GATE Electronics and Communications (EC) 2022 Solved Paper

For a vector x̅ = [x[0], x[1],......x[7]] the 8-point discrete Fourier transform (DFT) is denoted by X̅ = DFT (x̅) = X[0], X[1], ...., X[7]], where
$\mathit{X}\left[\mathit{k}\right]=\sum _{\mathit{n}=0}^7\mathit{x}\left[\mathit{n}\right]\exp \left(-\mathit{j}\frac{2\mathit{\pi }}{8}\mathit{n}\mathit{k}\right)$
Here j = √-1, if X̅ = [1, 0, 0, 0, 2, 0, 0, 0] and y̅ = (DFT (x̅)), then the value of y[0] is ________ (rounded off to one decimal place).