-1, 0,. . . 2.15 Perform the following convolutions: a. y(n) [(n)-25 (n 3)]* u (n+1)...
Signals and system Class
2.15 Compute the following convolutions without computing any integrals (b) 11(1) * [211 (t) _ 211 (t-3)] (c) u(t) [(t - 1) u(t - 1)]
Problem 1 Compute graphically and plot x[n] *h[n] and x[n] *h[n] (convolutions) for (a). Find a way to derive x[n] *h[n] and x[n] * ñ[n] for (b) without any computation, by using your result of (a) and the properties of convolution. State which property you use. 0 1 2 3 4 5 6 | * 3-2-10 1 2 3 Notation: In the following problems, x[n]={a.b.c) means that_x[-1)=a, x[0]=b, x[1]=c and x[n]=0 otherwise.
4. Compute and plot the results of each of the following convolutions: (a) ut) u(t- 2) (b) a(t-1)、n(t-2) (d) u2) ut) t- 2)] (e) u2) [ul) - u(t - 2)]
ЕЕ306 HW2 Problem 1 Compute graphically and plot x[n] * h[n] and x[n] * h[n] (convolutions) for (a). Find a way to derive x[n] h[n] and x[n] * h[n] for (b) without any computation, by using your result of (a) and the properties of convolution. State which property you use. 0 1 23 0123456 n (a) hpl 3-2-10 1 23 2 3 45 (b) Notation: In the following problems, x[n]={a, b,c} means thatx[-11-a, x[0]=b , x[1]=c and x[n]=0 otherwise. Problem...
Consider the following transfer function: [mark 25%] 4. Y(s) U(s) 5s1 2 G(s) (3) a. If U(s) b. If U (s) (1 - e-)/s, what is the output whent » co? If u(t) 6(t) that is, the unit impulse at t 0, what is the output when t > co? d. Ifu(t) sin(4t), what is y(t) when t co? 3/s, what is the value of the output when t 10? C.
Consider the following transfer function: [mark 25%] 4. Y(s)...
15. Suppose Ui ~ iid Unif(0, 1) for n = 6. Let X = U(1), Y = U(6), and W = X/Y. Find: ~Ll b) Fw(w) c) E(W) d) Var(W)
2.4. Compute and plot y[n] - x[n] * h[n], where x[n] - 0, otherwise 1. 4 sn s 15 0, otherwise h[n] = 2.6. Compute and plot the convolution y[n] - x[n] * h[n], where 2.1. Let x[n] = δ[n] + 2δ[n-1]-δ[n-3] and h[n] = 2δ[n + 1] + 2δ[n-l]. Compute and plot each of the following convolutions: (a) y [n] x[n] * h[n] (c) y3 [n] x[n] * h[n + 2]
Question 1: (35 points: Consider the following sequences: x[n] = u[n] + 4" u[-n- 1] y[n] = x[n - 5) a) [10 points| Determine the Z-transform X(z) b) [10 points| Determine and draw the Region of Convergence (ROC) of x(n) c) [10 points] Determine the z-transform Y(z) d) [05 points) Determine the transfer function H(z)=Y(z)/X(z)
1 point) Show that Φ(u, u) (Au + 2, u-u, 7u + u) parametrizes the plane 2x -y-z = 4, Then (a) Calculate Tu T,, and n(u, v). þ(D), where D = (u, u) : 0 < u < 9,0 < u < 3. (b) Find the area of S (c) Express f(x, y, z in terms of u and v and evaluate Is f(x, y,z) ds. (a) Tu n(u,v)- T, (b) Area(S)- (c) JIs f(z, y,2) ds-
1 point)...
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]