## Contents

# Homework 7, ECE438, Fall 2014, Prof. Boutin

Hard copy due in class, Wednesday October 29, 2014.

## 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.

## 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 4

Compute the inverse z-transform of

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

## Question 5

Compute the inverse z-transform of

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

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

## Question 8

Compute the inverse z-transform of

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

## Question 9

Compute the inverse z-transform of

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

## Discussion

You may discuss the homework below.

- write comment/question here
- answer will go here