Fourier transform from Laplace transform-The Fourier transform of finite support signals, which a...
Problem 8.3.1 Determine the Laplace transform of the following signals using Laplace Transform table and the time-shifting property. In other words, represent each signal using functions with known Laplace transforms, and then apply time-shifting property to find Laplace transform of the signals. thre (e) Optional: find the Laplace transforms and the ROC for the above signals using direct integration. Problem 8.3.2 Find the Laplace transforms of the following functions using Laplace Transform table and the time-shifting property (if needed) of...
5.5 Starting with the Fourier transform pair 2 sin(S2) X(t) = u(t + 1) – ut - 1) = X(92) = S2 and using no integration, indicate the properties of the Fourier transform that will allow you to compute the Fourier transform of the following signals (do not find the Fourier transforms): (a) xz(t) = -u(t + 2) + 2u(t) – u(t – 2) (b) xz(t) = 2 sin(t)/t (C) X3 (t) = 2[u(t + 0.5) - ut - 0.5)]...
Q4) Calculate the Fourier transform of the following time domain signals. Use the properties of the Fourier transform found in the "Properties of Fourier Transforms" table in textbook and the "Famous Fourier Transforms Table" in textbook instead of direct integration as much as possible to simplify your calculation wherever appropriate: 2-2
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)
Please answer all questions with math detail 3. (21 points) Laplace Transform (a) (15 points) Find the Laplace transforms of the following signals and determine their region of convergence sinwot)-iu i. f(t) -i, e-2(t-3 2<t otherwise (b) (6 points) The Laplace transform of a causal signal x(t) is given by X (s) = s2 , ROC: Re{s) > -1 Which of the following Fourier transforms can be obtained from X(s) without actu- ally determining the signal x(t)? In each case,...
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...
Find and plot the Fourier transforms of the following signals. (if the Fourier transform is a complex function, plot the magnitude absolute value) and phase (argument) parts separately) [70 points]. [Hint: You can use the time shifting property if applicable] 5, 0 <ts3 Xs(t)-〈0, otherwise
3) (Fourier Transforms Using Properties) - Given that the Fourier Transform of a signal x(t) is X(f) - rect(f/ 2), find the Fourier Transform of the following signals using properties of the Fourier Transform: (a) d(t) -x(t - 2) (d) h(t) = t x( t ) (e) p(t) = x( 2 t ) (f) g(t)-x( t ) cos(2π) (g) s(t) = x2(t ) (h)p()-x(1)* x(t) (convolution) 3) (Fourier Transforms Using Properties) - Given that the Fourier Transform of a signal...
Problem 7.3 r(t) has the Fourier transform Xjw Determine the Fourier transforms of the following signals. (a) Fal)-5r(3t -2) (b) r(t)(t 1)sin(2t) (c) elt)5) HINT: Find the value of r(t) first. (d) ralt) (t)cos(2mt
In MATLAB Use symbolic math to solve and plot Laplace Problem 3.17. Problem 3.17 Obtain the inverse Laplace transform of each of the following 4(s-4) x1(s) 22+16) a. 4 4s b. x2s) (s2+9) (s+5)e 25 x3(s)(s+1)(s+3) c. In MATLAB Use symbolic math to solve and plot Laplace Problem 3.17. Problem 3.17 Obtain the inverse Laplace transform of each of the following 4(s-4) x1(s) 22+16) a. 4 4s b. x2s) (s2+9) (s+5)e 25 x3(s)(s+1)(s+3) c.