Homework 2, ECE438, Fall 2010, Prof. Boutin
Due Wednesday September 8, 2010 (in class)
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).
