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1 MODEL IDENTIFICATION AND DATA ANALYSIS – Module 1, A.Y. 2023/2024 Prof. Simone Formentin – April 22nd, 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 an all-pass filter with input 𝑢𝑢(𝑡𝑡) and output 𝑦𝑦(𝑡𝑡). I nput and output are proportional at each time step, namely 𝑦𝑦(𝑡𝑡) = 𝛼𝛼 𝑢𝑢(𝑡𝑡), ∀𝑡𝑡, where 𝛼𝛼 is a suitable constant. If 𝑢𝑢(𝑡𝑡) is a stationary process, the spectrum of the output is proportional to the spectrum of the input. If 𝑢𝑢(𝑡𝑡) is constant, 𝑦𝑦(𝑡𝑡) is constant. If 𝑢𝑢(𝑡𝑡) is sinusoidal, 𝑦𝑦(𝑡𝑡) is sinusoidal. 2. Consider the system with input 𝑢𝑢(𝑡𝑡), output 𝑦𝑦(𝑡𝑡) and transfer function 𝑊𝑊(𝑧𝑧) = 𝑧𝑧+1 𝑧𝑧+0.5. If 𝑢𝑢(𝑡𝑡) is a white noise, the spectrum of 𝑦𝑦(𝑡𝑡) is minimal at 𝜔𝜔= 0. If 𝑢𝑢(𝑡𝑡) is a white noise, the spectrum of 𝑦𝑦(𝑡𝑡) is null at 𝜔𝜔= π. If 𝑢𝑢(𝑡𝑡) is constant, namely 𝑢𝑢(𝑡𝑡) = 𝑐𝑐, ∀𝑡𝑡, with 𝑐𝑐 ≠0, then for any 𝑐𝑐, 𝑦𝑦(𝑡𝑡) is null,…