Symmetry in Trignometric Fourier Series Coefficients
Let xt be a p...
Question
Let x(t) be a periodic signal with time period T. Let y(t)=x(t−t0)+x(t+t0)for someto.
The Fourier series coefficients of y(t) are denoted by bk.Ifbk=0 for all odd K. Thent0 can be equal to
A
T4
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B
T8
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C
2T
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D
T2
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Solution
The correct option is AT4 y(t)=x(t−t0)+x(t+x0)
Since, x(t) is periodic with period T.
Therefore, x(t−t0) and x(t+t0) will also be periodic with perriod T.
∴bk=ake−jkω0t0+akejkω0t0
(By property) ak is Fourier series coefficient of signal x(t) therefore,