Evaluate the following convolution: (Show all your work) y(t) = {u(t+2) – u(t-2)}*{u(t+4) – u(t-4)}
solution :
Evaluate the following convolution: (Show all your work) y(t) = {u(t+2) – u(t-2)}*{u(t+4) – u(t-4)}
1. Evaluate and sketch the convolution integral (the output y(t)) for a system with input x(t) and impulse response h(t), where x(t) = u(1-2) and h(t)= "u(t) u(t) is the unit step function. Please show clearly all the necessary steps of convolution. Determine the values of the output y(t) at 1 = 0,1 = 3,1 = 00. (3 pts)
please show all your work (The operator ?? denotes convolution.)? PROBLEM sp-10-F.4: For each of the following time-domain signals, select the correct match from the list of Fourier transforms below. Write your answers in the boxes next to the question.(The operator *denotes convolution.) x()u(t +4)- u(t-4) x(1)=?(1-2) * e-1 + in(1-1)*3(1-1) x(t)-cos(rt) * ?(1-4) -00 Each of the time signals above has a Fourier transform that should be in the list below [0] X(jo) not in the list below 40...
please show all work ising convolution. integral is from 0 to t Use convolution theorem and solve y'-st 0 sin(t - 2)y()dA = cost, y(0) = 1. *integral is from zero to to t I
x(t) = u(t)-u(t-2) w(t) = 2[u(t-1) - u(t-4)] Graphical approach of using convolution. y(t) = x(t) * w(t) Please help, I'm kind of lost on getting the integrals and the final answer should look like a trapezoid.
2(a). Compute and plot the convolution of ytryh)x where h(t) t)-u(t-4), x(t)u(t)-u(t-1) and zero else b). Compute and plot the convolution y(n) h(n)*x (n) where h(n)-1, for 0Sns4, x(n) 1, n 0, 1 and zero else.
6. (20 pts) se the definition of convolution to compute tu(t) * u(t); Check your answer using Laplace transform. 7. (40 pts) Solve the following ODE. y" 4y 4y = e-4*[u(t) - u(t - 1)] (0) = 0; y'(0)= -1
1. Solve the ODE/TVP: y" +2y'+y=5(1-2),y(0)-0.7(0) =0. Use the Convolution Theorem everywhere possible, in parts (b) and (c). (a) Find Y(s), the Laplace Transform of y(t), (b) Express y(t) in terms of the convolution product ONLY with explicit functions of t, e.g., f(t)-g(t) or f(t) g(t) * h(t), but do not evaluate any of the convolution product(s); (c) Obtain y(t) by working out completely the convolution product(s) in part (b), show all your intermediate work and results, and simplify your...
4. A linear time invariant system has the following impulse response: h(t) =2e-at u(t) Use convolution to find the response y(t) to the following input: x(t) = u(t)-u(t-4) Sketch y(t) for the case when a = 1
Prove the following: Using Convolution, determine y(t) when x(t) = 4u(t) and h(t) = e-2t u(t) for t > 0 answer: y(t) = 2[1-e-2t]
3. Find the continuous-time convolution of r(t) = 10e (i 2)u(t - 2) with h(t) = 5e ( 4)u(t – 4)