If x(n) is a real sequence and X(k) is its N-point DFT, then which of the following is true?Select one:a. X(N-k)=X*(k)b. All of the mentionedc. X(-k)=X*(k)d. X(N-k)=X(-k)
Question
If x(n) is a real sequence and X(k) is its N-point DFT, then which of the following is true?Select one:a. X(N-k)=X*(k)b. All of the mentionedc. X(-k)=X*(k)d. X(N-k)=X(-k)
Solution
To determine which statement is true, let's analyze each option:
a. X(N-k) = X*(k) This statement is not true. The DFT of a real sequence does not have a conjugate symmetry property, so X(N-k) is not equal to the complex conjugate of X(k).
b. All of the mentioned This option cannot be selected as it is not a specific statement.
c. X(-k) = X*(k) This statement is true. The DFT of a real sequence has a symmetry property where X(-k) is equal to the complex conjugate of X(k).
d. X(N-k) = X(-k) This statement is not true. The DFT of a real sequence does not have a symmetry property where X(N-k) is equal to X(-k).
Therefore, the correct answer is c. X(-k) = X*(k).
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