Given the following function used in binary telecommunications:
I'd like to know how I would obtain $P(f)$ the Fourier transform of this function. The function can be written as:
$$ p(t) = \left\{ \begin{array}{ll} +1 & \quad 0 \leq \frac{Tb}{2} \\ -1 & \quad \frac{Tb}{2} \lt Tb \end{array} \right. $$
I thought of maybe expressing it as some sort of shifted and truncated $sgn(x)$ function but I'm looking for the easiest/simplest mathematical solution.