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4. Find the z-transform (if it exists) and the corresponding region of convergence for each of...
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)...
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]
3. For each of the following discrete-time sequences: (i) Find the Z-transform (ZT), if it exists, and plot the region of convergence (ROC) in the Z-plane (ii) Find the poles and zeros and plot them in the 2-plane (iii) Determine whether the DTFT of the sequence exists (a) x[n] = 8[n – 1] + 28[n – 3] (b) [n] = (0.9e-j*)" u[n + 2] – 2-ul-n - 1] (c) x[n] = 2-" un + 1]
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
5. Calculate the z-transform of x[n] = 0.2"u[n – 3], and determine its region of convergence.
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:...
(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)
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]
Use the properties of transform and properties to find the DTFT of the following signals: (a) x[n] = (n - 2)(u[n + 4] - u[n - 5]) (a) x[n] = (1/3) n u[n + 2] Use the tables of transforms and properties to find the inverse DTFT’s of the following signals. (a) X (e jw) = j sin(4w) – 2 (b) X(ejw) = e-j(4w+ π/2 ) d/dw [2/(1+1/4 e-j(w-π/4 )) + 2/(1+1/4 e-j(w + π4 ))]
BC:6.1 For the following signals, use the defini- tion to calculate the z-transform and find the region of convergence for each signal below. Does it matter whether you use the 1-sided or 2-sided definition for these signals? If this matters, calculate it using each definition c.) zefn] = (0.5)"-7uln-3] un +5