HW11s09

# HW11s09 - GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of...

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GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL and COMPUTER ENGINEERING ECE 2025 Spring 2009 Problem Set #11 Assigned: 27-March-09 Due Date: Week of 6-April-09 Quiz #3 will be held in lecture on Friday, 17-Apr-09. It will cover material from Chapters 9, 10, and 11 as represented in Problem Sets #10, #11, and #12. Reading: In SP First , Chapter 9: Continuous-time signals and LTI systems H) Please check t-square often. All official course announcements are posted there. BOTH 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. Your homework is due in recitation at the beginning of class. After the beginning of your assigned recitation time, the homework is considered late and will be given a zero. Please follow the format guidelines (cover page, etc.) for homework. PROBLEM 11.1 : The delay property of Fourier transform states that if X.j!/ is the Fourier transform of x.t/ , the Fourier transform of x.t t d / is e j!t d X.j!/ , i.e., x.t t d / () e j!t d X.j!/: Use this property to find the Fourier transforms of the following signals: (a) x.t/ D ı.t C 1/ C 2ı.t/ C ı.t 1/ (b) x.t/ D sin .100 .t 2// .t 2/ (c) x.t/ D e t .u.t/ u.t 4// which can be rewritten as x.t/ D e t u.t/ e t u.t 4/ D e t u.t/ e 4 e .t 4/ u.t 4/ PROBLEM 11.2 :

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