Which of the following relation is true if the signal x(n) is real?(a) X*(ω)=X(ω)(b) X*(ω)=X(-ω)(c) X*(ω)=-X(ω)(d) None of the mentionedThis question was posed to me in class test.The question is from Frequency Analysis of Discrete Time Signal topic in portion Frequency Analysis of Signals and Systems of Digital Signal Processing

Which of the following relation is true if the signal x(n) is real?(a)

1.	Which of the following relation is true if the signal x(n) is real?(a) X(ω)=X(ω)(b) X(ω)=X(-ω)(c) X*(ω)=-X(ω)(d) None of the mentionedThis question was posed to me in class test.The question is from Frequency Analysis of Discrete Time Signal topic in portion Frequency Analysis of Signals and Systems of Digital Signal Processing
Answer» Right choice is (b) X(ω)=X(-ω) The explanation: We know that, X(ω)=\(\sum_{N=-∞}^∞ x(n)e^{-jωn}\) => X(ω)=\([\sum_{n=-∞}^∞ x(n)e^{-jωn}]^\) Given the signal x(n) is REAL. THEREFORE, X(ω)=\(\sum_{n=-∞}^∞ x(n)e^{jωn}\) => X*(ω)=X(-ω).

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