3.3. Determine the z-transform of each of the following sequences. Include with your answer the ROC in the z-plane and a sketch of the pole-zero plot. Express all sums in closed form; a can be complex. (a) xa[n] = a»l. (b) xb[n] = 0< la] < 1. [ 1, 0sn< N 1, 0, otherwise. 0snsN- 1, (c) xe[n] = { 2N – 1 - n, N
3.3. Determine the z-transform of each of the following sequences. Include with your answer the ROC in the z-plane and a sketch of the pole-zero plot. Express all sums in closed form; a can be complex. (a) xa[n] = a»l. (b) xb[n] = 0< la] < 1. [ 1, 0sn< N 1, 0, otherwise. 0snsN- 1, (c) xe[n] = { 2N – 1 - n, N
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![3.3. Determine the z-transform of each of the following sequences. Include with your answer
the ROC in the z-plane and a sketch of the pole-zero plot. Express all sums in closed form;
a can be complex.
(a) xa[n] = a»l.
(b) xb[n] =
0< la] < 1.
[ 1, 0sn< N 1,
0, otherwise.
0snsN- 1,
(c) xe[n] = { 2N – 1 - n, N<n < 2(N – 1),
n+1,
0.
otherwise.
Hint: Note that x,ln] is a rectangular sequence and xin] is a triangular sequence. First,
express xeln] in terms of xp[n].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb96368a-ac4c-4265-87bf-d83448278845%2F4ccdad70-63d6-4462-92e5-fe9d9bf2374c%2Fdfcl91b.jpeg&w=3840&q=75)
Transcribed Image Text:3.3. Determine the z-transform of each of the following sequences. Include with your answer
the ROC in the z-plane and a sketch of the pole-zero plot. Express all sums in closed form;
a can be complex.
(a) xa[n] = a»l.
(b) xb[n] =
0< la] < 1.
[ 1, 0sn< N 1,
0, otherwise.
0snsN- 1,
(c) xe[n] = { 2N – 1 - n, N<n < 2(N – 1),
n+1,
0.
otherwise.
Hint: Note that x,ln] is a rectangular sequence and xin] is a triangular sequence. First,
express xeln] in terms of xp[n].
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