Consider the signal x[n] = 6\delta [n + 2] + 3\delta [n + 1] + 8\delta [n] + 7\delta [n−1] + 4\delta [n−2] . If X(e^{j\omega }) is the discrete-time Fourier transform of x[n], then \frac{1}{\pi }\int ↙\stackrel{\pi }{−\pi }⁡X (e^{j\omega }) \sin ^{2} (2\omega ) d\omega \: is equal to _________.

GATE Electronics and Communications (EC) 2016 Shift 1 Solved Paper

Question : 45 of 65

Marks: +1, -0

Consider the signal

x[n] = 6δ [n + 2] + 3δ [n + 1] + 8δ [n] + 7δ [n−1] + 4δ [n−2]

.
If

X(e^{jω })

is the discrete-time Fourier transform of

x[n]

,
then

\;{1}/{π\;}∫ ↙{−π }↖{π }⁡X (e^{jω }) sin \;^{2} (2ω ) dω \:

is equal to _________.

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