## Contents

# Homework 8, ECE301, Spring 2011, Prof. Boutin

# Due by 6pm Wednesday March 23, 2011

This homework consists of a double-blind peer-review of homework 7. In other words, you will be grading each other's homework! Of course, we are giving you the solution.

Every student who handed in a scan of their homework in the appropriate homework section of the instructor's Assignment Box before the deadline can participate in this review.

In case you were unable to do so on time, or if something went wrong, there is now a second assignment box for you to drop your homework 7. It is called "ECE301: Homework 7 -second batch".

To begin the review, go to your own dropbox and click on your "Assignment" tab. There, you should see a file (anonymous) waiting to be reviewed, along with a space to write/upload your review. Open the file and grade each question according to the instructions described below. It is recommended that you print out the file and mark out all mistakes using a red pen; you can then scan and upload the graded homework (in pdf format). When you are done grading, add up all the points and write the total on the front page of the assignment.

Note 1: if you are having problems with the system or the file, please let us know by writing a comment on the hw8 discussion page or by emailing your instructor as soon as possible

Note 2: If the answer to a problem is pretty much unreadable, feel free to give zero points for that problem.

## Total Points: 165 points

## Overall Presentation: 10 points

All problems solutions should be clearly written, in the correct order. The paper should be free of stains and tears (e.g., not torn out of a spiral book). The scan should be of good enough quality to be easy to read. The file should be in pdf format.

## Question 1: 20 points

- 15 pts for the computation of the Fourier transform of the discrete-time signal. If an integral was used in place of a summation, give zero points. Check every step of the computation and remove point for any mistakes. Take points off if the explanation is not clear/logical/rigorous. In particular, any statement that is not true should be marked down. Make sure to explain why you are taking off points and how many points. If the student used the table of pairs or the table or properties at any point in this question, give 0 points.
- 5 points for checking the answer using the table. If the answer obtained with the table does not match with the answer previously obtained, give zero points. Take points off if the explanation is not clear/logical/rigorous. In particular, any statement that is not true should be marked down. Make sure to explain why you are taking off points and how many points.

## Question 2: 20 points

- 15 pts for the computation of the inverse Fourier transform. If a summation was used in place of the integral, give zero points. Check every step of the computation and remove point for any mistakes. Take points off if properties or pairs from a table were used. (Anything except linearity should incur a large penalty). Take points off if the explanation is not clear/logical/rigorous. In particular, any statement that is not true should be marked down. Make sure to explain why you are taking off points and how many points.

- 5 points for checking the answer using the table. If the answer obtained with the table does not match with the answer previously obtained, give zero points. Take points off if the explanation is not clear/logical/rigorous. In particular, any statement that is not true should be marked down. Make sure to explain why you are taking off points and how many points.

-The question statement does not ask to check the answer, should these points count?

## Question 3: 45 points

Give 15 points for part a), 15 points for part b), and 15 points for part c). Take off points if the properties/pairs that were used are not clearly stated. Take points off if the explanation is not clear/logical/rigorous. In particular, any statement that is not true should be marked down. Make sure to explain why you are taking off points and how many points.

The essential part of that problem is the use of the fact that the output of the system is the inverse Fourier transform of the product of the frequency response of the system and the Fourier transform of the input. An answer that either does not use this fact or uses it incorrectly should receive little credit (perhaps even zero points).

## Question 4: 25 points

Read the explanation and the answer carefully. If the answer is correct, but the explanation is wrong, you should feel free to give zero points. Take points off if the explanation is not clear/logical/rigorous. In particular, any statement that is not true should be marked down. Make sure to explain why you are taking off points and how many points.

## Question 5: 45 points

a) 25 points Read the explanation and the answer carefully. If the answer is correct, but the explanation is wrong, you should feel free to give zero points. Take points off if the explanation is not clear/logical/rigorous. In particular, any statement that is not true should be marked down. Make sure to explain why you are taking off points and how many points.

b) 20 points There are two correct ways to answer this question: multiply the two frequency response and invert, or invert each frequency response and convolve the respective results. Both methods can receive full credit, as long as the explanation is clear, logical and correct. If the answer is correct, but the explanation is wrong, you should feel free to give zero points. Take points off if the explanation is not clear/logical/rigorous. In particular, any statement that is not true should be marked down. Make sure to explain why you are taking off points and how many points.