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**Unformatted text preview: **GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL and COMPUTER ENGINEERING ECE 2025 Spring 2009 Problem Set #13 Assigned: 10-Apr-09 Due Date: 24-Apr-09 This homework is OPTIONAL. However, it will be covered on the final exam. If you turn it in, the grade will replace your lowest homework grade. This Homework can be turned at the last lecture on Friday, 24-April before Noon, or earlier that week. Final Exam will be given on Monday, 27-April at 2:50 PM; Review on Sunday, 26-April at 6 PM. One page ( 8 1 2 00 11 00 ) of handwritten notes allowed. Calculators OK. Reading: In SP First , Chapter 11: Continuous-Time Fourier Transform Chapter 12: Filtering, Modulation and Sampling, (applications of the Fourier Transform). H) Please check t-square often. All official course announcements are posted there. ALL of the STARRED problems will have to be turned in for grading. A solution will be posted to the web. Some problems have solutions similar to those found on the CD-ROM. PROBLEM 13.1 : The system below involves the cascade of several modulators followed by a filter: Lowpass Filter h.t/; H.j!/ cos .66 t/ cos .15 t/ cos .51 t/ z.t/ v.t/ x.t/ w.t/ y.t/ The signals are defined by v.t/ D x.t/ cos .66 t/ w.t/ D v.t/ cos .15 t/ z.t/ D w.t/ cos .51 t/ Suppose that the Fourier transform of x.t/ is X.j!/ D j! f u.! C 7 / u.! 7 / g (a) Sketch a plot of the magnitude of the Fourier transform, j X.j!/ j . (b) Determine the Fourier transforms, V.j!/ , W.j!/ , and Z.j!/ . Give your answers as plots that sketch the magnitude of each one....

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