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Midterm Exam 2004 Spring

# Midterm Exam 2004 Spring - EE 448 Midterm Exam March 8 2004...

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EE 448 Midterm Exam March 8, 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) (4 points) Write down the expression of the N -point DFT X [ k ] of a sequence x [ n ] , and the expression of the corresponding IDFT. (b) (4 points) Write down the expression of the z -transform X ( z ) of sequence x [ n ] . What does ROC stand for? (c) (6 points; 2 points each) Consider an N -point sequence x 1 [ n ] , 0 n N 1 , and an M -point sequence x 2 [ n ] , 0 n M 1 : i. Let y L [ n ] denote the linear convolution of x 1 [ n ] and x 2 [ n ] . Write down an analytical expression that relates y L [ n ] to x 1 [ n ] and x 2 [ n ] . What is the length of y L [ n ] ? ii. Let y C [ n ] denote an L -point circular convolution of x 1 [ n ] and x 2 [ n ] . Write down an analytical expression that relates y C [ n ] to x 1 [ n ] and x 2 [ n

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Midterm Exam 2004 Spring - EE 448 Midterm Exam March 8 2004...

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