![Problem 6) 13 marks] Consider the following LTI differential equation system where x(t) represents an input and y(t) indicates the corresponding output. dt2 dt (a) What is the transfer function of this system? (b) Is this system stable or not? Explain. (c) An input x(t)-e-t u(t) İs applied to the system. Which of the following plots can be the output y(t)? Circle your answer and Explain. [Note: A response with no justification will not receive any credits.]](http://img.homeworklib.com/questions/c16d3150-adef-11ea-bcf5-f7cea7ba880d.png?x-oss-process=image/resize,w_560)
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A DSP problem, can you help me solving this problem? O1) (10 points) The input x[n]...
A DSP problem, can you help me solving this problem?
O1) (10 points) The input x[n] and output y[n] of a causal discrete-time LTI system are related by Inn-1+In] The system input is given by x[n]-(n + 1)()nu[n] a) Find the system impulse response. b) Find the system output. esponse,
Help me do this problem step by step LSM1 Problem (50 pts) Consider a causal continuous-time...
Help me do this problem step by step
LSM1 Problem (50 pts) Consider a causal continuous-time LTI system with input-output relationship dt+)t). (a) Find the transfer function H(s) of the system and specify its ROC. (b) Find the impulse response h(t) of the system. (12 pts) (12 pts) (c) Using the convolution property of the Laplace transform, find the output y(t) of the system in response to the input (t)ut) e2-u(t 1 (26 pts)
please help. Note: u(t) is unit-step function Consider the system with the differential equation: dyt) +...
please help.
Note: u(t) is unit-step function Consider the system with the differential equation: dyt) + 2 dy(t) + 2y(t) = dr(t) – r(e) dt2 dt where r(t) is input and y(t) is output. 1. Find the transfer function of the system. Note that transfer function is Laplace transform ratio of input and output under the assumption that all initial conditions are zero. 2. Find the impulse response of the system. 3. Find the unit step response of the system...
- PLEASE ANSWER ALL QUESTIONS!! ALL QUESTIONS - PLEASE WRITE WITH GOOD HANDWRITING TO LET ME...
- PLEASE ANSWER ALL QUESTIONS!! ALL
QUESTIONS
- PLEASE WRITE WITH GOOD HANDWRITING TO LET ME
UNDERSTAND!
Q3. Consider a causal LTI system whose input and output are related by the following differential equation: dy(t) +4y(t) x(t) dt and the input is x(t) cos(2Tut) sin(4t), find: (a) The transfer function of the system H(ja) (5 m) (5 m) (10 m) (5 m) (b) The impulse response of the system h(t) (c) The output y(t) (d) The power of y(t)
Problem 3. The input and the output of a stable and causal LTI system are related...
Problem 3. The input and the output of a stable and causal LTI system are related by the differential equation dy ) + 64x2 + 8y(t) = 2x(t) dt2 dt i) Find the frequency response of the system H(jw) [2 marks] ii) Using your result in (i) find the impulse response of the system h(t). [3 marks] iii) Find the transfer function of the system H(s), i.e. the Laplace transform of the impulse response [2 marks] iv) Sketch the pole-zero...
PARTB 4. You are designing a system to enable a robot to stand on a trapeze. For small rotations, the robot can be assu...
PARTB 4. You are designing a system to enable a robot to stand on a trapeze. For small rotations, the robot can be assumed to obey the following differential equation d2 θ (t) dP--θ (t) = F(t) dt2 where θ(t) is the output angle (between the robot and a vertical reference) and F(1) is the input force exerted by a motor. a) Write the transfer function for the robot (ie a plant that converts the input to the output) b)...
a). Sketch y(t)...can you explain how you sketched it? b). Find Y(s) ) Consider the LTI...
a). Sketch y(t)...can you explain how you sketched it?
b). Find Y(s)
) Consider the LTI system shown below, - hít) | yết) x(t) where the input x(t) and impulse response h(t) are defined by the following plots: + x(t) ht)
3. (l’+2° +1²=4') Topic: Laplace transform, CT system described by differential equations, LTI system properties. Consider...
3. (l’+2° +1²=4') Topic: Laplace transform, CT system described by differential equations, LTI system properties. Consider a differential equation system for which the input x(t) and output y(t) are related by the differential equation d’y(t) dy(t) -6y(t) = 5x(t). dt dt Assume that the system is initially at rest. a) Determine the transfer function. b) Specify the ROC of H(s) and justify it. c) Determine the system impulse response h(t).
2.6.1 Consider a causal continuous-time LTI system described by the differential equation u"(t) +...
2.6.1-2.6.62.6.1 Consider a causal contimuous-time LTI system described by the differential equation$$ y^{\prime \prime}(t)+y(t)=x(t) $$(a) Find the transfer function \(H(s)\), its \(R O C\), and its poles.(b) Find the impulse response \(h(t)\).(c) Classify the system as stable/unstable.(d) Find the step response of the system.2.6.2 Given the impulse response of a continuous-time LTI system, find the transfer function \(H(s),\) the \(\mathrm{ROC}\) of \(H(s)\), and the poles of the system. Also find the differential equation describing each system.(a) \(h(t)=\sin (3 t) u(t)\)(b)...
