5. (22+2=4") Topic: The z-transform, z-transform properties Use the z-transform properties to determine the z-transform the...
2-Use tables and properties to determine z-transform of the following signal x[n] = (+)*u[n] – (3) "u[n]
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
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:...
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]
Problem 5. Determine the z-transform of the signal x[n] :=(-1)"nu[n]. You may use already known z-transforms, such as those listed in Table 5.1 (page 492) of the textbook, and properties of the z-transform. Moreover, notice that -1 = ejt. TABLE 5.1 Select (Unilateral) Z-Transform Pairs x[n] X[z] 8[n-k] ? 2-1 ոս[ո] (z - 1) z(z+1) (2-1)3 nºu[n] nu[n] z(z? + 4z +1) (2-1) Yºu[n] yn-u[n- 1] z-y 12 ny"u[n] (z-7) yz(z+y) (z-7)3 ny"u[n] n(n - 1)(n-2) (n-m+1) ym! lyl" cos...
5. Calculate the z-transform of x[n] = 0.2"u[n – 3], and determine its region of convergence.
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]
Find the Z-transform of the following sequences using the Z-transform properties table. Identify clearly the name of the properties that you use: a. x(n) = n(1/2)nu(n) b. x(n) = -n(1/3)nu(-n-1) c. x(n) = (-1)nu(n) d. x(n) = (-1)ncos(npi/3)u(n)
[2 Marks] 18. If (z) and u[n]-cos(2n)지지 the correct value of V(z) will be (2z-1) js 2 2zei5-1 2ze-15-1 2 2zel5-12ze-15-1 19. Determine the Z-transform of x[n]. [2 Marks each] n] sinl0n)u[n]0.3" n] 0.5" cos (10n)u[n] In]-(0.3) u[/n] The transfer function of a discrete time system is H(z)- 20. 1+2z3z Use the inverse Z-transform to determine the system difference equation [4 Marks] 21. An LTI system is described by the following input/output difference equation: yln] 0.12yln x[n] (assume zero initial...
(40pts) Find the z transform of the following discrete-time signals. Please remember to include the "region of convergence" for each signal: (a) x(n)=3e * (n) +2 (4) (-1-1) +5d(n) (b) x(n)=nu(n-1) x(n) = 4 cos(ant)u(n) x(n) = 2 cos[0.27(n-1)Ju(n) (e) x(n)=(n-1) cos[@nju(n-1)