10Sp_Exam2 - ECE 210/211 Analog Signal Processing Spring...

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Unformatted text preview: ECE 210/211 Analog Signal Processing Spring 2010 University of Illinois Basar, Beauchamp, Peck Exam 2 Thursday, March 18, 2010 — 7:00—8:15 PM Name: Section: circle one Class: circle one ECE 210 ECE211 Please clearly PRINT your name IN CAPITAL LETTERS and circle your section in the boxes above. This is a closed book and closed notes exam. Calculators are not allowed. Please show all your work. Backs of pages may be used for scratch work if necessary. All answers should include units wherever appropriate. Problem 1 (25 points) Problem 2 (25 points) Problem 3 (25 points) Problem 4 (25 points) Total (100 points) Problem 1 (a) Convert each of the following time domain signals into phasor. . _ . It (I) fl(t) — 5 s1n[3t— 6] (ii) f2 (t) = Cos t + Sin t F2 (b) Convert each of the following phasors into a time domain signal. Assume 0) = 1 rad/sec. (DE=2+% gm: (mg=+T—T——7— gt: eHJA +eJA(1 +eJA) 0 (c) Determine the Thevenin impedance ZT of the following circuit between terminals a and b. 20 m a 3 cos 2t ]F b ZT = (d) An LTI circuit has the following steady state response functions: input f(t) = —2 Sin 2t —> outputy(t) = Cos £t+£ 3 4 4 4 inputf(t) =4 —> outputy(t) =2 Find the values of the frequency responses (magnitude and the phase angle): Problem 2 For the time — domain circuit shown below: 2H 1/212 (a) Draw the phasor circuit for co = 2 rad/s. Include and label all impedances and source phasors for the co = 2 rad/sec circuit. (b) Determine the phasor voltage VR at co = 2 rad/s. (c) Determine the dc voltage VR at co = 0. (d) Determine the steady-state voltage vR (t). (e) Find the average power absorbed by the 30 resistor. Problem 3 (a) The following circuit is given: 1H + f(t) C 10 y(t) (i) Find the frequency responSe function H(m) for this circuit. Simplify your answer. (ii) Find H(u)) for the following frequencies. m=o m=1rad/sec (D——)OO HOD) = (b) The frequency response function of a system is given as ju) H((D) : 2+ja) (i) Sketch the magnitude spectrum (0 > o of this system. Label axes carefully. (ii) Find y(t) if f(t) =3 + Cos 2t. Problem 4 -1t -1t/4 0 1t/4 1t 7 7% 2. 7t 9% cos(2t), —%<t< 7% 0, 1% <t<7% (a) What is the period T and the fundamental frequency 030 ? The periodic signal shown above is given by f (t) = T: ,co= 0 (b) Is the complex Fourier coefficient Fn (circle the correct answer) totally real, totally imaginary, or both parts non-zero? (c) Write the integral equation for Fn (leave in integral form): (d) Compute F0: (e) Compute Fl : 0 I n=0 W«:(Fn:4l/VI; “70 E: (1') Given input Fourier coefficient 6“ = IZn'ingall 9 system response H(co) = 1 1 + jw , fundamental frequency (00 = 2, write the equation for the output Fourier coefficient Yn in polar form. and . a m ~ . I I .I ‘ ‘2‘1 + Em an c0801(000 + bn Sm(n(0°t) 30.7 1' ZIP] (val-1 cos(ncnot + 6p) A-M a . n,yg(t)HGn,--e _ . - ' Evenfunc‘tiéfis‘“ - f(—t).=f(t)i ' f(t).= %Q.+Z;”;1aat:os(nw°t) -- “ f(-t)=—f(t) .— ' f(t)=::::1bnsin(nw°t)~ . n—I Pal; mtn2dt='z::_ognm2 F_n' = ...
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This note was uploaded on 04/04/2012 for the course ECE 210 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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10Sp_Exam2 - ECE 210/211 Analog Signal Processing Spring...

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