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Unformatted text preview: MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.003: Signals and Systems — Spring 2009 Final Exam Review Packet Final Date: Wednesday, May 20, 2009 Time: 1.30 PM–4.30 PM. Location: Johnson Coverage: All material covered in the course. Notes: The exam is closed book except for three 8 . 5 ′′ × 11 ′′ two-sided sheet of notes. No calculators are allowed. We will provide copies of all the tables in O&W that we used this term, namely, the Tables of CT and DT Fourier Series properties on pages 206 and 221 of O&W, the Tables of CT Fourier transform pairs and properties on pages 328 and 329, the Tables of DT Fourier transform pairs and properties on pages 391 and 392, the Tables of Laplace transform pairs and properties on pages 691 and 692, and the Tables of z-transform pairs and properties on pages 775 and 776. Marathon Office Hours: The TAs will jointly hold office hours in the week of May 11. A sched- ule will be posted on course website. Final Exam Review Session: The TAs will hold an optional final review session on the following date, time and location: Review session: Friday, May 15, 1:30–4:30 PM in 34-101. Practice Problems: The attached set of problems should provide you with ample opportunity to exercise your understanding of and facility with the material covered on this quiz. These problems will be covered in the quiz review session. The solutions to these problems will be posted on the 6.003 website on the same day as the review session. A practice final exam from a previous semester will be available online. Both of these sets of problems should help to spark questions you might want to discuss with the TAs during their office hours. 1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.003: Signals and Systems — Spring 2009 Final Exam Review Problems Problem #1 The purpose of this problem is to test your understanding of continuous-time con- volution. A CT LTI system has input x ( t ), impulse response h ( t ), and output y ( t ) as shown below. Note that the scales for x ( t ) are not necessarily the same as for h ( t ) and y ( t ). A t x(t) h(t) y(t) t t 1 3 6 9 12-6-4-2 2 4 6 2 4 6-6-2-4-T T Determine the values of the parameters of x ( t ): A and T....
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