Obtain the Laplace transform of the functions plotted in Figures 1 and 2. Obtain the Laplace transform of the functions plotted in Figures 1 and 2. ft) f(t) 14 0 10 20 30 40 Figure 1 Figure 2
to transform any formula into a Conjunctive Prove that the procedure normal form preserves satisfiability, i.e. if the original formula is satisfiable, then the obtain formula is also satisfiable. to transform any formula into a Conjunctive Prove that the procedure normal form preserves satisfiability, i.e. if the original formula is satisfiable, then the obtain formula is also satisfiable.
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)
1. Obtain Laplace transform of the following functions using the Laplace transform definition a. x(t)-sin!) b. x(t)-t
F(s), (10 points: 5+5) Obtain the Laplace transform for each of the functions given below. ĢIT when the Laplace transform of the function with a time shift of T is given by Aft-T) 1t-T)]-F(s)e ) |0 0S1<1,123 0 f(t) = t-1 1ste2 1 22 F(s), (10 points: 5+5) Obtain the Laplace transform for each of the functions given below. ĢIT when the Laplace transform of the function with a time shift of T is given by Aft-T) 1t-T)]-F(s)e ) |0...
Use the convolution theorem to obtain a formula for the solution to the initial value problem. y ′′ + y = g, y(0) = 0, y′ (0) = 1 , where g = g(t) is a given function. 1. (10 pts) Use the convolution theorem to obtain a formula for the solu- tion to the initial value problem y"+y=g, y(0) = 0, y'(0) = 1, where g = g(t) is a given function.
(10 pts). Using the transform integral, determine the Fourier transform of each of the following signals: a. x(t) - ecos(200t)u(t) b. x(t) -e ltl 5. Scrambled Answers 4-1400-200)+4+](400 +2o), jo, a 1+?
1. Use the symbolic tool in MATLAB to obtain Laplace transform for each of the Following and Graph both results time domain (t) and frequency domain (s)
4. Problem: By the partial fraction expansion method, obtain the inverse z transform of *(z)=1 (1 - z-')(1 - 0.22-1)
Please help with detailed steps [2] [8 points) Please use the inverse Fourier transform formula (2D continuous case) to obtain the Fourier transform of the Laplacian, F(V2) , v). (Express Fourier transform of the Laplacian as a function of u, V and F(u, v), where F(u, v) is the FT of f)