Which of the following relations are true if x(n) is real?(a) X(ω)=X(-ω)(b) X(ω)=-X(-ω)(c) X*(ω)=X(ω)(d) X*(ω)=X(-ω)I got this question in an interview.I would like to ask this question from Properties of Fourier Transformfor Discrete Time Signals topic in division Frequency Analysis of Signals and Systems of Digital Signal Processing

Which of the following relations are true if x(n) is real?(a) X(ω)=X(

1.	Which of the following relations are true if x(n) is real?(a) X(ω)=X(-ω)(b) X(ω)=-X(-ω)(c) X(ω)=X(ω)(d) X(ω)=X(-ω)I got this question in an interview.I would like to ask this question from Properties of Fourier Transformfor Discrete Time Signals topic in division Frequency Analysis of Signals and Systems of Digital Signal Processing
Answer» CORRECT choice is (d) X(ω)=X(-ω) For explanation: We know that, if x(n) is a real sequence XR(ω)=\(\sum_{n=-∞}^∞\) x(n)cosωn=>XR(-ω)= XR(ω) XI(ω)=-\(\sum_{n=-∞}^∞\) x(n)sin⁡(ωn)=>XI(-ω)=-XI(ω) If we COMBINE the above two equations, we get X(ω)=X(-ω)

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