A continuous-time LTI system has unit impulse response h(t). The Laplace transform of h(t), also called the “transfer function” of the LTI system, is
.
For each of the following cases, determine the region of convergence (ROC) for H(s) and the corresponding h(t), and determine whether the Fourier transform of h(t) exists.
(a) The LTI system is causal but not stable.
(b) The LTI system is stable but not causal.
(c) The LTI system is neither stable nor causal
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A continuous-time LTI system has unit impulse response h(t). The
Laplace transform of h(t), also called...
Consider a continuous-time LTI system impulse response h(t) as given below. h(t) = 2/3 e^-tu(t)-1/3 e^2t...
Consider a continuous-time LTI system impulse response h(t) as given below. h(t) = 2/3 e^-tu(t)-1/3 e^2t u(-t) (a) Determine Laplace Transform H(s) of h(t). Determine and clearly sketch its ROC. (b) Is it possible to find the Fourier Transform H(j!) of h(t) by using Laplace Transform? If possible, determine H(j!). Why, or why not? Explain. (c) Is this system causal? Is this system stable? Explain your answers.
a continuous time causal LTI system has a transfer function: H(s)=(s+3)/(s^2 +3s +2) a) find the...
a continuous time causal LTI system has a transfer function: H(s)=(s+3)/(s^2 +3s +2) a) find the poles and zeros b) indicate the poles and the zeros on the s-plane indicate the region of convergence (ROC) c) write the differential equation of the system. d) determine the gain of the system at dc (ie the transfer function at w=0) e) is the system described by H(s) stable? explain f) for the system described by H(s), does the Fourier transform H(jw) exist?...
Term brua 2019 Instructor: Ahnet A 1. Determine the Laplace transform and the associated region of...
Term brua 2019 Instructor: Ahnet A 1. Determine the Laplace transform and the associated region of convergence and pole-zero plot for each of the following functions of time (b) r(t)te-24 elsewhere (d) a(t) (t)+u(t) 2. Determine the function of time, a(t), for each of the following Laplace transforms and their associated regions of convergenice: )부부, Rds) > 1 d)승부 R1(s) >-1 3. Consider an LTI systern with input r(t)-ε-lu(t) and impulse response h(t)-e-2u(t). (a) Determine the Laplace transforms of ar(t)...
Problem 6 (20 pts) Suppose that the impulse response of a causal LTI system has a...
Problem 6 (20 pts) Suppose that the impulse response of a causal LTI system has a Laplace transform which is given by 5+1 H(3) and that the input to this system is x(t) = ell! $+ 25 +2 a) Determine the Laplace transform of the output y(t), along with its associated region of convergence. (12 pts) b) Determine the output y(t). (8 pts)
Question 1 (10 pts): Consider the continuous-time LTI system S whose unit impulse response h is given by Le., h consists of a unit impulse at time 0 followed by a unit impulse at time (a) (2pts)...
Question 1 (10 pts): Consider the continuous-time LTI system S whose unit impulse response h is given by Le., h consists of a unit impulse at time 0 followed by a unit impulse at time (a) (2pts) Obtain and plot the unit step response of S. (b) (2pts) Is S stable? Is it causal? Explain Two unrelated questions (c) (2pts) Is the ideal low-pass continuous-time filter (frequency response H(w) for H()0 otherwise) causal? Explain (d) (4 pts) Is the discrete-time...
Assume amplitude a = 4 The input to an LTI system is shown in the graph...
Assume amplitude a = 4
The input to an LTI system is shown in the graph below. Assume a = 4. X(t) 20 t @ by 0 Ingineering Given that the Laplace transform of the output is Y(s) = - (s + 3)(1 – e-45)2 s(s + 5)2 a) Find the transfer function of the system and the region of convergence for o = Re(s). H(s) = RoC: For regions of convergence, answer in interval notation e.g. (-INF, a),(a,b) or...
Question 6 1 pts An LTI system has impulse response h[n] = (-1)”[n+1] Is the system...
Question 6 1 pts An LTI system has impulse response h[n] = (-1)”[n+1] Is the system causal? Is it stable? (a) It is both causal and stable. (b) It is causal, but not stable. (e) It is stable, but not causal. (d) It is neither stable, nor causal (e) The system is stable, but the information provided is insufficient to determine causality (f) The system is elusal, but the information provided is insufficient to determine stability (g) Neither causality nor...
Laplace Transform 5. Given a causal LTI system with pole-zero cancellation such as H(s)= S+1 what...
Laplace Transform
5. Given a causal LTI system with pole-zero cancellation such as H(s)= S+1 what is the region of convergence and why. (5+1)(3+2) i. ROC = undefined ii. ROC = Re(s) > 0 iii. ROC = Re(s) >-2 iv. ROC = Re(s) >-1
Problem 2 (3 points) Given the unilateral Laplace transform of the impulse response for a causal...
