Practice Quiz 7 no calculators allowed 1 Assume x t is a periodic function with Fourier series representation x t c e x k jk o t x t is the input to an LTI system with output y t 3x t 2 The Fourier series coefficients cky are related to the ckx in which of the following ways a cky 3 jk 0 e jk o 2 ckx b cky 3 jk 0 e jk o 2 ckx c cky 3 jk 0 e jk o 2 ckx d cky 3 jk 0 e jk o 2 ckx Problems 2 5 refer to the following spectrum plot for a signal x t with fundamental frequency o 2 All angles are multiples of 90 degrees Magnitude 3 2 1 0 3 2 1 0 Harmonic 1 2 3 2 1 0 Harmonic 1 2 3 Phase degrees 100 0 100 200 3 2 What is the average value of x t a 13 3 What is the average power in x t a 13 13 7 13 b 7 b 13 5 d 3 c 35 d 3 c e 3 4 If x t is the input to a system with transfer function 2 1 3 H else 0 the output y t in steady state will be a 12 cos 2t b 4 cos 2t 90o c 8cos t 90o d 8 cos 2t 90o e 6cos 2t 5 The average power in y t is a 4 b 8 c 16 d 32 Problems 6 8 refer to the following plot all angles are multiples of 45 degrees 2 Amplitude 1 5 1 0 5 0 4 3 2 1 0 Harmonic 1 2 3 4 3 2 1 0 Harmonic 1 2 3 4 Phase degrees 200 100 0 100 4 6 Is this a valid spectrum plot for a real valued function x t a Yes b No 7 Assuming the magnitude portion of the spectrum is correct what is the average power in x t a 4 b 7 c 11 d 12 8 Assuming the plot is a valid spectrum plot for a real valued function x t the average value of x t is a 1 b 2 c 7 4 d 1 Problems 9 13 refer to the following Fourier series representation of a periodic signal k jkt 2 e2 k 2 jk x t 2 9 The average value of x t is a 1 b 2 c 3 d 4 10 The average power in the DC component of x t is a 1 b 2 c 4 d 8 e 9 f 18 11 If x t is the input to a system with transfer function 2 0 4 H else 0 the output y t in steady state will be a 0 b 3 c 6 d 1 79 cos 0 5t 26 6o e 6 3 58cos 0 5t 26 6o 12 If x t is the input to a system with transfer function 2 0 4 H else 0 the output y t in steady state will be a 2 x t b 2 x t 3 c 2 x t 6 d none of these 13 If x t is the input to a system with transfer function 0 0 4 0 6 H else 2 the output y t in steady state will be a 1 79 cos 0 5t 26 6o b 3 58 cos 0 5t 26 6o c 2 x t 1 79 cos 0 5t 26 6o d 2 x t 3 58cos 0 5t 26 6o For problems 14 and 15 assume x t 1 3sin 2t 45o 14 The average value of x t is a 0 b 1 c 2 d 4 15 The average power in x t is a 1 b 13 4 c 5 5 d 19 Problems 16 and 17 refer to the periodic function x t defined over one period T0 3 as x t t 0 t 3 which has the Fourier series representation x t 3 3 j jk 23 t e 2 k 0 k 2 16 The average power in x t is a 0 b 3 2 c 9 4 d 3 e 9 2 17 If this signal is the input to a transfer function H j 0 5e j 0 25 the steady state output will be j 0 25 c 0 5 t 0 25 d none of these a 0 5 t 0 25 b 0 5te Answers 1 c 2 e 3 c 6 b 7 c 8 d 9 c 10 e 11 c 14 b 15 c 16 d 4 d 5 d 12 c 13 d 17 a
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