Question

Problem 2. (35 marks) Time-Domain Analysis of Systems (a) (10 marks) x(t) = u(t – 3) – u(t – 5) and h(t) = E=-1 8(t - k). Determine y(t) = x(t) * h(t). (b) (25 marks) An LTID system is specified by the following equation: 2y[n + 1] – 3y[n] + y[n – 1] = 4.x[n + 1] – 3x[n]. i) [8 marks] Draw a schematic diagram for the LTID system in terms of delay compo- nents "D". ii) [12 marks] Determine the impulse response h[n] of the LTID system, when n < 2. iii) [5 marks] Determine the impulse response h[n] for n > 0. (Hint: You can do it by either the following two ways. (1) Direct calculation. (2) 3,4,5,...) and discover the laws.) Calculate more values of n (e.g., n =

Answer 1

ult-s) 1= ult-3) - Ahlt! famula hitt * (H = (4-1) d (H = Ult)+ult-3)-ult-s -ult-6) (4 = ultR) tult-3) -ult-5)-014-61

3y(m) + g(m-1) - 4n(mti)-3) takig z- T -1 * 4 XIZ1 Z - 3x2) 3 YİZ) + Y(2) z Y{Z) [az-3+2"] - 14Z-3) pre) 42-3 HIZ!= 42-3 (42-3) Z 22-3 +z az-3+½ 2z-3241 HIZ) = 2(42-3) 3z?-37+1 4 { Z-43} R{z²%,2+k} 4Z-3 Ne thed 3z 321! Hiz! (Z-413) (7- 43) { (Z-1)(Z-Y2)) HIZ) HIZ- HIZ! a HIZ) = h(m)=[4, I26

(3) um) + (-1%) (k)"arm) blo) = hl이- -13 -1o h12) = lu)4. -3
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