1 . (1) ae (2) bcd (3) de (4) e (5) cd 2. (a) stable, final value = 0.5 at position 0

1. Digital Signal ProcessingSolutions to Midterm Exam 2011Edited by Shih-Ming HuangConfirmed by Prof. Jar-Ferr YangLAB: 92923 R, TEL: ext. 621E-mail: smhuang@video5.ee.ncku.edu.twPage of MediaCore: http://mediawww.ee.ncku.edu.tw

2. 1. (1) ae (2) bcd (3) de (4) e (5) cd 2. (a) stable, final value = 0.5 at position 0 (b) stable, initial value = 0.5 at position 0 (c) unstable, initial value = 1 at position 0 (d) unstable, final value = 5/2 at position -1 (e) stable, final value = 1/6 at position 0 (f) stable, initial value = 1 at position 0 3. Stable: b c d e Casual: a. c Memory: All

3. 4. Q: what are the resulting sampling sequences, x[n] after sampling and perfect reconstruction? Ans: The sampling frequency should be at least twice the highest frequency contained in the signal, expressed as Fs ≥ 2*Fo So, a, b can be reconstructed perfectly, but c, d cannot. xc(t) = sin(300πt) + cos(240πt) = sin(2*150πt) + cos(2*120πt) (a) T = 1/500, ,Yes (b) T = 1/360, ,Yes (c) T = 1/220, ,No (d) T = 1/120, ,No

4. 5. (a) (b)

5. 6 (a) (b)

6. 7 (a) (b)

7. 8

8. 9 (a) (b) (c)

9. Let (d)

10. 10 • (b) (c) (d)

11. 11. with 1 < |z| < 4