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Unformatted text preview: EE 448 Final Exam May 9, 2005 Name: ID (last 4 digits): Score: Instructions: This exam is closedbook and closednotes with the exception of an 8 . 5 00 × 11 00 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. (25 points) Mixed Problems: (a) (5 points) Consider an analog signal g a ( t ) with highest frequency Ω m . Let g [ n ] = g a ( t )  t = nT Write down a frequencydomain expression that relates the DTFT G ( e jω ) 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 Ω to digital fre quency ω . (c) (5 points) Let H ( z ) be the transfer function of a stable causal system. Which of the following statements is true? Justify your answer. i. All zeros of H ( z ) must be inside the unit circle. ii. All poles of H ( z ) must be inside the unit circle. iii. Both zeros and poles of H ( z ) must be inside the unit circle....
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 Spring '08
 
 Digital Signal Processing, Lowpass filter, Butterworth IIR

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