3.96 Determine the z-transforms of the following sequences and their respective ROCs: (a) x1[n] = -a"u[-n-1],...
Determine the z-transform of the following sequences and their ROCs: a) x(n) = (0.5)" for n> 5, and zero for all other values of n; b) x(n)= (0.5)"[u(n) - u(n-7)]; c) x(n)=(-1)"a"u(n), 0 <a<1.
Using partial fractions or power series expansions, determine all possible inverse z-transforms of the following z-transforms, sketch their ROCs, and discuss their stability and causality properties: 10+z2 1+0.25z-
Problem 7.1 (10 points) Express the unilateral z-transforms of the following functions as rational functions. Find also the ROC. You may use tables. (a) xl[n]-1-0.2)" (b) x2[n] (0.3)" +2(-5) -0.2n Problem 7.2 (10 points) Express the unilateral z-transforms of the following functions as rational functions. Find also the ROC. You may use tables. (a) xl[n] = 3e-j02" (b) x2[n]- 5cos(5n) (c) x3[n] = e-0.gn sin(0.7n) Problem 7.3 (10 points) The signals given are sampled every 0.3 s, beginning att-0. Find...
1. Determine the z-transforms of the following sequences: (a) x = [3, 0, 5, 6, 0, 1] (b) x = [1, 0, 0, 4] 2. Compute the transfer fuctions for the following impulse responses: (a) h = [1, −5, 4, 0, 5] (b) h = [1, −0.5, 0.25, −1.125] 3. If h(n) = 3^ -n for n ≥ 0, express H(z) as a ratio of polynomials. 4. Find the 10 roots of unity, that is, solve z^10 − 1 =...
Matt’s utility is given by u(x1,x2)=min{x1,x2}+min{x3,x4}. Which of the following four bundles (A, B, C, and D) will he most prefer? Bundles are written (x1,x2,x3,x4). a. A = (2, 2, 2, 2) b. B = (6, 0, 0, 2) c. C = (4, 2, 1, 1) d .D = (6, 1, 3, 1)
3) Compute the Z-Transforms of the following time series: (a) x(n)k2"u(n) (b) + 1) x(n) = u(-n (c) x(n) -k2"u-1) (d) x(n) 0.5%1(n) + 3"11(-n) (e) x(n) = 4-nu(n) + 5-nu(n + 1) In the above, u(n) stand for the unit step signal in the discrete time domain. Also, if you can in each case determine the region of convergence of the Z-Transform you obtain.
2. Consider the following LP: Min z = -4x1 - 5x2 + 3x3 Subject to X1 + x2 + x3 = 10 X1 X2 > 1 X1 + 3x2 + x3 = 20 X1, X2, X3 20 (a) Solve the problem by Big M method. (b) Solve the problem by two-phase method.
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)
Determine whether the system is consistent 1) x1 + x2 + x3 = 7 X1 - X2 + 2x3 = 7 5x1 + x2 + x3 = 11 A) No B) Yes Determine whether the matrix is in echelon form, reduced echelon form, or neither. [ 1 2 5 -7] 2) 0 1 -4 9 100 1 2 A) Reduced echelon form B) Echelon form C) Neither [1 0 -3 -51 300 1-3 4 0 0 0 0 LOO 0...
1. Determine the Laplace/Z transforms of the following signals, including the regions of vergence Con (a) (t)e-u(t 2) 2e u(t)ut)3e'u-t) 2" u 3(2)"u 4-1)"un2(-3)u[-n 1 (b) (t) (c) n (d) n 2 2l-