Homework 2, ECE438, Fall 2010, Prof. Boutin
Due Wednesday September 8, 2010. Hard copy due by 5pm 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).
Instructions:
- Hand in a hard copy of your homework on September 8 in class.
- hand in an anonymous scan of your solution (e.g., white 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.
