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Problem 3 (5 points): If K is an integer, an LTI system is given by, emis of t hete tem scausa.
Problem 1: Let the impulse response of an LTI system be given by 0 t< h(t)...
Problem 1: Let the impulse response of an LTI system be given by 0 t< h(t) = 〉 1 0 < t < 1 0 t>1 Find the output y(t) of this system if the input is given by a) x(t) = 1 + cos(2nt) b) x(t)-cos(Tt) c) x(t) sin (t )l d) x(t) = 1 0 < t < 10 0 t 10 e) x(t) = δ(t-2)-5(t-4) f) a(t)-etu(t) Problem 2: For the same LTI system in Problem 1,...
3-(10 points) Consider a C-T. LTI system given below X(t) - h(t) y(t) The impulse response...
3-(10 points) Consider a C-T. LTI system given below X(t) - h(t) y(t) The impulse response is h(t)=sinc(200t). We apply an input signal x(t)=sinc(100t) to produce the output y(t). Find and plot Y(m). Find y(t).
5. The figure below shows a system consisting of a continous- time LTI system followed by a sampler (, conver...
5. The figure below shows a system consisting of a continous- time LTI system followed by a sampler (, conversion to a sequence (, and an LTI discrete-time system. The continous-time LTI system is causal and satisfies the linear, constant-coefficient differential equation The input is a unit impulse a. Determine . (10 points) b. Determine the frequency response and the impulse response such that. (10 points). Conversiony(n) of %(t) w(n) inpuse train H(ew) to a sequence P(t) low shows a...
Problem #2 Consider a continuous-time LTI system given by: dy[ + 2y(t) = x(t). Using the...
Problem #2 Consider a continuous-time LTI system given by: dy[ + 2y(t) = x(t). Using the Fourier transform, find the output y(t) to each of the following input signals: (a) x(t) = e-'u(t), and (b) x(t) = u(t).
4. Consider a CT LTI system whose impulse response is given by h(t)( 3) (t 2))...
4. Consider a CT LTI system whose impulse response is given by h(t)( 3) (t 2)) (a) Sketch h(t), and label a mportant points. 2 2. b) Is the system causal? Circle your answer. No justification needed yes r ノ(c) Is the system stable? Circle your answer. No justification needed. or no ye d) Suppose the input to the system is r(t) ut 5). Over what range of t is the system output not equal to 0? Circle your answer....
2.7.5 The impulse response of a continuous-time LTI system is given by h(t) = f(t) -...
2.7.5 The impulse response of a continuous-time LTI system is given by h(t) = f(t) - et u(t). (a) What is the frequency response H (w) of this system? (b) Find and sketch H(w). (c) Is this a lowpass, bandpass, or highpass filter, or none of those? 2.7.6 The impulse response of a continuous-time LTI system is given by h(t) = S(t – 2). (This is a delay of 2.) (a) What is the frequency response H (w) of this...
Given a zero-state LTI system whose impulse response h(t) = u(t) u(t-2), if the input of...
Given a zero-state LTI system whose impulse response h(t) = u(t) u(t-2), if the input of the system is r(t), find the system equation which relates the input to the output y(t) 4. (20 points) If a causal signal's s-domain representation is given as X (s) = (s+ 2)(s2 +2s + 5) (a) find all the poles and zero of the function. 2 1 52243 orr
Question 5 An LTI system has an input signal given by x(t) = e-tu(t). The output...
Question 5 An LTI system has an input signal given by x(t) = e-tu(t). The output of the system is measured and found out to be given by y(t) = e-tu (t) + e-t+1 u(t-1). Find the system transfer function, H(s) 4 marks a. b. Find the system impulse response, h(t) 4 marks c. Describe in words what is the functionality of this svstem (i.e., what does it do on the inputs sigmal to produce the output simal?). [2 marks]
Consider the LTI system. Design a state-feedback control law of the form u(t)= -kx(t) such that...
Consider the LTI system. Design a state-feedback control law of
the form u(t)= -kx(t) such that x(t) goes to zero faster than
e^-t;
Problem 1: (15 points) Consider the LTI system 3 -1 (t)1 3 0 (t)2ut 0 0-1 Desig lim sate-feedback control law of the form u(t)ka(t) such that (t goes to zero faster than e i.e. Hint: fhink of where you want to place the eigenvalues of the closed-loop system.
