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MODEL IDENTIFICATION AND DATA ANALYSIS – Module 1, A.Y. 2023/2024 Prof. Luigi Piroddi, Prof. Simone Formentin – July 26th, 2024 SURNAME NAME UNIV. ID NUMBER SIGNATURE The total number of pages is 4. Answer in the allotted space. Extra pages will not be considered. Clarity, order and precision will be strongly considered for the final evaluation. EXERCISE 1: Multiple choice ques tions (values are rounded to the 4 th decimal; check with an × the correct answer; wrong answers are penalized with a negative score, whereas missing answers yield 0 points). Let S1: z z+1/2 2(t) 1(t) + + +  y(t) S2: y(t) = 1 15 [ y(t1) + 2 y(t2) + 5 e(t1) + 17 e(t2) + 6 e(t3)] , e(t) ~ WN(0,1) With reference to S1 and assuming 1(ꞏ) ~ WN(0, 1) and 2(t) = 1(t), t, compute the variance of process y(t).  Var[y(t)] = ?  a) 2.3333  b) 0.6667  c) 1.7500  d) 0.2500 With reference to S1 and assuming 1(ꞏ) ~ WN(0, 1) and 2(t) = 1(t), t, determine the value of the power spectral density () for  = /3.   (/3) = ?  a) 1.0000  b) 0.4286  c) 2.3333  d) 1.2500 With reference to S1 and assuming 1(ꞏ) ~ WN(0, 1), 2(ꞏ) ~ WN(0, 1) and that 1(t) and 2(t) are uncorrelated processes, compute the variance of process y(t).  Var[y(t)] = ?  a) 1.2500  b) 0.7500  c) 1.6667  d) 0.3333 With reference to S1 and assuming 1(ꞏ) ~ WN(0, 1), 2(ꞏ) ~ WN(0, 1) and that 1(t) and 2(t) are uncorrelated processes, determine the parameters , , and 2 of the canonical representation of the process y(t) = y(t1) + (t) + (t1), (ꞏ) ~ WN(0, 2).  Parameter  = ?  a) 0.5000  b) 0.5000  c) 1.0000  d) 0.3333  Parameter  = ?  a) 0.2500  b) 0.5000  c) 0.5000  d) 0.0000  Parameter 2 = ?  a) 1.0000  b) 1.2500  c) 0.2500  d) 0.7500 With reference to S2,…