Given is the function $f(t)=\begin{cases}4&\text{$-1 \leq t \leq 1$,}\\0&\text{$-2 \leq t < -1 ∧ 1 < t \leq 2$.}\end{cases}$
I've calculated its fourier transformation and got $$g(t) =2 + \sum_{n=1}^\infty \frac{(8\cdot \sin(\frac{n\pi}{2}))}{n\pi}\cos(\frac{n\pi}{2}t)$$
Now I must tell in which points the function $f(t)$ is equal to its fourier transformation $g(t)$ and in which they differ. I've plotted the fourier transformation with wolfram alpha but I'am not sure about the answer. I guess that they are equal, when $t = 0$ and maybe when $t=-2$ and $t=2$, otherwise they differ. Does this make any sense?