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Unformatted text preview: 6.003 Homework 13 The following problems are from a previous final examination in 6.003. Doing these problems can be an excellent way to prepare for your final, but only if you (1) treat the problems as an exam, (2) do them by yourself in a quiet environment, and (3) time yourself. These problems will not be graded. Answers (but not fully worked solutions) will be posted. 1. Matching time and frequency representations 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. t A B C D t A B C D t 1 1 A B C D Here are the choices for the Fourier transform magnitude: ! ! A B ! ! C D 6.003 Homework 13 / Fall 2009 2 2. Discretetime periodicity Here are two periodic discretetime signals: x 3 [ n ] = ..., , , 1 , , , 1 , , , 1 ,... x 5 [ n ] = ..., , , , , 1 , , , , , 1 ,... Mark the period of their sum x 3 [ n ] + x 5 [ n ] as an on the thermometer: 2 4 6 8 10 12 14 16 18 20 3. Find the output signal A given linear, timeinvariant system turns the unit pulse into the triangle: system 1 1 2 3 1 1 2 3 The system is given the following input signal: 1 1 2 3 Sketch the output signal on the following graph:21 1 2 3 4 5 6 1 2 4. Frequency response a. Here is a resistorcapacitor circuit: 1 1 1 1 1 cos t y ( t ) 6.003 Homework 13 / Fall 20096....
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This note was uploaded on 08/24/2011 for the course EECS 6.003 taught by Professor Dennism.freeman during the Spring '11 term at MIT.
 Spring '11
 DennisM.Freeman

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