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Official PYQ · 2017

GATE EC 2017 Set 1 Q8 — Continuous-time Signals

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A periodic signal x(t)x(t) has a trigonometric Fourier series expansion

x(t)=a0+∑n=1∞(ancos⁡nω0t+bnsin⁡nω0t)x( t )= a_{0}+\sum_{n=1}^{ \infty } ( a_{n} \cos n\omega _{0}t+b_{n}\sin n\omega _{0}t )

If x(t)=−x(−t)=−x(t−πω0)x(t)= -x(-t)=-x(t-\frac{\pi }{\omega _{0}}), we can conclude that

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Answer: A

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