final_F07

final_F07 - 6.003 (Fall 2007) 17 December 2007 Final exam...

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6.003 (Fall 2007) Final exam 17 December 2007 Name: Please circle your section number: Section Instructor Time 1 Jeffrey Lang 10 2 Jeffrey Lang 11 3 Karen Livescu 11 4 Sanjoy Mahajan 12 5 Antonio Torralba 1 6 Qing Hu 2 Partial credit will be given, according to the conceptual features that a proposed answer shares with the correct answer. Explanations are not required and do not affect your grade. You have three hours. Have fun! Please put your initials on all subsequent sheets. Enter your answers in the boxes. This quiz is closed book, but you may use three 8 . 5 × 11 sheets of paper (six sides). No calculators, computers, cell phones, music players, or other aids. 1. ) ) ) / 15 ( ) ) / 100 ( ) /15 ( ) 5. /05 ( ) 9. /10 ( / 30 ( ) 2. /05 ( ) 6. /10 ( ) 10. /10 ( / 25 ( ) 3. /05 ( ) 7. /15 ( ) 11. /10 ( / 30 ( ) 4. /10 ( ) 8. /05 ( ) / 35 ( ) / 35 ( ) / 30 (
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3 Final exam / 6.003: Signals and Systems (Fall 2007) 1. Matching time and frequency representations [15 points] For each time signal, choose the magnitude of its Fourier transform from the four choices below. The time signals are zero outside the plotted region. Each time and frequency figure has its own scale, with the origin where the axes intersect. If you are unsure of the correct answer, you can also select a second answer, in which case you will receive the average of the scores for the two answers. t t t 1 1 A B C D A B C D A B C D Here are the choices for the Fourier transform magnitude: ω ω A B ω ω C D
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4 Final exam / 6.003: Signals and Systems (Fall 2007) 2. Discrete-time periodicity [5 points] Here are two periodic discrete-time signals: x 3 [ n ] = . . . , 0 , 0 , 1 , 0 , 0 , 1 , 0 , 0 , 1 , . . . x 5 [ n ] = . . . , 0 , 0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 , 1 , . . . Mark the period of their sum x 3 [ n ] + x 5 [ n ] as an on the thermometer: 0 2 4 6 8 10 12 14 16 18 20 If you are unsure of the correct value, you can also mark a second value, in which case you will receive the average of the scores for the two values.
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5 Final exam / 6.003: Signals and Systems (Fall 2007) 3. Find the output signal [5 points] A given linear, time-invariant system turns the unit pulse into the triangle: system 0 1 0 1 2 3 0 1 0 1 2 3 The system is given the following input signal: 0 1 0 1 2 3 Sketch the output signal on the following graph: -2 -1 0 1 2 3 4 5 6 1 2
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6 Final exam / 6.003: Signals and Systems (Fall 2007) 4. Frequency response [10 points]
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7 Final exam / 6.003: Signals and Systems (Fall 2007) a. Here is a resistor–capacitor circuit: 1 1 1 1 1 cos t y ( t ) The input signal is cos
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final_F07 - 6.003 (Fall 2007) 17 December 2007 Final exam...

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