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) ) = ___________.

Consider a discrete time periodic signal x$$\left[ n \right]$$= $$\sin \left( {{{\pi n} \over 5}} \right)$$. Let a_k 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 _________________.

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

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