1
GATE ECE 2014 Set 4
+2
-0.6
The N-point DFT X of a sequence x[n] 0 ≤ n ≤ N − 1 is given by
$$X\left[ k \right] = {1 \over {\sqrt N }}\,\,\sum\limits_{n = 0}^{N - 1} x \,[n\,]e{\,^{ - j{{2\pi } \over N}nk}}$$, 0$$\le k \le N - 1$$
Denote this relation as X = DFT(x). For N= 4 which one of the following sequences satisfies DFT (DFT(x) ) = ___________.
A
x = $$\left[ {1\,2\,3\,4} \right]$$
B
x = $$\left[ {1\,2\,3\,2} \right]$$
C
x = $$\left[ {1\,3\,2\,2} \right]$$
D
x = $$\left[ {1\,2\,2\,3} \right]$$
2
GATE ECE 2014 Set 1
Numerical
+2
-0
Consider a discrete time periodic signal x$$\left[ n \right]$$= $$\sin \left( {{{\pi n} \over 5}} \right)$$. Let ak be the complex Fourier serier coefficients of x$$\left[ n \right]$$. The coefficients $$\left\{ {{a_k}} \right\}$$ are non- zero when k = Bm $$\pm$$ 1, where m is any integer. The value of B is _________________.
3
GATE ECE 2013
+2
-0.6
The DFT of a vector [a b c d] is the vector [α β γ δ ]. Consider the product The DFT of the vector [ p q r s] is a scaled version of
A
$$\left[ {{\alpha ^2}{\beta ^2}{\Upsilon ^2}{\delta ^2}} \right]$$
B
$$\sqrt {\alpha \,} \,\sqrt \beta \,\sqrt \gamma \,\sqrt \delta$$
C
$$\left[ {\alpha + \beta \,\beta + \delta \, + \gamma \,\gamma \, + \alpha } \right]$$
D
$$\left[ {\delta {\rm{ }}\beta \,\gamma \,\delta } \right]$$
4
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
EXAM MAP
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