MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.003: Signals and Systems--Fall 2003 PROBLEM SET 5 Issued: October 2. 2003 Due: October 22. 2003 REMINDER: Quiz 1 will be held from 7: 30 to 9: 30 p. m. Tuesday, October 14 The quiz will cover material in Chapters 1-3 of o&w Lectures and Recitations through september 26, Problem Sets 1-3 and that part of Problem Set 4 involving problems from Chapter 3 Reading assignments Lectures #9-11 PS#5: Chapters 4&5 of O&w, plus begin Chapter 6(through Section 6 Lectures #12-13 &z PS#6: Chapters 6&7(through Section 7.2)and Chapter 8 (through Section 8.4)of O&w PLEASE NOTE: The time interval over which you have to work on this problem set is just under three weeks. This is due not only to the fact that there is a quiz in this period but also, simply to the way the schedule worked out. As a result, this problem set is longer than previous problem sets(and subsequent ones) in order to match the coverage of the course. You should use your own judgment in planning the time you devote to this problem set, but it is strongly advised that you not leave it all to the last minute. Exercise for home study(not to be turned in, although we will provide solutions (E1)O&W4.47 Problems to be turned in Problem 1 Consider the signal a(t)with spectrum depicted in Figure p4. 28(a)of O&W Sketch the spectrum of y(t)=x(1)[cos(t/2)+cos(3t/2)MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.003: Signals and Systems—Fall 2003 Problem Set 5 Issued: October 2, 2003 Due: October 22, 2003 REMINDER: Quiz 1 will be held from 7:30 to 9:30 p.m. Tuesday, October 14 The quiz will cover material in Chapters 1-3 of O&W, Lectures and Recitations through September 26, Problem Sets 1-3, and that part of Problem Set 4 involving problems from Chapter 3. Reading Assignments: Lectures #9-11 & PS#5: Chapters 4&5 of O&W, plus begin Chapter 6 (through Section 6.1) Lectures #12-13 & PS#6: Chapters 6&7 (through Section 7.2) and Chapter 8 (through Section 8.4) of O&W PLEASE NOTE: The time interval over which you have to work on this problem set is just under three weeks. This is due not only to the fact that there is a quiz in this period, but also, simply to the way the schedule worked out. As a result, this problem set is longer than previous problem sets (and subsequent ones) in order to match the coverage of the course. You should use your own judgment in planning the time you devote to this problem set, but it is strongly advised that you not leave it all to the last minute. Exercise for home study (not to be turned in, although we will provide solutions): (E1) O&W 4.47 Problems to be turned in: Problem 1 Consider the signal x(t) with spectrum depicted in Figure p4.28 (a) of O&W. Sketch the spectrum of y(t) = x(t) [cos(t/2) + cos(3t/2)] . 1