Question

Determine the system response y(t) for h(t)=u(t)tu(t-2) and x(t)=u(t). [Hint: use Laplace Transform multiplication: C[x(t) *h(t)) = X(s)H(s). y(t) = tu(t)-(t +2)u(t + 2) y(t) = tu(t) + (t - 2)u(t + 2) y(t) = tu(t) + (t - 2)u(t - 2) y(t) = tu(t)-(t - 2)u(t - 2) Question 8 (10 points) What is the Fourier Transform of f(t) = 55(t - 1)? ew 5e-sw 5e-510 را که م

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Answer 1

ROMA Solm Sih h(t) = = Uft) tult-2) and alt) ult) Here LYH) = x(+) *hlt we L[yct] know that L[xl-4 *h1] = X(S). His) Yls) た X15). H15) 2114) LIT X15) U14) LIT 7 X (5) = Yu Y hlt) LTHCS) UH) +ult-2). -T7 Now, -25 Y(s) = [ Ś t e es 링 25 Y15) = ē? 7 52 52

transform taking inverse Laplace L'[y(s)] = t -25 te get) = tult) + = tult) + -1) ult-2) =) 94+) = tult) +-2) 1-2) 3rd option is Correct. fit) = 55t-1) using definition of fouries transform. flw)= dt 5) flw) S brease that js -jut 55(1-1) e fiw) jwil .se blt-1) dt flwl -jw 5e And option is correct

NOTE : . X(t) b(-a) alar.blt-a)