulation 23 of the Monash University (Academic Board) Regulations or may constitute an act of academic misconduct under Part 7 of the Monash University (Council) Regulations.
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Instructions
Page 1 of 10
Once your exam finishes, you will be given time to scan a QR code and upload your answers using
your smartphone and laptop.
Here’s how to do it.
This is a practice assessment. Please use it to familiarise yourself with the eAssessment platform.
It is similar in style and length to the final assessment for ECE2111. All of the question types that appear on the final assessment also appear in this practice assessment.
Please note that the questions have not been checked as carefully for clarity, difficulty, etc, as questions on a final assessment would be.
Solutions will be provided on the Moodle page for ECE2111.
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This is a practice environment. Please go to https://eassessment.monash.edu for your exams. – 1 year old
Instructions
Information
This is a practice assessment. Please use it to familiarise yourself with the eAssessment platform.
It is similar in style and length to the final assessment for ECE2111. All of the question types that appear on the final assessment also appear in this practice assessment.
Please note that the questions have not been checked as carefully for clarity, difficulty, etc, as questions on a final assessment would be.
Solutions will be provided on the Moodle page for ECE2111.
Page 3 of 10
Question 1
A discrete-time LTI system with input x and output y is defined by the difference equation
y[n] = x[n]−0.5x[n−1]−0.5x[n−2]+x[n−3] for all n. Marks
Write down an expression for the impulse response of the system in terms of the discrete-time unit impulse signal.
(When writing in the text box, please use delta[n] rather thanδ[n] to denote the value of the unit impulse signal at time n.)
Question 2
Drag and drop the system labels onto the diagram so that the outputy and input x are related by the difference equation
y[n] = x[n]−0.5x[n−1]−0.5x[n−2]+x[n−3] for all n.
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Question 3
Let x(t) = u(t + 1) − u(t − 1) be a pulse of length two. The signalxm(t) = cos(aπt)x(t) is shown below for −1 ≤ t ≤ 2.
[2 marks] What is the value of a? Briefly explain your answer. 2 Marks
[2 marks] Write down an expression for the continuous-time Fourier transformX of x. 2
(If necessary, please use w instead ofω and use pi instead of π when writing in the text box.)
[3 marks] Find an expression for the Fourier transformXm of xm, in terms of X. Briefly explain how 3
you obtained your answer.
(If necessary, please use w instead ofω and pi instead of π when writing in the text box.)
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Question 4
A demodulator system involves multiplication by a cosine at frequencyωc and then low-pass filtering the result using an ideal low-pass filter. The filter has frequency response
H(ω) = A(u(ω + B) − u(ω − B)) where u is the unit step and A and B are positive constants. A schematic of this system is shown in the diagram below.
In the diagram, the multiplication system labelled × takes in signals x1 and x2 and outputs the signal defined by y(t) = x1(t)x2(t) for all t.
[3 marks] Is the demodulator system a linear system? Explain your answer. 3 Marks
[4 marks] The input x to the demodulator is periodic with fundamental frequencyωc , and has Fourier 4
series coefficients that satisfy X1 = X−1 = 0.5. The corresponding output is y(t) = 2 for all t. Write down a possible value for the passband gain A and the cutoff frequency B (in rad/sec) of the low-pass filter. Justify your answers.
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Question 5
A causal, BIBO stable, continuous-time LTI system is described by a linear, constant coefficient differential equation of the form
d2 y + a dy + by(t) = x(t) dt2 dt
where a and b, are real numbers. Let p and q be the poles of the transfer function of the system.
[3 marks] Choose values of p and q that are consistent with the information given in the question, and briefly 3
explain why your choices are valid.
(Note that answers may vary from student to student.)
[3 marks] For the choice ofp and q you made in part (a), find the corresponding values ofa and b in the 3
differential equation defining the system. Show the key steps of your working.
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Question 6
You have decided to test the limits of your speakers by playing back a very loud tone at 440Hz, allowing the sound to propagate through the air, and then recording the output of the speaker with a microphone (as shown below):
Propagation of sound through the air is modelled by the series interconnection of a gain of 0.5 with a delay of 0.1 seconds. The microphone is assumed to be perfect, so that its output w equals its input y.
You found that the signal measured by the microphone was approximately given by
y(t) = 0.5 cos(880π(t − 0.1)) + 0.1 cos(660π(t − 0.1)) + 0.1 cos(1100π(t − 0.1)).
[2 marks] Find the fundamental frequency ofy. Explain how you obtained your answer. 2 Marks
[4 marks] Write down an expression for the impulse response and the frequency response of the sound 4
propagation system (which consists of the series interconnection of a gain of 0.5 and a delay of 0.1 seconds).
(When writing in the text box, if necessary please use w instead ofω and delta instead of δ.)
[2 marks] Find an expression forz(t), the output of the speaker at timet. 2 Marks
[3 marks] Is the speaker system linear and time-invariant? Explain your answer. 3 Marks
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Question 7
[2+4+2] A causal continuous-time linear time-invariant system has input x(t) = e−atu(t) and output y. (a) [2 marks] If the Laplace transform of the input is
(b) [4 marks] If the Laplace transform of the output is
find the value of a and the region of convergence RoC(x).
1 X(s) = s + 2
1 Y(s)= s(s−1)
with region of convergence RoC(y) = {s ∈ C : Re(s) > 1}, find an expression for y(t), the output at time t.
(c) [2 marks] Find the transfer function H of the system.
Please answer question on your blank piece of paper.
After your exam finishes, you’ll have extra time to access your phone to scan a QR code and upload your answer.
Clearly label each page with Student ID and this question number (and sub part if applicable) (for example, ‘Question 7a’)
Do not write your Name on it No. of answer sheets: 2
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Question 9
Question 8
[4+3+2 marks] A continuous-time signal x with bandwidth 20π/3 rad/sec is sampled with sampling period Ts = 0.1 seconds to obtain a discrete-time signal
xs[n] = x(nTs) for all n.
The discrete-time Fourier transform Xs of the sampled signal is shown below:
(a) [4 marks] Let X be the continuous-time Fourier transform of the input signal x. Sketch X(ω) vs ω for −10π ≤ ω ≤ 10π. Label all features of your plot.
(b) [3 marks] Find the energy of the discrete-time signal xs, i.e., compute
E= ∑ |xs[n]|2.
(c) [2 marks] Given that the bandwidth of x is 20π/3 rad/sec, what is the longest sampling period we could use so that no aliasing occurs when sampling x?
Please answer question on your blank piece of paper.
After your exam finishes, you’ll have extra time to access your phone to scan a QR code and upload your answer.
Clearly label each page with Student ID and this question number (and sub part if applicable) (for example, ‘Question 7a’)
Do not write your Name on it No. of answer sheets: 2
[4+2 marks] The input of a discrete-time LTI system isx[n] = (0.5)nu[n] and the output is y[n] = (0.25)nu[n].
Please answer question on your blank piece of paper.
After your exam finishes, you’ll have extra time to access your phone to scan a QR code and upload your answer.
Clearly label each page with Student ID and this question number (and sub part if applicable) (for example, ‘Question 7a’)
Do not write your Name on it No. of answer sheets: 1
(a) [4 marks] Find the transfer function H of the system. Show your working/explain your answer.
(b) [2 marks] Is the system an infinite impulse response (IIR) system or a finite impulse response (FIR)
system? Explain your answer.
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