Question

ages/Microsoft.Microsoft Edge_8wekyb3d8bbwe/TempState/Downloads/BEE%20235-HW_4.pdf DEL LJJ LOLLILTUVUS HIC LICA JYSICS Due: 3:00pm of May 6 (Wednesday) Problem Set #4 The system shown in Figure 4 is made up of three LTI systems, whose impulse responses are hio), ha(t) and h(t), respectively. h(t) halt) re hi(t) y(t) h(t) Figure 4 hi(t) = (t - 2) ha(t) = u(t-1) - ult-2) ha(t) = u(t) - ult-3) Does there exist any single LTI system h(t) which is equivalent to the system shown in (a), i.e., for any input (t), can a single LTI system produce exactly the same output (t)? Justify your answer. If yes, give the impulse response of this single LTI item. Sketch ils overall impulse response. For the LTI systems below, determine from the impulse response whether the system is causal and/or stable: a) h(t) = -2(t+2) b) h(t) = eu(1 - 1) c) h(t) = sin(t)u(t) d) h(t) = +

Answer 1

oyu hilt=j (4-2) halts= Ult-1)-4(1-2) halt) = wis - U16-3) .. yes, for any input sects a single LTS system produce exactly the same output yets. single ows put hit = h,14) *[hale?+hy ks] *convolusimo => h(t)= h, (Asthalts + hilts & halt) hl0 = 514-2) * (U14-1) - U17-2)) + Sl4-2) * (uw) – (4-3)) or; hlu) = U66-134867-2) - U14-2)* 814-2) +01H*84-2) - U16-3) * 818-2) As we know; alt=t,)*81f-tz) = alt-te-t,) 'h(t)= ult-2-1)- U(+-2-2) + ult-2) - Ult-2-3) = Ult-3) - U16-4) + ult-2) - Ulf-5) 6(4) = 4(4+2)+464-3) – 464-47 - U14-5) |

h(t) = U17-2) + u1f-3) - UCH-4) – U11-5) phet overall impulse response. AX #=2 #3 #4 = 5 @ @ hl4=24414+2) slet +=1 hlle é? U13) ' future value. Oprouebit depend on fufcire value so non caused for bounded in pinta output also bounded so; Stuble system. Ahli 6 564) = eful1-6) 1. let t=0= hlo)= e. ull) w depends on future value so non cawal system, - plaets o for bounded input =) bounded output => stable systesn. = © 614? = stort ult) L depends on presenz vallee so causal system. Le stable systems. (d.) h1t) = 6 hels 1 st Le causal systers. Ly. Unstable system | Unbounded output of h»fe outu0).