A24942 Any calculator Page 1 of 8 TURN OVER Calculators may be used in this examination but must not be used to store text. Calculators with the ability to store text should have their memories deleted prior to the start of the examination. Special Requirements: ATTACHMENT 1 (page 2 of exam paper) ATTACHMENT 2 (page 3 of exam paper) School of Engineering Department of Electronic, Electrical and Systems Engineering Level M 04 30057 Introductory Module for Computer Engineering January Examinations 2019 Time Allowed: 2 hours Answer TWO questions The allocation of marks within each question is stated in the right-hand margin. Any calculator A24942 Page 2 of 8 TURN OVER Table of Laplace Transforms () () , a constant 1 2 , a positive integer ! +1 , a constant 1 − (), a real constant 2+2 (), a real constant 2+2 −(), and real constant (+)2+2 −(), and real constant + (+)2+2 ′() () − (0) ′′() 2() − (0) − ′(0) ∫ () 0 () () (−1) () ( − ), a real constant − ( − ), a real constant − Any calculator A24942 Page 3 of 8 TURN OVER Table of z-Transforms [] () [], (unit pulse sequence) 1 [] = 1, (unit step sequence) −1 , a constant − (−1)2 −1, a constant (−)2 −, a constant −− [ − 0] 1 0 () [ + 0] 0() − ∑ []0− 0−1 =0 (), , constants (−cos()) 2−2 cos()+1 (), , constants sin() 2−2 cos()+1 [], a constant (−1) [], a positive integer (− ) () [] ∗ ℎ[], (convolution) ()() Any calculator A24942 Page 4 of 8 TURN OVER 1. (a) Find the Laplace transform of the following functions: (i) () = −(2) [3] (ii) () = { 2 −3 + 3 < 2 2 ≤ < 3 3 ≤ [4] (b) Find the inverse Laplace transform of the following function: F(s) = s2 − 4 s3+6s2 + 9s [4] (c) Solve the differential equation y′′ + 4y′ + 8y = e2t − 2δ(t − 2π),y(0) = 2, y′(0) = 0 where y′ and y′′ denotes the first and second derivative, respectively. [9] 2. (a) Use the z-transform to calculate the convolution between 0.8( − 1) and ( + 1), where () denotes the unit step sequence. [7] (b) Consider the system in Figure 1, Figure 1 where is a constant and H(z) is characterised by the difference equation y[k + 2] − 2y[k + 1] + y[k] = 0.25w[k + 1] + 0.25w[k] with the initial conditions: [0] = 0, [1] = 0, [0] = 0. Determine the transfer function from [] to [], i.e., ()/(). [9] (c) Consider a linear constant-coefficient discrete-time system. Give the definition of a stability of such a system in terms of impulse response. Explain what needs to be fulfilled for such a system characterised by the system transfer function () to be stable. [4] Any calculator A24942 Page 5 of 8 TURN OVER 3. (a) Let = [ 4 3 ] and = [ −6 3 ]. Show that and are linearly independent. [3] (b) Let be the matrix = [ 9 7 7 −1 ]. (i) Calculate the eigenvectors and eigenvalues of . [6] (ii) Write down two matrices and such that = and is diagonal. [2] (c) Figure 2 is taken from International Standard ISO9241 Part 210 (2010) – Human-Centred Design for Interactive Systems – and illustrates four human-centred design activities that should take place during the design of interactive systems, once the human centred design process has been planned and before the design team can conclude that the designed solution meets user requirements. Two of the four activity descriptions (boxes labelled ‘A’ and ‘B’) have been omitted. Figure 2 (i) What design activity should be included in Box A? [1] (ii) What design activity should be included in Box B? [1] Any calculator A24942 Page 6 of 8 END OF PAPER (iii) For the activity described in Box A, give two examples of the four specific tasks listed and summarised in the ISO standard that should be undertaken by designers to help reveal the important requirements and constraints of current and future interactive systems. [2] (iv) When evaluating new or existing interactive technology designs against early requirements, usability is an important aspect that designers need to consider and measure. What are Dey Alexandra’s “FIVE Es” of usability, to be considered when designing or evaluating an interactive system? [2] (v) With reference to the ISO9241 activity entitled “Evaluate the Designs Against Requirements”, experimental design, execution and analysis are important processes. Consider the following: Two designs of computer workstation were tested to see which resulted in fewer complaints of back pain. 25 office workers worked at Workstation A and 23 office workers worked at Workstation B. After working for 4 hours, each participant rated their level of back pain on a 10-point rating scale. For this experiment, choose one of the options from the list below that accurately describes what the dependent variable(s) and the independent variable(s)? a. The dependent variable was pain rating, the independent variable was the workstation design b. The dependent variable was pain rating, the independent variables were the office workers c. The dependent variables were Workstation A and Workstation B, the independent variable was time d. The dependent variable was time, the independent variable was pain e. The dependent variable was workstation design, the independent variable was pain rating [3] Any calculator A24942 Page 7 of 8 THIS PAGE IS INTENTIONALLY BLANK A24942 Introductory Module for Computer Engineering Page 8 of 8 Important Reminders Coats/outwear should be placed in the designated area. Unauthorised materials (e.g. notes or Tippex) must be placed in the designated area. Check that you do not have any unauthorised materials with you (e.g. in your pockets, pencil case). Mobile phones and smart watches must be switched off and placed in the designated area or under your desk. They must not be left on your person or in your pockets. You are not permitted to use a mobile phone as a clock. If you have difficulty seeing a clock, please alert an Invigilator. You are not permitted to have writing on your hand, arm or other body part. Check that you do not have writing on your hand, arm or other body part – if you do, you must inform an Invigilator immediately Alert an Invigilator immediately if you find any unauthorised item upon you during the examination. Any students found with non-permitted items upon their person during the examination, or who fail to comply with Examination rules may be subject to Student Conduct procedures. Do not complete the attendance slip, fill in the front of the answer book or turn over the question paper until you are told to do so
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