5. Calculate the z-transform of x[n] = 0.2"u[n – 3], and determine its region of convergence.
5. (22+2=4") Topic: The z-transform, z-transform properties Use the z-transform properties to determine the z-transform the following signal and specify the region of convergence. x[n]=(1)"u[n]*2":[-n-1]+)?[n-2]
In-class Assignment 4 Z-transform OGY 8 2. Determine the z-transform and the associated region of convergence ROC 5) u(k) e2(k) = ( ) k u(k-1) 3. The error signal e(t) = Be-"u(t) is sampled at the rte of 20Hz. The z-transform of the resulting number sequence is E(c) , Determine B and a. -0.8 4. Determien the initial and value of the sequence e(k) if the E(z) is given be 2z E (z) = z2-1
4. Find the z-transform (if it exists) and the corresponding region of convergence for each of the following signals. To the extent possible, use the properties of the z-transform to enable the re-use of standard results and reduce calculations. Simplify your expressions. (Recall that for real-valued signals, the transform should only have real-valued coefficients.) (a) z[n] = (1)(n-1) sin(竽幔)u[n-2] (b) x[n-2"u[n] + 0.5"u[n-2] (d)-[n] = n(j)nuln-3]
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:...
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. Find the region of convergence (if it exists) in the z plane, of the z transform of these signals: (a) x[n] = u[n] + [n] (b) x[n] = u[n] - u[n - 10] (c) x[n] = 4n un + 1] (Hint: Express the time-domain function as the sum of a causal function and an anticausal function, combine the z-transform results over a common denominator, and simplify.) (d) x[n] = 4n u[n - 1] (e) x[n] = 12 (0.85)" cos(2tn/10)...
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)
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?
3. The signal x[n] =-(b)”u[-n – 1]+ (0.5)”u[n], a) find the z-transform X(z) [5] b) plot the ROC. [3] С
3. (Oppenheim Willsky) Determine the z-transform for each of the following sequences. Sketch the pole-zero plot and indicate the region of convergence. Indicate whether or not the discrete-time Fourier transform of the sequence exists. (a) 8[n +5] (b) (-1)"u[n] (c) (-3)”u[-n – 2] (d) 27u[n] +(4)”u[n – 1]