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Homework 2, ECE438, Fall 2011, Prof. Boutin
Due Wednesday September 6, 2011 (in class)
Question 1
Pick a signal x(t) representing a note of the middle scale of the 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) $.
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.
Question 3
If you have not done so already, answer all the "collectively solved practice problems" posted on the course wiki and share your answers on the corresponding pages. Contact your instructor if you would like to be given an "anonymous" login (to be used in place of your career account login).
Discussion
Please discuss the homework below.
