Consider a continuous time periodic signal x(t) with fundamental period T and Fourier series coefficient X[k]. What is the Fourier series coefficient of the signal y(t) = x(t – t0) + x(t + t0) ?

\(2\sin \left( {\frac{{2\pi }}{T}K{t_0}} \right)X\left[ K \right]\)

\(2\cos \left( {\frac{{2\pi }}{T}K{t_0}} \right)X\left[ K \right]\)

\({e^{ - {t_0}}}X\left[ K \right] + {e^{{t_0}}}X\left[ { - K} \right]\)

\({e^{ - {t_0}}}X\left[ { - K} \right] + {e^{{t_0}}}X\left[ K \right]\)

Consider a continuous time periodic signal x(t) with fundamental perio

1.	Consider a continuous time periodic signal x(t) with fundamental period T and Fourier series coefficient X[k]. What is the Fourier series coefficient of the signal y(t) = x(t – t0) + x(t + t0) ?
A.	\(2\cos \left( {\frac{{2\pi }}{T}K{t_0}} \right)X\left[ K \right]\)
B.	\(2\sin \left( {\frac{{2\pi }}{T}K{t_0}} \right)X\left[ K \right]\)
C.	\({e^{ - {t_0}}}X\left[ K \right] + {e^{{t_0}}}X\left[ { - K} \right]\)
D.	\({e^{ - {t_0}}}X\left[ { - K} \right] + {e^{{t_0}}}X\left[ K \right]\)
Answer» B. \(2\sin \left( {\frac{{2\pi }}{T}K{t_0}} \right)X\left[ K \right]\)

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Consider a continuous time periodic signal x(t) with fundamental period T and Fourier series coefficient X[k]. What is the Fourier series coefficient of the signal y(t) = x(t – t0) + x(t + t0) ?

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