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3. Given a signal x(t) = e-stuſt – 1), calculate its Laplace transform X(s) with ROC.
Laplace Transform 3. If the ROC for a Laplace Transform pair x(t) <-> X(s) contains the...
Laplace Transform
3. If the ROC for a Laplace Transform pair x(t) <-> X(s) contains the entire w . axis, which of the following two statements are true: The Fourier Transform for x(t) does not exist. The Fourier Transform for x(t) exists. The Fourier Transform for x(t) exists provided that x(t) is absolutely integrable, if not then it does not exist. The system is unstable. The system is stable. There is not enough information to determine existence or non-existence of...
Problem 1 (20 points) Given a signal x(t) = e-지디 1) Plot the signal x(t) in...
Problem 1 (20 points) Given a signal x(t) = e-지디 1) Plot the signal x(t) in time domain. 2) Find the Laplace transform X(s) of this signal. 3) Plot the pole-zero plot and the region of convergence (ROC).
Laplace Transform Problem 3. (15 points) Given f(t) = 4e-2tu(t) + 29u(-t) a) Using the Laplace...
Laplace Transform
Problem 3. (15 points) Given f(t) = 4e-2tu(t) + 29u(-t) a) Using the Laplace Transform table 9.2 find the bilinear Laplace transform, F($) and sketch the region of convergence (ROC) in the s-plane showing all poles. State the ROC as an inequality. b) Another function is added so that fa(t) = 4e-2tu(t) + 7u(-t) – 10e-10t u(-t). Find the Bilinear Laplace Transform of fa(t) and sketch the region of convergence in s-plane also showing all the poles. State...
A signal x(t) has the following Laplace transform X(s)= 2s+4 $2+45+5 Get x(t) (inverse Laplace Transform)...
A signal x(t) has the following Laplace transform X(s)= 2s+4 $2+45+5 Get x(t) (inverse Laplace Transform) (assume x(t)=0 for t<0) Answer:
Laplace Transform 4. If y(t) is of finite duration and x(t) is absolutely integrable then: į....
Laplace Transform
4. If y(t) is of finite duration and x(t) is absolutely integrable then: į. The ROC is the entire s-plane ii. The ROC is the entire s-plane except for maybe the origin iii. The ROC changes depending on the value of a in the transform such as x(t) = e -at u(t) <-> 1/(s+a)
4. Laplace Transform. (15 pts) Find the Laplace Transform of the following signals and sketch the...
4. Laplace Transform. (15 pts) Find the Laplace Transform of the following signals and sketch the corresponding pole-zero plot for each signal. In the plot, indicate the regions of convergence (ROC). Write X(s) as a single fraction in the form of DO (a) (5 pts)-(t-e*ta(t) + e-8tu(t). Show that X(s) =は,,늚. with ROC of Re(s) >-6. (b) (5 pts)-(t) = M(-t) +Au(-t). (c) (5 pts)-(t) 6(t)-a(-t). (s+6) (s+8)
1. Laplace Transform. (10 pts) Find the Laplace Transform of the following signals and sketch the...
1. Laplace Transform. (10 pts) Find the Laplace Transform of the following signals and sketch the corresponding pole-zero plot for each signal. In the plot, indicate the regions of convergence (ROC). Write X(s) as a single fraction in the forin of (a) (2 pts) z(t) = e-Mu(t) + e-6tu(t). Show that X(s)-AD10 (b) (4 pts)-(t) = e4ta(-t) + e8ta(-t). (c) (4 pts) (t)-(t)-u(-t) . with ROC of Re(s) >-4. (s+4)(8+6)
please solve this with clear answer and details Find the Laplace transform of the following signals...
please solve this with clear answer and details
Find the Laplace transform of the following signals and in each case determine the corresponding region of convergence: 3.4 (a) (b) the signal x(t)=e-ulu(t)-eatu-t)when (i) α > 0, (ii) α→0, a sampled signal Xi (t) = e (t n) CHAPTER 3: The Laplace Transform (c) the "stairs to heaven" signal (d) the sinusoidal signal r(t) [cos(2(1-1)) + sin(2π1)]a(1-1), (e) the signal y(t)=t2e-21 u(t) using that x(t)=tathasx(s)=2/s. Answers: (a) As α → 0,x(t)...
