Fall 2003: Quiz 1 NAME: Work Page for Problem 1 Linearity System A: YES I(t)y1(t)=1(t+2)sin(at +2 2(t)g2(t)=2(t+2)sin(ut +2) r3(t)=ax1(t)+br2(t)→(t)=x3(t+2)sin(t+2) ac1(t+2)sin(at+2)+bc2(t+2)sin(at +2) ay1(t)+ by2(t) System B: NO if a[n]=0, then yn]≠0 System C: NO not linear due to the r k+1]term Time Invarience System A: NO the output has time varying gain System B: NO the output has time varying gain System C: NO the number of summed terms depends on n Causality System A: NO y(t) depends on (t+2) System B: YES yn depends only on the current value of n System C: NO yn] depends on the future value of an Stability System A: YES bounded az(t)→→ bounded y(t) System B: NO System C: NO ifl]=-1→yl=∑h=12,y→∞asn� Fall 2003: Quiz 1 NAME: Work Page for Problem 1 Linearity System A: YES x1(t) ⇒ y1(t) = x1(t + 2)sin(wt + 2) x2(t) ⇒ y2(t) = x2(t + 2)sin(wt + 2) x3(t) = ax1(t) + bx2(t) ⇒ y3(t) = x3(t + 2)sin(wt + 2) = ax1(t + 2)sin(wt + 2) + bx2(t + 2)sin(wt + 2) = ay1(t) + by2(t) System B: NO if x[n] = 0, then y[n] = 0 → 2 System C: NO not linear due to the x [k + 1] term. Time Invarience System A: NO the output has time varying gain System B: NO the output has time varying gain System C: NO the number of summed terms depends on n Causality System A: NO y(t) depends on x(t + 2) System B: YES y[n] depends only on the current value of x[n] System C: NO y[n] depends on the future value of x[n] Stability System A: YES bounded x(t) −⇒ bounded y(t) 1 n System B: NO (−2 ) −⇒ √ as n −⇒ −√ System C: NO if x[n] = −1 −⇒ y[n] = n k=1 2, y −⇒ √ as n −⇒ √ 3