1
GATE ECE 2011
+2
-0.6
The first six points of the 8-point DFT of a real valued sequence are 5, 1 - j3, 0, 3- j4, 0 and 3+ j4. The last two points of the DFT are respectively
A
0, 1- j3
B
0, 1+ j3
C
1+j3, 5
D
1 – j3, 5
2
GATE ECE 2009
+2
-0.6
The 4-point Discrete Fourier Transform (DFT) of a discrete time sequence $$\left\{ {1,\,0,\,2,\,3} \right\}$$ is
A
$$\left[ {0,\, - 2 + 2j,\,2,\, - 2 - 2j} \right]$$
B
$$\left[ {2,\,2 + 2j,\,6,\,2\, - 2j} \right]$$
C
$$\left[ {6,\,1 - 3j,\,2,\,1 + 3j} \right]$$
D
$$\left[ {6,\, - 1 + 3j,\,0,\, - 1\, - 3j} \right]$$
3
GATE ECE 2008
+2
-0.6
{x(n)} is a real-valued periodic sequence with a period N. x(n) and X(k) form N-point. Discrete Fourier Transform (DFT) pairs. The DFT Y(k) of the sequence
y (n) = $${1 \over N}\,\sum\limits_{r = 0}^{N - 1} x \,\left( r \right)x\,(n + r\,)$$ is
A
$${\left| {X(k)} \right|^2}$$
B
$${1 \over N}\,\sum\limits_{r = 0}^{N - 1} X \,\left( r \right){X^*}\,(k + r\,)$$
C
$${1 \over N}\,\,\sum\limits_{r = 0}^{N - 1} X \,(r\,)X(k + r)$$
D
0
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