determine period of given signal

Question

i would like to compute Fourier coefficients from given signal,and i have following picture

i need to know period,just to make sure that i am not making mistake,period should be $\frac {T} {2}$ right?because starting from $0$ point,it repeats again peak after $\frac {T}{2}$ second am i right or i am making some mistake?thanks in advance

Answer 1

You can take your period as $[-T/2,T/2]$ and over a period your function can be written as $$ x(t)=\begin{cases} 1, & \frac{-T}{4}\leq t\leq\frac{T}{4}\\ 0, & else \end{cases} $$ So the coefficient $a_0$ is: $$a_{0}=\frac{1}{T}\int_{-T/2}^{T/2}1dt=\frac{1}{T}\int_{-T/4}^{T/4}1dt=\frac{1}{2}$$

Answer 2

the period is T here, as it takes T to reach the same phase in your signal