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GATE EC 2016 Set 2 — Question 43

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NAT+2 / -0MediumDFT & FFTDiscrete-Time SignalsSignals & Systems

Signals & Systems → Discrete-Time Signals → DFT & FFT

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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[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}X[k] = \{X[0], X[1], X[2], X[3]\} = \{12, 2j, 0, -2j\}. If X1[k]X_1[k] is the DFT of the 12-point sequence x1[n]={3,0,0,2,0,0,3,0,0,4,0,0}x_1[n] = \{3, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0\}, the value of ∣X1[8]X1[11]∣\left| \frac{X_1[8]}{X_1[11]} \right| is ________
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