Practice Quiz 5 no calculators allowed e j 0t For problems 1 and 2 assume z 3 2 j 1 The magnitude of z z is equal to a 1 5 b 1 13 c e j 0t 5 d e j 0t 13 e none of these 2 The complex conjugate of z z is equal to a z e j 0t 3 2 j b z e j 0t e j 0t c z d none of these 3 2 j 3 2 j For problems 3 and 4 assume we know z 10 450 3 The magnitude of the conjugate of z z is equal to a 10 b 10 c 5 d 5 e none of these 4 The phase of the conjugate of z z is equal to a 450 b 450 c 00 d none of these 5 Are the functions v1 t 1 and v2 t t orthogonal over the interval 0 1 a Yes b No 6 Are the functions v1 t 1 and v2 t t orthogonal over the interval 1 1 a Yes b No 7 Are the functions v1 t e jk o t and v2 t e jm o t oTo 2 orthogonal over the interval 0 To a Yes b No where k m k and m are integers and 8 Using Euler s identity we can write cos t as a e j t e j t e j t e j t b 2 2 c e j t e j t 2j d e j t e j t 2j 9 Using Euler s identity we can write sin t as a e j t e j t e j t e j t b 2 2 c e j t e j t 2j d e j t e j t 2j For problems 10 and 11 assume we have an LTI system with impulse response h t e t u t 1 10 Is the system causal a yes b no 11 Is the system BIBO stable a yes b no 12 Assume x t 2 cos 3t is the input to an LTI system with transfer function H j 2e j In steady state the output of this system will be a y t 4 cos 3t e j 3 b y t 4 cos 3t 3 c y t 4 cos 3t 1 d none of these Problems 13 15 refer to a system with transfer function H s system is x t 2 cos 3t 30o 13 In steady state the magnitude of the output will be a 20 3 b 20 18 c 20 8 d 20 6 14 In steady state the phase of the output will be o a 30 o b 45 o o c 15 d 45 15 The bandwidth 3 dB point of the system is a 10 Hz b 10 radians sec c 3 radians sec d 3 Hz 10 Assume the input to this s 3 16 Assume x t 2 3cos t 3cos 4t 2 cos 6t is the input to an LTI system with the transfer function shown graphically magnitude and phase below 4 3 5 3 H j 2 5 2 1 5 1 0 5 0 10 8 6 4 2 0 2 Frequency rad sec 4 6 8 10 8 6 4 2 0 2 Frequency rad sec 4 6 8 10 50 40 30 H j degrees 20 10 0 10 20 30 40 50 10 The steady state output of the system will be a 0 b y t 2 3cos t 3cos 4t 2 cos 6t c y t 4 6 cos t 6 cos 6t d y t 4 6 cos t 30 6 cos 6t 45 e y t 2 6 cos t 300 6 cos 6t 450 0 0 f y t 4 3cos t 300 2 cos 6t 450 3cos t 300 2 cos 6t 450 g y t 4 6 cos t 300 6 cos 6t 450 6 cos t 300 6 cos 6t 450 h none of these 17 Assume x t 3cos 2t 5 is the input to a system with transfer function 3e j 2 H j 2 3 else the output y t in steady state will be a y t 6cos 2t 5 c y t 9 cos 2t 5 e b y t 9cos 2t 5 j4 d y t 9cos 2t 9 18 Assume x t 2cos 3t is the input to system with transfer function H j 2e j In steady state the output of the system will be a y t 4 cos 3t e j b y t 4 cos 3t e j 3 c y t 4cos 3t 3 d y t 4cos 3t 3 e none of these 19 Assume x t 2cos t 5sin 2t 6sin 3t is the input to a system with transfer function H j 3 In steady state the output of the system will be 5 a y t 2 cos t 5sin 2t 6sin 3t 3rect 5 b y t 6cos t 15sin 2t 18sin 3t c y t 6cos t 15sin 2t d none of these 20 Assume x t 2cos 3t 4cos 5t is the input to a system with transfer function given by 2 4 6 H j else 0 The output of the system in steady state will be a y t 4cos 3t 8cos 5t b y t 8cos 5t c y t 4cos 3t d none of these 21 Assume x t cos t cos 5t cos 9t is the input to a system with transfer function given below 4 3 5 3 H j 2 5 2 1 5 1 0 5 0 10 8 6 4 2 0 2 4 6 8 10 The output of this system in steady state will be a y t 4cos t 4cos 5t b y t 4cos t 2cos 5t cos 9t c y t 4cos t 2cos 5t d none of these Answers 1 b 2 c 3 a 4 b 5 b 6 a 7 a 8 a 9 d 10 b 11 a 12 b 13 b 14 c 15 c 16 d 17 d 18 c 19 c 20 b 21 c
View Full Document
Unlocking...