Consider two real sequences with time–origin marked by the bold value x 1 [n] = { 1 , 2, 3, 0}, x 2 [n] = { 1 , 3, 2, 1}. Let X 1 (k) and X 2 (k) be 4-point DFTs of x 1 [n] and x 2 [n] respectively. Another sequence x 3 [n] is derived by taking 4-point inverse DFT of X 3 (k) = X 1 (k) X 2 (k). The value of x 3 [2] is _________.

GATE Electronics and Communications (EC) 2015 Shift 2 Solved Paper

Question : 54 of 65

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Consider two real sequences with time–origin marked by the bold value x₁[n] = {1, 2, 3, 0}, x₂[n] = {1, 3, 2, 1}. Let X₁(k) and X₂(k) be 4-point DFTs of x₁[n] and x₂[n] respectively. Another sequence x₃[n] is derived by taking 4-point inverse DFT of X₃(k) = X₁(k) X₂(k). The value of x₃[2] is _________.

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