final - 6.003 (Spring 2010) May 20, 2010 Final Examination...

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1 2 3 4 5 6 7 Total / 10 / 12 / 18 / 15 / 15 / 15 / 15 / 100 6.003 (Spring 2010) Final Examination May 20, 2010 Name: Kerberos Username: Please circle your section number: Section Instructor Time 1 Peter Hagelstein 10 am 2 Peter Hagelstein 11 am 3 Rahul Sarpeshkar 1 pm 4 Rahul Sarpeshkar 2 pm Grades will be determined by the correctness of your answers (explanations are not required). Partial credit will be given for ANSWERS that demonstrate some but not all of the important conceptual issues. You have three hours. Please put your initials on all subsequent sheets. Enter your answers in the boxes. This quiz is closed book, but you may use four 8 . 5 × 11 sheets of paper (eight sides total). No calculators, computers, cell phones, music players, or other aids.
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x [ n ] α 0 α 1 α 2 α 3 α 4 0 3 6 9 12 3 6 2 Final Examination / 6.003: Signals and Systems (Spring 2010) 1. Z Transform [10 points] Find the Z transform of x [ n ] defined as x [ n ] = α å n/ 3 æ u [ n ] where α represents a positive real number, u [ n ] represents the unit-step function, and å n/ 3 æ represents the largest integer that is n/ 3. The signal x [ n ] is plotted below. Enter a closed-form expression for X ( z ) in the box below. X
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final - 6.003 (Spring 2010) May 20, 2010 Final Examination...

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