Problem 2 (3 points) Given the unilateral Laplace transform of the impulse response for a causal system H(s) Determine h(t) the impulse response? Hint synthetic division! (s+10) 40 t-10 Problem 3 a) (2 points) What is the initial value of time function f(t) corresponding to the one sided Laplace Transform F(s) = (i.e. f(t) is causal) s(s+10)(2+4) lim f(t) = 0 40 lim f(t) = 1. t-0 10 x 4 lim f(t) = 0 t-0 lim f(t) cannot be computed...
Signal and Systems Problem 2 (3 points) Given the unilateral Laplace transform of the impulse response...
Signal and Systems
Problem 2 (3 points) Given the unilateral Laplace transform of the impulse response for a causal system H(s) Determine h(t) the impulse response? Hint synthetic division! (s+10) 40 t-10 Problem 3 a) (2 points) What is the initial value of time function f(t) corresponding to the one sided Laplace Transform F(s) = (i.e. f(t) is causal) s(s+10)(2+4) lim f(t) = 0 40 lim f(t) = 1. t-0 10 x 4 lim f(t) = 0 t-0 lim f(t)...
Term brua 2019 Instructor: Ahnet A 1. Determine the Laplace transform and the associated region of convergence and pole-zero plot for each of the following functions of time (b) r(t)te-24 elsewhere (d) a(t) (t)+u(t) 2. Determine the function of time, a(t), for each of the following Laplace transforms and their associated regions of convergenice: )부부, Rds) > 1 d)승부 R1(s) >-1 3. Consider an LTI systern with input r(t)-ε-lu(t) and impulse response h(t)-e-2u(t). (a) Determine the Laplace transforms of ar(t)...
Problem 6 (20 pts) Suppose that the impulse response of a causal LTI system has a Laplace transform which is given by 5+1 H(3) and that the input to this system is x(t) = ell! $+ 25 +2 a) Determine the Laplace transform of the output y(t), along with its associated region of convergence. (12 pts) b) Determine the output y(t). (8 pts)
Question 1 (10 pts): Consider the continuous-time LTI system S whose unit impulse response h is given by Le., h consists of a unit impulse at time 0 followed by a unit impulse at time (a) (2pts) Obtain and plot the unit step response of S. (b) (2pts) Is S stable? Is it causal? Explain Two unrelated questions (c) (2pts) Is the ideal low-pass continuous-time filter (frequency response H(w) for H()0 otherwise) causal? Explain (d) (4 pts) Is the discrete-time...
Assume amplitude a = 4
The input to an LTI system is shown in the graph below. Assume a = 4. X(t) 20 t @ by 0 Ingineering Given that the Laplace transform of the output is Y(s) = - (s + 3)(1 – e-45)2 s(s + 5)2 a) Find the transfer function of the system and the region of convergence for o = Re(s). H(s) = RoC: For regions of convergence, answer in interval notation e.g. (-INF, a),(a,b) or...
Question 6 1 pts An LTI system has impulse response h[n] = (-1)”[n+1] Is the system causal? Is it stable? (a) It is both causal and stable. (b) It is causal, but not stable. (e) It is stable, but not causal. (d) It is neither stable, nor causal (e) The system is stable, but the information provided is insufficient to determine causality (f) The system is elusal, but the information provided is insufficient to determine stability (g) Neither causality nor...
Laplace Transform
5. Given a causal LTI system with pole-zero cancellation such as H(s)= S+1 what is the region of convergence and why. (5+1)(3+2) i. ROC = undefined ii. ROC = Re(s) > 0 iii. ROC = Re(s) >-2 iv. ROC = Re(s) >-1
Problem 2 (3 points) Given the unilateral Laplace transform of the impulse response for a causal system H(s) Determine h(t) the impulse response? Hint synthetic division! (s+10) 40 t-10 Problem 3 a) (2 points) What is the initial value of time function f(t) corresponding to the one sided Laplace Transform F(s) = (i.e. f(t) is causal) s(s+10)(2+4) lim f(t) = 0 40 lim f(t) = 1. t-0 10 x 4 lim f(t) = 0 t-0 lim f(t) cannot be computed...
Signal and Systems
Problem 2 (3 points) Given the unilateral Laplace transform of the impulse response for a causal system H(s) Determine h(t) the impulse response? Hint synthetic division! (s+10) 40 t-10 Problem 3 a) (2 points) What is the initial value of time function f(t) corresponding to the one sided Laplace Transform F(s) = (i.e. f(t) is causal) s(s+10)(2+4) lim f(t) = 0 40 lim f(t) = 1. t-0 10 x 4 lim f(t) = 0 t-0 lim f(t)...
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