Question

3. Problem 3: (20 pts) Figure 1: Problem 3 An LTT system consisting of two LTI subsystems are shown in the Figure 1. Let the frequency responses of the two subsystems h, and hy be defined as: SMC5 HGW) = H ) = 10 otherwise 10 otherwise Let z(t) = 4008°() +-* sin(3) be the input into the system. (a) Determine , 's and wi's such that z(t) = d.get (10 pts) (b) Use the property of LTI system with eigenfunction est as input to determine the output y(t) from the system hı. (DO NOT USE OTHER METHOD) (5pts) (c) Determine the output z(t) from the system hy. (5pts)

Answer 1

ht hot Hain halt t2lH H, 1jw) 3<lul can than H l jw) = of howite w71 2 other wre gip olt) = 4 Ges? (At) te lat sin(at) tradice M Ca301 No . > 102. formula byly - 2{1+cy QR7 t} = {%A1 alt) = ?{ lt Cesar j - inst) 1H) = ?ť 26 141 2ť le les ejt (**) -ft1f to janet ja de 2} + elet nit) = 2te. that state the eJurist athile - te tilw) with terus Mit = just olp=, Ferien wat eiger function eigen volle teison fonction

انار = ( و یه > H اد سره - 0.933 666 ( ملل eige ] - (+) 1 = 1\2 = 2141 e + عکس پر ان سے رز- F 3Fم ) + ( 2 ۷۰۰ و ۰۷ و= v,ع د « H = ۷.م = 1 = = = = gel ا . عالم = 8 hiltl 2[ {{ حه مه = امه ( ) ( مللي، مع )( ZH ) = 8th 10 othewane eigenvaler = Mellall کے روبر (3) = ( ا ا ا د
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