3. Problem 3: (20 pts) Figure 1: Problem 3 An LTT system consisting of two LTI...
3. Problem 3: (20 pts) Figure 1: Problem 3 An LTT system consisting of two LTI subsystems are shown in the Figure 1. Let the frequency responses of the two subsystems h, and hy be defined as: SMC5 HGW) = H ) = 10 otherwise 10 otherwise Let z(t) = 4008°() +-* sin(3) be the input into the system. (a) Determine , 's and wi's such that z(t) = d.get (10 pts) (b) Use the property of LTI system with...
Problem 1: Let the impulse response of an LTI system be given by 0 t< h(t) = 〉 1 0 < t < 1 0 t>1 Find the output y(t) of this system if the input is given by a) x(t) = 1 + cos(2nt) b) x(t)-cos(Tt) c) x(t) sin (t )l d) x(t) = 1 0 < t < 10 0 t 10 e) x(t) = δ(t-2)-5(t-4) f) a(t)-etu(t) Problem 2: For the same LTI system in Problem 1,...
3-(10 points) Consider a C-T. LTI system given below X(t) - h(t) y(t) The impulse response is h(t)=sinc(200t). We apply an input signal x(t)=sinc(100t) to produce the output y(t). Find and plot Y(m). Find y(t).
5. The figure below shows a system consisting of a continous- time LTI system followed by a sampler (, conversion to a sequence (, and an LTI discrete-time system. The continous-time LTI system is causal and satisfies the linear, constant-coefficient differential equation The input is a unit impulse a. Determine . (10 points) b. Determine the frequency response and the impulse response such that. (10 points). Conversiony(n) of %(t) w(n) inpuse train H(ew) to a sequence P(t) low shows a...
Problem #2 Consider a continuous-time LTI system given by: dy[ + 2y(t) = x(t). Using the Fourier transform, find the output y(t) to each of the following input signals: (a) x(t) = e-'u(t), and (b) x(t) = u(t).
4. Consider a CT LTI system whose impulse response is given by h(t)( 3) (t 2)) (a) Sketch h(t), and label a mportant points. 2 2. b) Is the system causal? Circle your answer. No justification needed yes r ノ(c) Is the system stable? Circle your answer. No justification needed. or no ye d) Suppose the input to the system is r(t) ut 5). Over what range of t is the system output not equal to 0? Circle your answer....
2.7.5 The impulse response of a continuous-time LTI system is given by h(t) = f(t) - et u(t). (a) What is the frequency response H (w) of this system? (b) Find and sketch H(w). (c) Is this a lowpass, bandpass, or highpass filter, or none of those? 2.7.6 The impulse response of a continuous-time LTI system is given by h(t) = S(t – 2). (This is a delay of 2.) (a) What is the frequency response H (w) of this...
Given a zero-state LTI system whose impulse response h(t) = u(t) u(t-2), if the input of the system is r(t), find the system equation which relates the input to the output y(t) 4. (20 points) If a causal signal's s-domain representation is given as X (s) = (s+ 2)(s2 +2s + 5) (a) find all the poles and zero of the function. 2 1 52243 orr
Question 5 An LTI system has an input signal given by x(t) = e-tu(t). The output of the system is measured and found out to be given by y(t) = e-tu (t) + e-t+1 u(t-1). Find the system transfer function, H(s) 4 marks a. b. Find the system impulse response, h(t) 4 marks c. Describe in words what is the functionality of this svstem (i.e., what does it do on the inputs sigmal to produce the output simal?). [2 marks]
Consider the LTI system. Design a state-feedback control law of
the form u(t)= -kx(t) such that x(t) goes to zero faster than
e^-t;
Problem 1: (15 points) Consider the LTI system 3 -1 (t)1 3 0 (t)2ut 0 0-1 Desig lim sate-feedback control law of the form u(t)ka(t) such that (t goes to zero faster than e i.e. Hint: fhink of where you want to place the eigenvalues of the closed-loop system.
3. Problem 3: (20 pts) Figure 1: Problem 3 An LTT system consisting of two LTI subsystems are shown in the Figure 1. Let the frequency responses of the two subsystems h, and hy be defined as: SMC5 HGW) = H ) = 10 otherwise 10 otherwise Let z(t) = 4008°() +-* sin(3) be the input into the system. (a) Determine , 's and wi's such that z(t) = d.get (10 pts) (b) Use the property of LTI system with...
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