Homework 8, ECE438, Fall 2015, Prof. Boutin

Hard copy due in class, Wednesday October 28, 2015.

Questions 1

Compute the z-transform of the signal

$ x[n]= \left( \frac{1}{2} \right)^n u[-n] $

Questions 2

Compute the z-transform of the signal

$ x[n]= 5^n u[n-3] \ $

Questions 3

Compute the z-transform of the signal

$ x[n]= 5^{-|n|} \ $

Question 4

Compute the z-transform of the signal

$ x[n]= 2^{n}u[n]+ 3^{n}u[-n+1] \ $

Question 5

Compute the inverse z-transform of

$ X(z)=\frac{1}{1+z}, \text{ ROC } |z|<1 $

Question 6

Compute the inverse z-transform of

$ X(z)=\frac{1}{1+2 z}, \text{ ROC } |z|> \frac{1}{2} $

Question 7

Compute the inverse z-transform of

$ X(z)=\frac{1}{1+2 z}, \text{ ROC } |z|< \frac{1}{2} $

Question 8

Compute the inverse z-transform of

$ X(z)=\frac{1}{(1+ z)(3-z)}, \text{ ROC } |z|<1 $

Question 9

Compute the inverse z-transform of

$ X(z)=\frac{1}{(1+ z)(3-z)}, \text{ ROC } |z|>3 $

Question 10

Compute the inverse z-transform of

$ X(z)=\frac{1}{(1+ z)(3-z)}, \text{ ROC } 1< |z|<3 $

Hand in a hard copy of your solutions. Pay attention to rigor!

Presentation Guidelines

• Write only on one side of the paper.
• Use a "clean" sheet of paper (e.g., not torn out of a spiral book).
• Staple the pages together.
• Include a cover page.
• Do not let your dog play with your homework.

Discussion

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