ECE307HW.45.pdf - 75f 3 A signal x(t)= e u(z‘ is applied...

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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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