Prob. 5 (a) Let x(t) = u(t) and h(t) = e-looor u(t) + e-lotu(t). -00 <t< oo using graphical convolution(s). Determine y(t) = h(t) * x(t) for Prob. 5 (cont.) (b) Let zln] = uln] and h[n]-G)...
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]
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.
Question # 4 Let x(t) u(t) be a signal, let h(t) = e -5tu(t) be a linear time invariant system (a) Sketch x(t) and h(t) (b) Find the mathematival expression of output of the system y(t) by using convolution. (c) Sketch y(t)
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.
1. Let x(t)-u(t-1) _ u(t-3) + δ(t-2) and h(t)-u(t) _ u(t-1) + u(t-3)-u(t-5) a. Find and sketch x(t-t) and h(t). (Hint: Break x(t) into two signals) b. Find and sketch y(t) - x(t)*h(t) using the quasi-graphical method. Label and show every step (drawings and calculations)
2. Let f(x,y) = e-r-u, 0 < x < oo, 0 < y < oo, zero elsewhere, be the pdf of X and Y. Then if Z = X + Y, compute (a) P(Z 0). (b) P(Z 6) (c) P(Z 2) (d) What is the pdf of Z?
1. Problem 1: (20 pts) Let 3(t) = u(1 – t) and h(t) = tſu(t) - t - 2)). (a) Sketch h(t), 3(1), 2(t - T) and carefully label the values on the axes. (6 pts) (b) Determine y(t) = 3(t)h(t) by performing graphical convolution. No need to sketch y(t). (14 pts)
Problem: Let x[n] = δ[n] + 2δ[n-1] - δ[n-2] and h[n] = u[n] – u[n-4] – 2.δ[n-1]. Compute and plot the following convolutions. If you use the analytical form of the convolution equation to solve, verify your answer with the graphical method. a. y1[n] = x[n]*h[n] b. y2[n] = x[n]*h[n+1] c. y3[n] = x[n-1]*h[n]
Q2 (a) Given the signal x(t) and system h(t) as presented in Figure Q2(a). Determine the output y(t) using the graphical representation of convolution integral. (7 marks) x(1) h(t) 1 e-'u(t) e-2 (1) 0 Figure Q2(a) Q2 (b) Consider a system as shown in Figure Q2(b). t2 - 1 x(t) y(t) Advance by 1 second Х Figure Q2(b) Find the input-output relation between x(t) and y(t). (i) (1 mark) Examine whether the system is time variant or time invariant. (5...
By using convolution theorem, not laplace. !!!!!!! Determine the output y(t) for the following pairs of input signals x(t) and impulse responses h(t): (i) x(t)=u(t), h(t)=u(t): (iii) x(1) 11(1) _ 211(-1) + 11( -2), h(1) 11( 1) _ 11(-1);