Let x(t) be a periodic signal with time period T. Let y(t)

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Let x(t) be a periodic signal with time period T. Let y(t) = x(t – t₀) + x(t + t₀) for some t₀.
The fourier Series coefficients of y(t) are denoted by b. If b_k = 0 for all odd k, then t₀ can be equal to

1. T/8
2. T/4
3. T/2
4. 2T

Correct Option: B

y(t)= x(t – t₀) + x (t + t₀)
Since y(t) is periodic with period T, then x(t – t₀) and x(t + t₀) will also be periodic with T
Now, b_k = a_ke^-jkω₀t₀ + a_ke^jkω₀t₀
Where, a_k is fourier series coefficient of equal x(t),
b_k = a_k[e^-jkω₀t₀ + e^jkω₀t₀]
= 2a_k cos kω₀t₀
Given that, b_k = 0 for odd k
then, kω₀t₀ = k(π/2),
where k = 2m + 1, m is an integer

⇒ t₀ =	T		ω₀ =	2π
	4			T