5) Using Euler’s identity, we can write asa) b) c) d)6) Using Euler’s identity, we can write asa) b) c) d)Practice Quiz 6(no calculators allowed)Problems 1 and 2 refer to the following transfer functions1 23 4( ) cos( )( ) ( 1)( ) ( )2( )tth h t t u th he u ttt u t-= +� �=P =� �� �=1) Which of these systems are causal?2) Which of these systems are BIBO stable?3) Is the system 1( ) sin( ) 1y tx t� �=� �-� � BIBO stable? a) yes b) no4) Is the system ( ) 11( )x ty te-= BIBO stable? a) yes b) no5) Using Euler’s identity, we can write cos( )tw asa) 2j t j te ejw w-+ b) 2j t j te ew w-- c) 2j t j te ew w-+ d) 2j t j te ejw w--6) Using Euler’s identity, we can write sin( )tw asa) 2j t j te ew w-+ b) 2j t j te ejw w-- c) 2j t j te ejw w-+ d) 2j t j te ew w--7) Assume we are going to synthesize a periodic signal( )x t using 0( )jk tkx t c ew=� where21kjck=+. Will ( )x t be a real valued function? a) Yes b) No8) Assume we are going to synthesize a periodic signal( )x t using 0( )jk tkx t c ew=� where1kjkcjk=+. Will ( )x t be a real valued function? a) Yes b) No9) Assume ( )x t is a periodic function with period 2T = seconds. ( )x t is defined over one period as ( ) , 1 1x t t t= - < <. The average power in ( )x t (the power averaged over one period) isa) 0 b) 12 c) 13 d) 23Problems 10-14 refer to the following spectrum plot for a signal ( )x t with fundamental frequency2ow =. All angles are multiples of 90 degrees.-3 -2 -1 0 1 2 30123MagnitudeHarmonic-3 -2 -1 0 1 2 3-200-1000100Phase (degrees)Harmonic10) What is the average value of ( )x t? a) 13 b) 137 c) 135 d) 3 e) -311) What is the average power in ( )x t? a) 13 b) 137 c) 35 d) 312) What is the average power in the DC component of ( )x t ? a) 0 b) 3 c) 6 d) 9 e) 1813) 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 asa) ( ) 3 4cos(2 ) 6cos( )90 4ox t t t+=- + + b) ( ) 3 4cos(2 90 ) 6cos(4 )ox t t t= + + +c) ( ) 3 2cos(2 90 ) 3cos(4 )ox t t t= + + + d) ( ) 3 2cos(2 ) 3cos( )90 4ox t t t+=- + +e) ) 4cos( 2 90 ) 6cos(4 ) 6 cos( 4 )( ) 3 4 cos(2 90o ox t tt t t+ - - + ++ -=- +Problems 15-17 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)Harmonic15) Is this a valid spectrum plot for a real valued function( )x t? a) Yes b) No16) 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 isa) 1 b) 2 c) 74 d) -1 Problems 18 and 19 refer to the following Fourier series representation 22( ) 22jktkkx t ejk=�=- �= ++�18) The average value of ( )x t is a) 0 b) 1 c) 2 d) 319) The fundamental frequency (in Hz) is a)12p b) 0.5 c) 14p d) 220) Assume( ) 2 2 cos(3 ) 5cos(6 3)x t t t= + + + is the input to an LTI system with transfer function 22 1 | | 4) 4 4 | | 80(jjeeH jelsewwww w--�< <�= < <���The steady state output of the system is a) ( ) 4cos(3 3) 20cos(6 12)y t t t= - + - b) ( ) 4cos(3 3) 20cos(6 6)y t t t= - + -c)( ) 4cos(3 3) 10cos(6 12)y t t t= - + - d) none of theseAnswers: 1-42,h h, 2-1 3,h h, 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,
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