1
GATE ECE 2007
+2
-0.6
A 5-point sequence x [n] is given as x$$\left[ { - 3} \right]$$ =1, x$$\left[ { - 2} \right]$$ =1, x$$\left[ { - 1} \right]$$ =0, x$$\left[ { - 0} \right]$$ = 5, x$$\left[ { - 1} \right]$$ = 1. Let X$$({e^{j\omega }})\,$$ denote the discrete - time Fourier transform of x(n). The value of $$\int\limits_{ - \pi }^\pi x$$ ($$({e^{j\omega }})\,$$ d$$\omega$$ is
A
5
B
10$$\pi$$
C
16$$\pi$$
D
5+ j 10 $$\pi$$
2
GATE ECE 2005
+2
-0.6
A sequence x(n) has non-zero values as shown in Fig.
The sequence $$y(n)=\left\{\begin{array}{l}x\left(\frac n2-1\right)\;\;\;for\;n\;even\\0\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;for\;n\;odd\end{array}\right.$$\$
will be
A
B
C
D
3
GATE ECE 2005
+2
-0.6
A sequence x(n) has non-zero values as shown in figure. 1
The Fourier transform of y(2n) will be
A
$${e^{ - j2\omega }}\left[ {\cos {\mkern 1mu} 4\omega + {\mkern 1mu} 2\cos \,2\omega + 2} \right]$$
B
$$\left[ {\cos \,2\omega + \,2\cos \omega + 2} \right]$$
C
$${e^{ - j\omega }}\left[ {\cos \,2\omega + \,2\cos \omega + 2} \right]$$
D
$${e^{j2\omega }}\left[ {\cos \,2\omega + \,2\cos \omega + 2} \right]$$
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