Consider the discrete-time signal x[n] shown below. Let its DTFT be denoted by X (ein). 4-3 -2 (a) Evaluate X(ejº) (b) Evaluate X(ejπ) (c) Evaluate SX (e³³)dN 5 3 1 -1 -3 x[n] 1 • 2 3 4 n where x[n] is zero outside the interval from −4 to +4. Perform the following calcula- tions (for some of them, you may not need to computing the DTFT itself): (d) What values can ZX(e) take? (e) Determine and sketch the signal whose DTFT is Im[X(e¹¹)] (f) Evaluate (X(en)) ² dn

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Consider the discrete-time signal x[n] shown below. Let its DTFT be denoted by
X (ein).
4-3
-2
(a) Evaluate X(ejº)
(b) Evaluate X(ejπ)
(c) Evaluate SX (e³³)dN
5
3
1
-1
-3
x[n]
1
•
2
3 4
n
where x[n] is zero outside the interval from −4 to +4. Perform the following calcula-
tions (for some of them, you may not need to computing the DTFT itself):
(d) What values can ZX(e) take?
(e) Determine and sketch the signal whose DTFT is Im[X(e¹¹)]
(f) Evaluate (X(en)) ² dn
Transcribed Image Text:Consider the discrete-time signal x[n] shown below. Let its DTFT be denoted by X (ein). 4-3 -2 (a) Evaluate X(ejº) (b) Evaluate X(ejπ) (c) Evaluate SX (e³³)dN 5 3 1 -1 -3 x[n] 1 • 2 3 4 n where x[n] is zero outside the interval from −4 to +4. Perform the following calcula- tions (for some of them, you may not need to computing the DTFT itself): (d) What values can ZX(e) take? (e) Determine and sketch the signal whose DTFT is Im[X(e¹¹)] (f) Evaluate (X(en)) ² dn
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