$The discrete Fourier transform [DFT] of a discrete sequence if x [n] i s X [k] = [6, ↑ 7, 8, 9] the DFT of the sequence is G[k], then G[1] is ________w h e r e g [n] = x [n - 2]_{m o d N}$

7

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- 9

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9

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- 7

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Solution

The correct option is D $- 7$
$X [k] = \sum_{n = 0}^{N - 1} x [n] e^{- j \frac{2 π}{N} n K} g [n] = x [n - 2]_{m o d N} G [k] = e^{- j \frac{2 π}{N} (2) k} X [k] G [1] = e^{- j \frac{2 π}{4} (2) 1} X [1] = e^{- j π} X [1] G [1] = - X [1] = - 7$

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