Full exam for Model Identification and Data Analysis in the Computer Engineering degree programme at Politecnico di Milano. The document covers: 1 MODEL IDENTIFICATION AND DATA ANALYSIS – Module 1, A.Y. 2023/2024 Prof. Simone Formentin – June 24th, 2023 Surname Name University ID Number Signature ................................ ............................... .....................……… ………… .. ....................………
Full exam for Model Identification and Data Analysis in the Computer Engineering degree programme at Politecnico di Milano. The document covers: 1 MODEL IDENTIFICATION AND DATA ANALYSIS – Module 1, A.Y. 2023/2024 Prof. Simone Formentin – June 24th, 2023 Surname Name University ID Number Signature ................................ ............................... .....................……… ………… .. ....................………
Import quality: text was extracted directly from the original document.
Representative passages recognised in different parts of the material. The full extracted text remains available to search, while this compact preview makes the page easier to read.
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…
First page of the document.
