Practice Quiz 7 (no calculators allowed) 1) Assume ()xt is a periodic function with Fourier series representation ()ojk txkxtceω=∑. ()xt is the input to an LTI system with output () 3 ( 2)yt xt=−. The Fourier series coefficients ykc are related to the xkc in which of the following ways a) 203ojkyxkkcjkeωω+= c b) 203ojkyxkkcjkeωω−=− c c) 203ojkyxkkcjkeωω−= c d) 203ojkyxkkcjkeωω+=− c Problems 2-5 refer to the following spectrum plot for a signal ()xt with fundamental frequency2oω=. All angles are multiples of 90 degrees. -3 -2 -1 0 1 2 30123MagnitudeHarmonic-3 -2 -1 0 1 2 3-200-1000100Phase (degrees)Harmonic 2) What is the average value of ()xt? a) 13 b) 137 c) 135 d) 3 e) -3 3) What is the average power in ()xt? a) 13 b) 137 c) 35 d) 3 4) If ()xt is the input to a system with transfer function 21| |3()0Helseωω<<⎧=⎨⎩ the output in steady state will be ()yt a) 12 b) c) 8c d) 8 e) 6c cos(2 )t4cos(2 90 )ot + os( 90 )ot + cos(2 90 )ot +os(2 )t 5) The average power in y(t) is a) 4 b) 8 c) 16 d) 32Problems 6-8 refer to the following plot (all angles are multiples of 45 degrees) -4 -3 -2 -1 0 1 2 3 400.511.52AmplitudeHarmonic-4 -3 -2 -1 0 1 2 3 4-1000100200Phase (degrees)Harmonic 6) Is this a valid spectrum plot for a real valued function()xt? a) Yes b) No 7) Assuming the magnitude portion of the spectrum is correct, what is the average power in()xt? a) 4 b) 7 c) 11 d) 12 8) Assuming the plot is a valid spectrum plot for a real valued function ()xt, the average value of ()xt is a) 1 b) 2 c) 74 d) -1Problems 9-13 refer to the following Fourier series representation of a periodic signal 22() 22jktkkxtejk=∞=−∞=++∑ 9) The average value of ()xt is a) 1 b) 2 c) 3 d) 4 10) The average power in the DC component of ()xt is a) 1 b) 2 c) 4 d) 8 e) 9 f) 18 11) If ()xtis the input to a system with transfer function 2| |0.4()0Helseωω<⎧=⎨⎩ the output in steady state will be ()yt a) 0 b) 3 c) 6 d) 1.79 e) 6 cos(0.5 26.6 )ot − 3.58cos(0.5 26.6 )ot+− 12) If ()xtis the input to a system with transfer function 2| |0.4()0Helseωω>⎧=⎨⎩ the output in steady state will be ()yt a) 2()xt b) c) d) none of these 2() 3xt − 2() 6xt − 13) If ()xtis the input to a system with transfer function 00.4||0.6()2Helseωω<<⎧=⎨⎩ the output in steady state will be ()yt a) 1.79 b) 3.58 cos(0.5 26.6 )ot − cos(0.5 26.6 )ot −c) d) 2 ( ) 1.79cos(0.5 26.6 )oxt t−−2 ( ) 3.58cos(0.5 26.6 )oxt t−−For problems 14 and 15, assume () 1 3sin(2 45)oxt t=+ + 14) The average value of ()xt is a) 0 b) 1 c) 2 d) 4 15) The average power in ()xt is a) 1 b) 134 c) 5.5 d) 19 Problems 16 and 17 refer to the periodic function ()xt defined over one period as 03T =() 0 3xtt t=≤< which has the Fourier series representation 23033()22jk tkjxt ekππ≠=+∑ 16) The average power in()xt is a) 0 b)32 c) 94 d) 3 e) 92 17) If this signal is the input to a transfer function 0.25()0.5jHj eωω−=, the steady state output will be a) 0.5 b) ( 0.25)t −0.250.5jteω− c) 0.5( 0.25)t+ d) none of these Answers: 1) c 2) e 3) c 4) d 5) d 6) b 7) c 8) d 9) c 10) e 11) c 12) c 13) d 14) b 15) c 16) d 17)
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