# Homework 2, ECE438, Fall 2010, Prof. Boutin

Due Wednesday September 8, 2010. Hard copy due by 4:20pm in class, electronic copy in Prof. Boutin's dropbox (the ECE438 HW2 Assignment box) by 6pm.

## Question 1

Pick a signal x(t) representing a note of the middle scale of a piano (but not the middle C we did in class) and obtain its CTFT $ X(f) $. Then pick a sampling period $ T_1 $ for which no aliasing occurs and obtain the DTFT of the sampling $ x_1[n]=x(n T_1) $. More precisely, write a mathematical expression for $ X_1(\omega) $ and sketch its graph. Finally, pick a sampling frequency $ T_2 $ for which aliasing occurs and obtain the DTFT of the sampling $ x_2[n]=x(n T_2) $ (i.e., write a mathematical expression for $ X_2(f) $ and sketch its graph.) Note the difference and similarities between $ X(f) $ and $ X_1(\omega) $. Note the differences and similarities between $ X_1(\omega) $ and $ X_2(\omega) $.

You may post your answers on this page for collective discussion/comments (but this is optional).

## Question 2

Pick five different DT signals and compute their z-transform. Then take the five z-transforms you obtained and compute their inverse z-transform.

You may post your answers on this page for collective discussion/comments (but this is optional).

I just realized that there is no class Monday so we will not be able to cover the inverse z-transform before Wednesday (when the homework is due). Therefore, I am changing the homework: the second part of the question (compute the inverse z-transforms) will be part of Homework 3 instead. Sorry about the confusion. Have a great labor day weekend! --Mboutin 19:54, 3 September 2010 (UTC)

Instructions:

- Hand in a hard copy of your homework on September 8 in class.
- hand in an anonymous scan of your solution (e.g., write out your name before scanning, or replace it by a pseudo-name) and drop it in Prof. Boutin's dropbox (in the ECE438 HW2 Assignment box).

We will then do a double-blind peer of the homework.