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evaluate the following convolution integral: y(t)= (u(t)-u(t-1))*(u(t)-u(t-1))
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)
Evaluate the following convolution: (Show all your work) y(t) = {u(t+2) – u(t-2)}*{u(t+4) – u(t-4)}
Problem 1 Use the convolution integral to find the zero-state response for x(t)-u(t), and h(t)- eu(t)
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.
Find the convolution integral of the following figure pairs: use
the graph method
y(t) X(t) 0 1 2 3 4
1 R 12. Use the transformation T: u = -x and very to evaluate the integral [jx?dA where R is the region bounded on the xy-plane by the ellipse 9x + 4y = 36. . Let S be the image of Runder T on the uv-plane. Sketch regions and S. Set up the integral 7as an iterated integral of a function f(u, v) over region S. Use technology to evaluate the integral. Give the exact answer. R S Y
1 3 12. Use the transformation T: u = -x and very to evaluate the integral [JxºdA where R is the region R bounded on the xy-plane by the ellipse 9x² + 4y2 = 36. Let S be the image of R under T on the uv-plane. Sketch regions R and S. Set up the integral 7as an iterated integral of a function f(u, v) over region S. Use technology to evaluate the integral. Give the exact answer. R S...
Problem 4. Use the convolution integral to find the response y(t) of the LTI system with impulse response h(t) to input x(t) a) x(I)-2expl_2t)u(t) , h(1)-expl-t)u(t)
Problem 4: Evaluation of the convolution integral too y(t) = (f * h)(t) = f(t)h(t – 7)dt is greatly simplified when either the input f(t) or impulse response h(t) is the sum of weighted impulse functions. This fact will be used later in the semester when we study the operation of communication systems using Fourier analysis methods. a) Use the convolution integral to prove that f(t) *8(t – T) = f(t – T) and 8(t – T) *h(t) = h(t...
1. Evaluate the line integral S3x2yz ds, C: x = t, y = t?, z = t3,0 st 51. 2. Evaluate the line integral Scyz dx - xz dy + xy dz , C: x = e', y = e3t, z = e-4,0 st 51. 3. Evaluate SF. dr if F(x,y) = x?i + xyj and r(t) = 2 costi + 2 sin tj, 0 st St. 4. Determine whether F(x,y) = xi + yj is a conservative vector field....