EC > GATE 2022 > Discrete Fourier Transform
For a vector x̄ = [x[0], x[1], …, x[7]], the 8-point discrete Fourier transform (DFT) is denoted by X̄ = DFT(x̄) = [X[0], X[1], …, X[7]], where
X[k] = ∑n=07 x[n] exp(−j(2π/8)nk).
Here, j = √−1. If x̄ = [1, 0, 0, 0, 2, 0, 0, 0] and ȳ = DFT(DFT(x̄)), then the value of y[0] is _________ (rounded off to one decimal place).
X[k] = ∑n=07 x[n] exp(−j(2π/8)nk).
Here, j = √−1. If x̄ = [1, 0, 0, 0, 2, 0, 0, 0] and ȳ = DFT(DFT(x̄)), then the value of y[0] is _________ (rounded off to one decimal place).
Correct : 24.0
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