The Discrete Fourier Transform (DFT) of the 4-point sequence x[n] = \{x[0],x[1],x[2],x[3]\} = \{3,2,3,4\} is X[k] = \{X[0],X[1],X[2],X[3]\} = \{12,2j,0,−2j\}. If X_{1}[k] is the DFT of the 12-point sequence x_{1}[n] = \{3,0,0,2,0,0,3,0,0,4,0,0\}, the value of | {X_{1} [8] }/{X_{1} [11] _{\:}}{{}/{}|} is ________

GATE Electronics and Communications (EC) 2016 Shift 2 Solved Paper

Question : 43 of 65

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The Discrete Fourier Transform (DFT) of the 4-point sequence

x[n] = \{x[0],x[1],x[2],x[3]\} = \{3,2,3,4\}

X[k] = \{X[0],X[1],X[2],X[3]\} = \{12,2j,0,−2j\}

.
If

X_{1}[k]

is the DFT of the 12-point sequence

x_{1}[n] = \{3,0,0,2,0,0,3,0,0,4,0,0\}

, the value of

|\;{X_{1}\;[8]\;}/{X_{1} [11] _{\:}}{{}/{}|}

is ________

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