A function is equal to zero outside a unit area square centered at (0,0) and inside a central quarter-unit area square similarly oriented. Elsewhere the function is equal to unity. I am trying to find the formula of the function and its Fourier Transform. Now, I have two issues with the wording of this problem. Firstly, is a "quarter-unit area square" a square with side lengths $\frac{1}{2}$ (which gives one fourth the area) or side lengths $\frac{1}{4}.$ Secondly, what does it mean for a function to be equal to unity? I can't seem to find a definition anywhere on the web or in the reference manual that stated this function. Anyways, making assumptions of side length $\frac{1}{2}$ and unity $= 1$, I've got the following function:
$$ f(x,y) = \left\{ \begin{array}{lr} 1 & \text{if} \;\frac{1}{2} \leq max(|x|,|y|) \leq 1 \\ 0 & \text{otherwise} \end{array} \right. $$
Now, if all that is correct, how do I find the Fourier transform of this?