Question

a). Sketch y(t)...can you explain how you sketched it?

) Consider the LTI system shown below, - hít) | yết) x(t) where the input x(t) and impulse response h(t) are defined by the following plots: + x(t) ht)

b). Find Y(s)

Answer 1

Given xH) hlt) L y(t) X() x (+) = 1867-1) + 28(7-) Output 464) = m(t) * hét) (* > convolution) = ($(t-1) +28(-4)) hit) = $(t-1) * htt) + 28(7-4) *hlt) =h(t-1) + 2 hét-4) l: 617-a) * f(t) = f(t-a)) th(t-1) gh (t-4) 2 + 2 x o 1 2 3 4
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:: y(t) =h(t-1) + 2h(t-4) 740+) IA 21 3 4 5 © (5,4) Laplace transform of yf) w est dt y(s) = 1 y(t) e 44 12,2) 2 y(t) = 257-2 Pet.2 l ta = 4€ -16 45655 1 O otherwise. Oy=mx+c|m= 2-0 4 -2x+c 2 I AL (1,0) ► 0=2+C =C=-2 y=an-2 46)="jcat-se *dt + Jaublika 4 y=mx+c Im-4-0! 15-4 -st . 2 st dt ate de 17 4=48+cl=4 At (4,0) 0=4X4+C » c =-16 I 4-44-16 - 5 st. 5 It -st -like dt 14te de +
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b. Now I te dt stat ſusza - Spondet un ) (tekst r lige nu este SL .-st 1 100 te dt = Ja -st e dt = O -gt I-SE 2 Thedt - 21 edt + 4 te :. 40) = 2 İtedt - eje*atu ujue al - 16 Jes de 72 st Ite - 2 - 2 -S
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NO G5 -US +uls че loll| : ( 一) (y 01 ) 十 .: Vie) (5) (一) = (s) e
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