1. Digital Signal Processing Solutions to Midterm Exam 2009 Edited by Shih-Ming Huang Confirmed by Prof. Jar-Ferr Yang LAB: 92923 R, TEL: ext. 621 E-mail: smhuang@video5.ee.ncku.edu.tw Page of MediaCore: http://mediawww.ee.ncku.edu.twsmhuang@video5.ee.ncku.edu.twhttp://mediawww.ee.ncku.edu.tw

2. 1. (1) a e (2) c d (3) d (4) a b c e 2. Stable: b c e f Casual: e Memory: All 3. (a) stable, casual, initial value = 1/3 at position 1 (b) unstable, non-casual, final value = -1 at position 1 (c) unstable, non-casual, final value = 2 at position 2 (d) stable, non-casual, None (e) unstable, non-casual, final value = 1 at position 2 (f) unstable, non-casual, initial value = 1/2 at position -1

3. Sol: Step 1: y1[n]=T(x1[n])=nx1[2n] Step 2: y2[n]=T(x2[n])=nx2[2n] Step 3: y3[n]=T(x1[n] + x2[n])=n(x1[2n]+x2[2n]) Step 4: y3[n] = y1[n]+y2[n] 1 (1) is y[n] = nx[2n] linear?

4. 1 (2) is y[n] = x 2 [n] time-invariant? Sol: Step 1: y1[n]= x 2 [n-n 0 ] Step 2: y[n- n 0 ]= x 2 [n- n 0 ] = y1[n]= x 2 [n-n 0 ]

6. 4abcd4abcd

7. 5ab5ab

8. 6

9. 7ab7ab

10. 8. a b

11. 9. a b

12. 10. (a) (b)

13.  xc(t)xc(t)               …… …… x[n] v[n] w[n] y[n] yc(t)yc(t) 11.     …    1/T 1/3T T’/3T

14. 12. with 0.5r L < ROC Y < 0.5r U