7. Find the inverse Laplace Transform of X(so2 with ROC-1< Rels) 1.
7. Find the inverse Laplace Transform of X(so2 with ROC-1< Rels) 1.
Find the Laplace transform of the following continuous-time signal. x(t)=2 e-*cos(30)u(t) Your answer: 5+1 X(s) =...
Find the Laplace transform of the following continuous-time signal. x(t)=2 e-*cos(30)u(t) Your answer: 5+1 X(s) = s? + 25 + 10 Ox(s) = 25+ 2 52 + 25 + 10 X(s)= 25+2 52 + 25 +9 o X(s)= 5 + 1 s²+25+9 X(s) = 35+3 52 +2s + 10
Laplace Transform
3. If the ROC for a Laplace Transform pair x(t) <-> X(s) contains the entire w . axis, which of the following two statements are true: The Fourier Transform for x(t) does not exist. The Fourier Transform for x(t) exists. The Fourier Transform for x(t) exists provided that x(t) is absolutely integrable, if not then it does not exist. The system is unstable. The system is stable. There is not enough information to determine existence or non-existence of...
Problem 1 (20 points) Given a signal x(t) = e-지디 1) Plot the signal x(t) in time domain. 2) Find the Laplace transform X(s) of this signal. 3) Plot the pole-zero plot and the region of convergence (ROC).
Laplace Transform
Problem 3. (15 points) Given f(t) = 4e-2tu(t) + 29u(-t) a) Using the Laplace Transform table 9.2 find the bilinear Laplace transform, F($) and sketch the region of convergence (ROC) in the s-plane showing all poles. State the ROC as an inequality. b) Another function is added so that fa(t) = 4e-2tu(t) + 7u(-t) – 10e-10t u(-t). Find the Bilinear Laplace Transform of fa(t) and sketch the region of convergence in s-plane also showing all the poles. State...
A signal x(t) has the following Laplace transform X(s)= 2s+4 $2+45+5 Get x(t) (inverse Laplace Transform) (assume x(t)=0 for t<0) Answer:
Laplace Transform
4. If y(t) is of finite duration and x(t) is absolutely integrable then: į. The ROC is the entire s-plane ii. The ROC is the entire s-plane except for maybe the origin iii. The ROC changes depending on the value of a in the transform such as x(t) = e -at u(t) <-> 1/(s+a)
4. Laplace Transform. (15 pts) Find the Laplace Transform of the following signals and sketch the corresponding pole-zero plot for each signal. In the plot, indicate the regions of convergence (ROC). Write X(s) as a single fraction in the form of DO (a) (5 pts)-(t-e*ta(t) + e-8tu(t). Show that X(s) =は,,늚. with ROC of Re(s) >-6. (b) (5 pts)-(t) = M(-t) +Au(-t). (c) (5 pts)-(t) 6(t)-a(-t). (s+6) (s+8)
1. Laplace Transform. (10 pts) Find the Laplace Transform of the following signals and sketch the corresponding pole-zero plot for each signal. In the plot, indicate the regions of convergence (ROC). Write X(s) as a single fraction in the forin of (a) (2 pts) z(t) = e-Mu(t) + e-6tu(t). Show that X(s)-AD10 (b) (4 pts)-(t) = e4ta(-t) + e8ta(-t). (c) (4 pts) (t)-(t)-u(-t) . with ROC of Re(s) >-4. (s+4)(8+6)
please solve this with clear answer and details
Find the Laplace transform of the following signals and in each case determine the corresponding region of convergence: 3.4 (a) (b) the signal x(t)=e-ulu(t)-eatu-t)when (i) α > 0, (ii) α→0, a sampled signal Xi (t) = e (t n) CHAPTER 3: The Laplace Transform (c) the "stairs to heaven" signal (d) the sinusoidal signal r(t) [cos(2(1-1)) + sin(2π1)]a(1-1), (e) the signal y(t)=t2e-21 u(t) using that x(t)=tathasx(s)=2/s. Answers: (a) As α → 0,x(t)...
7. Find the inverse Laplace Transform of X(so2 with ROC-1< Rels) 1.
Find the Laplace transform of the following continuous-time signal. x(t)=2 e-*cos(30)u(t) Your answer: 5+1 X(s) = s? + 25 + 10 Ox(s) = 25+ 2 52 + 25 + 10 X(s)= 25+2 52 + 25 +9 o X(s)= 5 + 1 s²+25+9 X(s) = 35+3 52 +2s + 10
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