Final Exam 2004 Spring

Final Exam 2004 Spring - EE 448 Final Exam May 3, 2004...

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EE 448 Final Exam May 3, 2004 Name: ID (last 4 digits): Score: Instructions: This exam is closed-book and closed-notes with the exception of an 8 . 5 ±± × 11 ±± crib sheet. You have 2 hours to complete the exam. Write your name and ID number on all pages of your answers. Show all work for full credit. Mark your final answers. Good luck! 1. (40 points) Mixed Problems: (a) (5 points) Consider an analog signal g a ( t ) with highest frequency m . Let g [ n ]= g a ( t ) | t = nT Write down a frequency-domain expression that relates the DTFT G ( e ) of g [ n ] to the CTFT G a ( j Ω) of g a ( t ) . How should you choose T to avoid aliasing? (b) (5 points) Write down the bilinear transform and an expression that relates analog frequency to digital fre- quency ω . (c) (3 points each) Determine whether the following statements are true or false. Briefly justify your answer. i. An LTI system is BIBO stable if and only if its ROC is outside the unit circle. ii. If f ( n ) is an eigenfunction to an LTI system, the output of the system subject to the input f ( n ) can be expressed as cf ( n ) , where c is a constant. iii. It is possible to design zero-phase causal digital filters.
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Final Exam 2004 Spring - EE 448 Final Exam May 3, 2004...

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