EE 341 Spring 2009 Final Exam Solutions corrected pages 3 and 4

EE 341 Spring 2009 Final Exam Solutions corrected pages 3 and 4

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EE 341 Spring 2009 Prof. Atlas Page 1 of 10 Final Exam June 10, 2009 Your Name: Solutions Exam Instructions: 1. Open book and notes. But as listed in our course syllabus: “No electronic devices (calculators, laptops, netbooks, PDAs, cell phones, beepers, etc.) are allowed for exams.” 2. Do not open this exam until 8:30! 3. Put all your answers in the appropriate space . Feel free to attach extra worksheets if 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 7 pages (including this page). 8. The weight (out of 200) of each section of each problem is located to the right of the problem in parentheses. 9. The total weight for this exam is 200 points. After this exam is graded, your score will be recorded on the back of the last page.
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EE 341 Spring 2009 Prof. Atlas Page 2 of 10 Problem 1 Consider the block diagram below, where x[n] and y[n] are the system’s input and output sequences, respectively. For your convenience, we label intermediate nodes’ sequences as [1 ] , [ ] , a n d ] wn + . The numbers in circles represent scalar multiplication. For example, [] 3[] y nw n = . a) Derive the difference equation for the above system as a function of input sequence x[n] and output sequence y[n]. (As you proceed to your solution, you should end up removing all temporary sequences, such as w[n].) (15 points) Solution: () 1 3 11 22 24 [] 3[] [] ][ ] [ ] (1 ) ( 1 ) yn xn =→ = += + =− Plug y[n] in for temporary variable w[n] 1 1 1 32 3 4 3 ] ( ) ) [ 1 ] 3[] ) ] ( ) ) 3 [ ] ++ + −= b) Find the input/output transfer function, ( ) H z , for the above system. (15 points) Solution: 1 2 2 3 () () 3 () ( ) ()3 Yzz Yz Xz Xzz Yz z z Xz z = = = 2 3 z
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EE 341 Spring 2009 Final Exam Solutions corrected pages 3 and 4

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