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# 09F_210Exam2 - ECE 210/211 Analog Signal Processing Fall...

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Unformatted text preview: ECE 210/211 Analog Signal Processing Fall 2009 University of Illinois Allen, Basar, Trick Exam 2 Thursday, October 22, 2009 — 7:00-8:15 PM Name: Section: circle one Class: ECE 210 ECE 211 circle one 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 (3) Compute the phasors associated with three signals below. f1(t)=25in(t+ 16‘.) FI= f t =-2C st 20 0 F2: f3 (t) = sin2t + Cos 2t F3= [V] = AV: (c) For the following signals, find period, fundamental frequency and average power for a IQ resistor. (i) f(t) = 2 Cos 10t + 5 sin 1005t T = (no Pav (ii) f(t) = 8 + 6 Cos 6t + 6 Cos (9t - 45°) T = we Pav Problem 2 (a) For the given circuit ﬁnd the open 5 09 5 0H a circuit voltage Vn (phasor) and the Thevenin equivalent impedance at V501) = terminals a-b. First draw the phasor 5 CO S t circuit in the box, then ﬁnd V0 and z. (b) What is the maximum available average power from the source, and what load impedance ZL connected to terminals a-b is necessary to receive the maximum available power? avg 4| Problem 3 Y (a) Determine the frequency response H(03) = ? for the following circuit. 19 ' + 1 Q f(oQ y(t) 2H ' ' H(03) = (b) Frequency response function of an LTI system is given as jw H0) =—— () 4-032+3j03 (i) Find its magnitude |H(03)| and sketch the magnitude spectrum for 0) > 0. 114(0))! (ii) If f(t) = 2 + 5 Cos t for this system, what is y(t) ? Problem 4 Justify your answers or no credit. (a) It can be shown that the Fourier coefﬁcients for this waveform are Fn = —J— cosnn,n=il,i2,etc. 117\$ . . . a ‘5” . Given the Fourier series f(t) = —° + 2 (an cos n wot+bnsm n wot) n=i 2 (b) Repeat Part (a) for this modiﬁed waveform. (c) Repeat Part (a) for this modiﬁed waveform. ...
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