Practice Quiz 6 no calculators allowed Problems 1 and 2 refer to the following transfer functions h1 t e t u t 1 h2 t cos t u t t h3 t P 2 h4 u t 1 Which of these systems are causal 2 Which of these systems are BIBO stable 1 y t sin x t 1 BIBO stable 3 Is the system 1 y t x t 1 e 4 Is the system BIBO stable a yes b no a yes b no 5 Using Euler s identity we can write cos wt as e jwt e jwt e jwt e jwt 2j 2 a b e jwt e jwt 2 c e jwt e jwt 2j d 6 Using Euler s identity we can write sin wt as e jwt e jwt e jwt e jwt 2j 2 a b e jwt e jwt 2j c e jwt e jwt 2 d x t ck e jkw0t 7 Assume we are going to synthesize a periodic signal x t using where j ck 1 k 2 Will x t be a real valued function a Yes b No x t ck e jkw0t x t 8 Assume we are going to synthesize a periodic signal using where jk ck 1 jk Will x t be a real valued function a Yes b No 9 Assume x t is a periodic function with period T 2 seconds x t is defined over one period as x t t 1 t 1 The average power in x t the power averaged over one period is a 0 1 b 2 1 c 3 2 d 3 Problems 10 14 refer to the following spectrum plot for a signal x t with fundamental frequency wo 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 10 What is the average value of x t a 13 11 What is the average power in x t a 13 13 b 7 13 b 7 13 c 5 d 3 c 35 d 3 12 What is the average power in the DC component of x t a 0 b 3 c 6 d 9 e 18 13 What is the average power in the second harmonic of x t a 3 b 6 c 9 d 18 14 We can write x t as o a x t 3 4 cos 2t 90 6cos 4t o c x t 3 2cos 2t 90 3cos 4t o b x t 3 4 cos 2t 90 6cos 4t o d x t 3 2 cos 2t 90 3cos 4t o o e x t 3 4 cos 2t 90 4 cos 2t 90 6cos 4t 6 cos 4t e 3 Problems 15 17 refer to the following plot all angles are multiples of 45 degrees Amplitude 2 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 15 Is this a valid spectrum plot for a real valued function x t a Yes b No 16 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 17 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 7 c 4 d 1 Problems 18 and 19 refer to the following Fourier series representation jkt k 2 x t 2 e2 2 jk k 18 The average value of x t is a 0 b 1 c 2 d 3 19 The fundamental frequency in Hz is 1 a 2p 1 b 0 5 c 4p d 2 20 Assume x t 2 2 cos 3t 5cos 6t 3 is the input to an LTI system with transfer function 2e jw 1 w 4 j 2w H jw 4e 4 w 8 0 else The steady state output of the system is a y t 4 cos 3t 3 20 cos 6t 12 b y t 4 cos 3t 3 20 cos 6t 6 c y t 4 cos 3t 3 10 cos 6t 12 d none of these Answers 1 h2 h4 2 h1 h3 3 a 4 a 5 c 6 b 7 b 8 a 9 c 10 e 11 c 12 d 13 d 14 a 15 b 16 c 17 d 18 d 19 c 20 d
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