UestionI. A system is represented by the following transfer function G(s)- (s+1)/(s2+5s+6) 1) Fin...
uestionI. A system is represented by the following transfer function G(s)- (s+1)/(s2+5s+6) 1) Find a state equation and state transition matrices (A,B, C and D) of the system for a step input 6u(t). ii) Find the state transition matrix eAt) ii) Find the output response of system y(t) to a step input 6u(t) using state transition matrix, iv) Obtain the output response y(t) of the system with two other methods for step input óu(t). Question IV. A system is described...
A DSP problem, can you help me solving this problem?
O1) (10 points) The input x[n] and output y[n] of a causal discrete-time LTI system are related by Inn-1+In] The system input is given by x[n]-(n + 1)()nu[n] a) Find the system impulse response. b) Find the system output. esponse,
Help me do this problem step by step
LSM1 Problem (50 pts) Consider a causal continuous-time LTI system with input-output relationship dt+)t). (a) Find the transfer function H(s) of the system and specify its ROC. (b) Find the impulse response h(t) of the system. (12 pts) (12 pts) (c) Using the convolution property of the Laplace transform, find the output y(t) of the system in response to the input (t)ut) e2-u(t 1 (26 pts)
please help.
Note: u(t) is unit-step function Consider the system with the differential equation: dyt) + 2 dy(t) + 2y(t) = dr(t) – r(e) dt2 dt where r(t) is input and y(t) is output. 1. Find the transfer function of the system. Note that transfer function is Laplace transform ratio of input and output under the assumption that all initial conditions are zero. 2. Find the impulse response of the system. 3. Find the unit step response of the system...
- PLEASE ANSWER ALL QUESTIONS!! ALL
QUESTIONS
- PLEASE WRITE WITH GOOD HANDWRITING TO LET ME
UNDERSTAND!
Q3. Consider a causal LTI system whose input and output are related by the following differential equation: dy(t) +4y(t) x(t) dt and the input is x(t) cos(2Tut) sin(4t), find: (a) The transfer function of the system H(ja) (5 m) (5 m) (10 m) (5 m) (b) The impulse response of the system h(t) (c) The output y(t) (d) The power of y(t)
Problem 3. The input and the output of a stable and causal LTI system are related by the differential equation dy ) + 64x2 + 8y(t) = 2x(t) dt2 dt i) Find the frequency response of the system H(jw) [2 marks] ii) Using your result in (i) find the impulse response of the system h(t). [3 marks] iii) Find the transfer function of the system H(s), i.e. the Laplace transform of the impulse response [2 marks] iv) Sketch the pole-zero...
PARTB 4. You are designing a system to enable a robot to stand on a trapeze. For small rotations, the robot can be assumed to obey the following differential equation d2 θ (t) dP--θ (t) = F(t) dt2 where θ(t) is the output angle (between the robot and a vertical reference) and F(1) is the input force exerted by a motor. a) Write the transfer function for the robot (ie a plant that converts the input to the output) b)...
a). Sketch y(t)...can you explain how you sketched it?
b). Find Y(s)
) Consider the LTI system shown below, - hít) | yết) x(t) where the input x(t) and impulse response h(t) are defined by the following plots: + x(t) ht)
3. (l’+2° +1²=4') Topic: Laplace transform, CT system described by differential equations, LTI system properties. Consider a differential equation system for which the input x(t) and output y(t) are related by the differential equation d’y(t) dy(t) -6y(t) = 5x(t). dt dt Assume that the system is initially at rest. a) Determine the transfer function. b) Specify the ROC of H(s) and justify it. c) Determine the system impulse response h(t).
2.6.1-2.6.62.6.1 Consider a causal contimuous-time LTI system described by the differential equation$$ y^{\prime \prime}(t)+y(t)=x(t) $$(a) Find the transfer function \(H(s)\), its \(R O C\), and its poles.(b) Find the impulse response \(h(t)\).(c) Classify the system as stable/unstable.(d) Find the step response of the system.2.6.2 Given the impulse response of a continuous-time LTI system, find the transfer function \(H(s),\) the \(\mathrm{ROC}\) of \(H(s)\), and the poles of the system. Also find the differential equation describing each system.(a) \(h(t)=\sin (3 t) u(t)\)(b)...
uestionI. A system is represented by the following transfer function G(s)- (s+1)/(s2+5s+6) 1) Find a state equation and state transition matrices (A,B, C and D) of the system for a step input 6u(t). ii) Find the state transition matrix eAt) ii) Find the output response of system y(t) to a step input 6u(t) using state transition matrix, iv) Obtain the output response y(t) of the system with two other methods for step input óu(t). Question IV. A system is described...
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