Spr 2009 341 Midterm Solutions

Spr 2009 341 Midterm Solutions - EE 341 Spring 2009 Prof...

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EE 341 Spring 2009 Prof. Atlas Page 1 of 4 Midterm Exam May 5, 2009 Your Name: Solutions Exam Instructions: 1. Open book and notes. But as listed in our course syllabus: “No electronic devices (calculators, laptops, Pilots, cell phones, beepers, etc.) are allowed for exams.” 2. Do not open this exam until 9:30. 3. Put all your answers in the appropriate space. But attach extra sheets in necessary. 4. Turn in your work and put your name at the top of all loose worksheets. This work will be looked at for possible partial credit. 5. Justify all of your answers. 6. The exam will be collected promptly at 10:20. Continuing to work after the bell will cause you to lose points . 7. This exam has a total of 4 pages (including this page). 8. The total weight for this exam is 100 points
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EE 341 Spring 2009 Prof. Atlas Page 2 of 4 Problem 1 For each of the following systems, determine whether the system is (1) linear and (2) time-invariant. Also, if it’s both linear and time- invariant , please (3) find its impulse response[] hn and (4) the z -transform () H z (including the ROC) of its impulse response. Please justify your answers . a) ] [ ) (sin ]} [ { n x n n x T π = (15 points) (1) The system is linear. Let 11 1 [] { [] } ( s i n ) [] yn Txn nxn == , and 22 1 [ ] { [ ]} (sin ) [ ] = = , now 12 1 2 12 { [ ] [ ]} (sin )( [ ] [ ]) (sin ) [ ] (sin ) [ ] [ ] [ ] Ta xn b xn na a nxn b nxn a yn b yn ππ += + = + (2) The system is not time-invariant. Let [ ] { [ ]} (sin ) [ ] T xn = = , then 00 0 ( s i n () ) yn n n n xn n
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Spr 2009 341 Midterm Solutions - EE 341 Spring 2009 Prof...

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