GATE EC 2014 Set 4 — Question 55
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Signals & Systems → Discrete-Time Signals → DFT & FFT
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Question
The -point DFT of a sequence , is given by Denote this relation as . For , which one of the following sequences satisfies ?
Correct answer
(B) x = [1 2 3 2]
Solution
The given DFT definition includes a normalization factor of . Let be the standard DFT matrix. Then .
Applying the DFT twice:From the properties of the DFT matrix, .
Thus, .
For the condition to hold, we must have for all .
For , this implies:
(A) (False)
(B) (True)
(C) (False)
(D) (False)
Option (B) is the only sequence that satisfies the symmetry condition.
Applying the DFT twice:From the properties of the DFT matrix, .
Thus, .
For the condition to hold, we must have for all .
For , this implies:
(A) (False)
(B) (True)
(C) (False)
(D) (False)
Option (B) is the only sequence that satisfies the symmetry condition.
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