MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.003: Signals and Systems--Fall 2003 PROBLEM SET 2 SOLUTIONS

Home Study Exercise (E1)O&W3.46(a)and(c) (t) and y(t) are continuous-time periodic signals with a period= To and Fourier series representations given b

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

Department of Electrical Engineering and Comput 6.003: Signals and Systems--Fall 2003 PROBLEM SET 6 Issued: October 21 2003 Due: October 29. 2003 Reading assignments Lectures #12-13& PS#6: Chapters 6&7(through Section 7. 2 )of O&w

The lowpass filter H(u) has a cutoff frequency wc=205T rad/ sec. Thus, c(t)is r(t) where all terms with frequency above we are removed by the lowpass filter. The terms which are kept have kwol 205T rad /sec k|< 10.25, so the output, ac(t),is r(t)= To obtain n, we sample c(t) every T=5 10-3 seconds with an impulse train The sampling frequency is 400T=2 x maximum frequency in c(t). Therefore

Reading Assignments Lectures #18-20 PS#9: Chapters 9 1l(through Subsection 11.3.4 )of O&W Lectures #21-22 PS#10: Chapters 10& 11(through Subsection 11. 3.4)of O&w Exercise for home study(not to be turned in, although we will provide solutions)

Department of Electrical Engineering and Computer Science 6.003: Signals and Systems-Fall 2003 PROBLEM SET 6 SOLUTIONS Issued: October 21. 2003

Department of Electrical Engineering and Computer Science 6.003: Signals and Systems--Fall 2003 PROBLEM SET 9 SOLUTIONS Home Study 1 O&w 9.25(e) We assume that the system we are considering, H(s)takes the following form:

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.003: Signals and Systems--Fall 2003 PROBLEM SET 10 SOLUTIONS Home study exercise(E1)O&W 11.32

Directions: The exam consists of 5 problems on pages 2 to 19 and work space on pages 20 and 21. Please make sure you have all the pages. Tables of Fourier series properties are supplied to you at the end of this booklet. Enter all your work and you answers directly in the spaces provided on the printed pages of this booklet