# 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.

## 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.

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