Unformatted text preview: 75f 3 A signal x(t)= e u(z‘) is applied to a circuit shown in Figure l. R=lQ C=0. lF. (a) Find the total energy EX contained 1n the signal X(t) e—lOt 1
E: jx(gm= Ie (#:16201J (b) Find the Fourier transform X(oo) of the input signal x(t).
X(w) = 1
j a) + 5
(c) Find the transfer function H(s) = Y(s)/X(s) of the circuit shown in Figure 2. Find
I{(w )= [email protected]) 5:112) l l
H(S)= Y(S) 2 SC : RC = 10 3 11(0)): _ 10
X(S) 12+; s+i s+10 ja)+10
SC RC (d) Find the Fourier transform of the y(t) given by Y(m) = H(m)X(oa).
W) = H<w>X<w> = # (ja)+5)(ja)+10)
(e)Fum¢Y(mn? 100 _ 100 Y(w)2 = ﬂ — —
lja)+5 ljw+10 (w +5 )(w +10) (f) Represent Y(oo)2 by partial fraction expansion, i.e., ﬁnd A and B in the following equation: A B (A +}B)a)2 +100A +253
2 2 + 2 2 Z 2 2 2 2
a) +5 0) +10 (co +5 )(0) +10) A+B=0, 100A+25B=100, A = 4/3, B = 4/3. twat = (g) Find the total energy Ey contained in the output y(t). 4 —4 l —a’(o+L —,d(z) E =2—”_[Y((u)d(u=2—ﬂ_ (a +5 27r_ (0 +10 ...
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 Fall '07
 Z.Aliyazicioglu
 Kang, #, 1 j, 4 l, GM=

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