## Homework #7

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## Homework #7

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Lecture Notes

- Pages:
- 2
- School:
- California State University, Northridge
- Course:
- Ece 351 - Linear Systems Ii

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ECE 351 Linear Systems II Homework 7 1 Find F z the z transform of each of the following sequences a k 1 k fk 5 2 3 4 uk 2 b 1 fk 2 k 2 uk 2 k c 1 fk u k 2 2 Answer F z 5z 2z 3z z 1 z 1 z 4 2 1 1 z z 2 1 1 4z z 2 1 3 1 2 1 z z z 4 4 64 F z Answer 4 1 z 4 Answer F z k d Answer F z 1 fk k u k 4 3 2 Find yk the inverse z transform for each of the following k 1 k 1 6z 3 29z 2 17z a Y z Answer yk 4 2 3 uk 1 1 3 2 6 z z z 1 2 3 b Y z 9z 2 z 2 z2 1 c Y z 3z z z 2 d Y z 2 Y z f Y z k k Answer yk 2 1 uk 6z 4 18z 3 16z 2 8z z 1 z 1 2 e k Answer yk 2 k 4 1 3 uk 2z 5z 8 z 2 2 3 3 k Answer yk 2 k k 2 uk 2 4z 3 6z 2 z 2 z 2 2z 2 k Answer yk 3k 2 7k 2 1 4 uk k Answer yk 2 2 2 2 cos 3 4k 4 2 sin 3 4k u k k k g Y z 3z 3 6z 2 8 z z2 4 k k k k Answer yk 2 k 1 3 2 cos uk 2 2 sin uk 2 2 3 Solve the following difference equations using Z transforms a yk 2 yk 1 yk 0 y0 1 y1 2 2 k 2 k Answer yk cos 3 sin uk 3 3 k k k k b yk 2 3yk 1 2yk 2 3 uk y0 1 y1 0 Answer yk 3 1 3 2 3 uk 1 1 c yk yk 1 uk 1 uk 2 y 1 0 2 2 1 4 1 k Answer yk k uk 3 3 2 Read and perform the exercises in MATLAB Tutorial 7 before attempting problems 4 6 For each problem turn in your MATLAB commands along with the results 4 Use the residuez command in MATLAB to confirm the partial fraction expansion in problem 2a 5 Use the residuez command in MATLAB to confirm the partial fraction expansion in problem 2b 6 Use the residuez command in MATLAB to confirm the partial fraction expansion in problem 2c

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