Consider the DT signal x[n] shown in the plot below. You can assume that x[n] = 0 for all values of n not shown in the plot. er A -3 -2 -1 \x[n] 3 4 5 >n (a) Is X(e) purely even, odd or neither? Solve this part without computing the DTFT. (b) Is X (e) real, imaginary or neither? Solve this part without computing the DTFT. (c) Now derive the DTFT X(e¹¹). (Do verify that the expression you obtain satisfies the answers you have for Parts a and b).

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Consider the DT signal x[n] shown in the plot below. You can assume that x[n] = 0
for all values of n not shown in the plot.
er
A
-3 -2 -1
\x[n]
3 4 5
>n
(a) Is X(e) purely even, odd or neither? Solve this part without computing the
DTFT.
(b) Is X (e) real, imaginary or neither? Solve this part without computing the DTFT.
(c) Now derive the DTFT X(e¹¹). (Do verify that the expression you obtain satisfies
the answers you have for Parts a and b).
Transcribed Image Text:Consider the DT signal x[n] shown in the plot below. You can assume that x[n] = 0 for all values of n not shown in the plot. er A -3 -2 -1 \x[n] 3 4 5 >n (a) Is X(e) purely even, odd or neither? Solve this part without computing the DTFT. (b) Is X (e) real, imaginary or neither? Solve this part without computing the DTFT. (c) Now derive the DTFT X(e¹¹). (Do verify that the expression you obtain satisfies the answers you have for Parts a and b).
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