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GATE Electronics and Communications (EC) 2022 Solved Paper

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Question : 60

Total: 65

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
X[k]=

x[n]‌exp(−j‌

nk)
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).

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