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1 MODEL IDENTIFICATION AND DATA ANALYSIS – Module 1, A.Y. 2023/2024 Prof. Simone Formentin – June 24th, 2023 Surname Name University ID Number Signature ................................ ............................... .....................……… ………… .. ....................……… …………….. =========================================================================================================== - Write the solutions (including procedures and intermediate steps) in the blank areas (use the back of the page, if needed) - The number of pages is 4. Additional papers will not be considered. - Clarity, order and precision will be strongly considered for the final evaluation. =========================================================================================================== 1. [True or false] Say whether the following statements are true (T) or false (F), by writing T or F in the small box preceding each statement. Every correct answer is worth 1 point, while 0.5 points are deducted for every wrong answer. No point is credited or subtracted for any unanswered item. 1. Consider the process 𝑦𝑦(𝑡𝑡) = 𝑊𝑊(𝑧𝑧)𝑒𝑒(𝑡𝑡), where 𝑊𝑊(𝑧𝑧) = 1 + 2𝑧𝑧−1 + 5𝑧𝑧−2 + 3𝑧𝑧−3 and 𝑒𝑒(𝑡𝑡) is a white noise of mean 𝑚𝑚 and variance 1. The process covariance is denoted by 𝛾𝛾(𝜏𝜏). 𝐸𝐸[𝑦𝑦(𝑡𝑡)] = 3𝑚𝑚. 𝛾𝛾(0) = 4𝑚𝑚2. 𝛾𝛾(8) = 1. 𝛾𝛾(5) = 0.5. 2. Consider the system with input 𝑢𝑢(𝑡𝑡), output 𝑦𝑦(𝑡𝑡) and transfer function 𝑊𝑊(𝑧𝑧) = 𝑧𝑧+2 𝑧𝑧+0.5. If 𝑢𝑢(𝑡𝑡) is a white noise of mean 1 and variance 1, then 𝐸𝐸[𝑦𝑦(𝑡𝑡)] = 10. If 𝑢𝑢(𝑡𝑡) is a white noise of mean 1 and variance 1, 𝑦𝑦 �(𝑡𝑡|𝑡𝑡 −1) = 6. If 𝑢𝑢(𝑡𝑡) is a white noise of mean 1 and variance 1, the variance of 𝑦𝑦(𝑡𝑡) − 𝑦𝑦 �(𝑡𝑡|𝑡𝑡 −1) is 1. If 𝑢𝑢(𝑡𝑡) = 1 for any 𝑡𝑡, then, 𝑦𝑦(𝑡𝑡) = 4, ∀𝑡𝑡. 3. Consider the process 𝑦𝑦(𝑡𝑡) = 𝑒𝑒(𝑡𝑡) + 𝑒𝑒(𝑡𝑡 −1), where 𝑒𝑒(𝑡𝑡) is a white noise…