3. The signal x[n] =-(b)”u[-n – 1]+ (0.5)”u[n], a) find the z-transform X(z) [5] b) plot...
a) Find the transform of the following signals and plot the ROC . I x(n)-(0.5)'u(-n-3)+2(0.75) u(n+2) x(n)--on2u(n-2) a) Find the transform of the following signals and plot the ROC . I x(n)-(0.5)'u(-n-3)+2(0.75) u(n+2) x(n)--on2u(n-2)
Q1-20 points) a) Find the transform of the following signals and plot the ROC. 1 x(n)=(-0,357u(n-4)+(0.25?u(n+2) IL- x(n)=-cu-n-1) b) Find the Inverse Z-transform of: z(2-1.5) for (2-0.33)(2-0.5) ROC: z>0.5
2+z-1 1. The Z-transform of a signal x[n] is given as X(z) = }</21 < a) Find the signal x[n] [7] b) Draw the pole – zero plot of the z-transform .[3] c) Is x[n] causal or not? Justify your answer [2]
4. Consider the discrete time signal x[n] = u[n-2] - u[n – 6] a. Plot the signal b. Find the Fourier Transform of x[n]
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.
(a) Find the z-transform of (i) x[n] = a"u[n] +b"u[n] + cºul-n – 1], lal <151 < le|| (ii) x[n] = n*a"u[n] (iii) x[n] = en* [cos (în)]u[n] – en" (cos (ien)] u[n – 1] (b) 1. Find the inverse z-transform of 1-jz-1 X(2) = (1+{z-1)(1 – {z-1) 2. Determine the inverse z-transform of x[n] is causal X(x) = log(1 – 2z), by (a) using the power series log(1 – x) = - 95 121 <1; (b) first differentiating X(2)...
2-Use tables and properties to determine z-transform of the following signal x[n] = (+)*u[n] – (3) "u[n]
For x[n]-(0.3). 1. a. (2 pts) Find the z-transform, X(z b. (3 pts) Sketch the pole-zero plot. c. (3 pts) Find the region of convergence of the transform. Sketch it in the z-plane. d. (3 pts) Use your answer in part a to write down the DTFT of x,[n]=(0.3)"u[n]. Why is it necessary to multiply by the unit step function to get the DTFT?
2-If X1(z)Find the Z-Transform of X2[x]-X, ln +3]u[n] Find theZ-Transform of X211 ( I-hind the Inverse Z-transform of given function. a) R(Z) =- (1-e") (-(z-e-ar) 3 +282+8-1 b) F (Z) = (2-2)2(2+2) Find the Z-Transform of X2 [x] = X1 [n + 3] u [n] 3- Solve the difference equation 3 4 With initial conditions y-1] 1 and yl-2] 3 4- Let the step response of a linear, time-invariant, causal system be 72 3) ulnl 15 3 a) Find the...
For each signal x(n) in Problems #(1)-(5), use Z Transform Tables to do the following: (a) Write the formulas for its Z Transform, X(e), and Region of Convergence, RoCr (b) List the values of all poles and all zeros. (c) Sketch the pole zero diagram. Label both axes. Give key values along both axes. sin ( (-n))u-n]. (Hints: cos(π/3) (5) x1n] , 1/2, sin(π/3)-V3/2) ," For each signal x(n) in Problems #(1)-(5), use Z Transform Tables to do the following:...