4405W19Amidterm_questions_v2

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Carleton University *

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4405

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Jan 9, 2024

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1 SYSC 4405 Winter 2019 Midterm Version A Permitted Aids: Calculator and Provided Reference pages) Q1(20) Q2(20) Q3(20) Q4(20) Q5(20) Q6(20) Total(/120) Last Name: ________________________________ First Name: ______________________________ Student Number: __________________________ This exam is 75 minutes (1 hour, 15 minutes) long. Attempt all questions. A separate reference document has been provided that will not be handed out, answers on the reference pages will not be graded. Use the backs of the pages for rough work. Do not ask a question unless you believe that you have found a typo. Be sure that you have clearly written your name and student number above. The answers to all questions should be entered on the exam paper. Round answers to three decimal places. Answer the questions on the exam paper provided. Use the backs of pages! There are two extra pages provided if required. Clearly indicate where answers for question are if not on the front/back of the actual page for the question. All rights reserved : No part of this document may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without prior written permission from the instructor.
2 Question 1 (20 marks) For each of the following Ordinary Difference Equations (ODE), justify and state if the system presented is: A) Recursive or non-Recursive? B) FIR or IIR? C) Causal or non-Causal? D) Linear or non-Linear? E) Time invariant or Time variant? F) LTI? 1.1: y[n] = x[n] + x[n-1] + x[n+2] 1.2: y[n] = x[n] + x[n+1] + x[n-2] 1.3: y[n] = x[n] + x[n-1] + x[2] 1.4: y[n] = x[n] + x[n+1] + x[n-2] y[n-6] 1.5: y[n] = x[n] + 8 1.6: y[n] = x[n] + x[1-n] + x[n-2] y[n-1]
3 Question 2 (20 marks) For each of the following ODEs: A) Provide a block diagram of the system in either Direct Form 1 or 2. B) Calculate the impulse response h[n] for the system. If the system is FIR all terms of h[n] are required. If the system is IIR, only the first 6 terms are required. 2.1: y[n] = 6x[n] x[n-1] 2 x[n-2] 2.2: y[n] 1.3y[n-1] + 0.42y[n-2] = 8 x[n]
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4 Question 3 (20 marks) Given: {x[n]} 0 4 = {1, 1, 1, 2, 2} {h[n] } 0 4 = {1, 2, 3, 1, 2} Show each of the following sequences: 3.1: x[-n] 3.2: h[n-3] 3.3: x[n] * h[n] Note * means discrete convolution
5 Question 4 (20 marks) For each of the following signals, provide the following: A) Phasor plot for the sampled signal showing the actual phasors for the signal and the alias phasors if occurring. B) State if the signal is being aliased and if the aliasing is folding or non-folding. Provide the frequency of the aliased signal in rad/sample. C) Calculate the output for the above signals if passed through the following system: ?[𝑛] = ?[𝑛] − 0.5?[𝑛 − 1] Hint: You will need to find H(e jw ) to solve part C 4.1: y(t) = 4 cos( 4000(2 )t + /4) sampled at 10000Hz 4.2: y(t) = 8 cos( 5000(2 )t - /3) sampled at 8000Hz 4.3: y(t) = -4 cos( 11000(2 )t) sampled at 8000Hz
6 Question 5 (20 marks) For the following ODEs, provide: A) The system response function H(z) B) The plot of the poles and zeros of H(z) on the z-plane. Ensure to indicate if there are multiple poles or zeros at a location. C) Through calculation of the inverse z-transform find h[n] and the ROC for the discrete time signal? 5.1: y[n] = 4x[n] x[n-1] 5 x[n-2] 5.2: y[n] 1.1y[n-1] + 0.30y[n-2] = 6 x[n]
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7 Question 6 (20 marks) For each of the pole-zero plots below (You can assume the system gain factor is 1 and causal.): A) Is the system a stable, marginally stable or unstable system (assume causal)? B) Describe the expected frequency response H(e jw ) if it is within the ROC. An exact calculation is not required of H(e jw ). A sketch of the response is acceptable. 6.1:
8 6.2: 6.3:
9 6.4: Note Magnitude of all poles in this question is 1. 6.5: Note Magnitude of all poles in this question is 1.
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10 Extra page 1 clearly indicate the question for this material
11 Extra page 2 clearly indicate the question for this material