# What is the 2D Fourier Transform of this function?

$f(x, y) = \begin{cases} 1,\hspace{30px} x > 0 \\ 0,\hspace{30px} else\\ \end{cases}$

i.e. $f(x,y)$ is a bi-variate function which is zero everywhere to the left of the y-axis and one everywhere to the right of the y-axis.

• Can you show us what you did so far? – jojek Feb 28 '15 at 17:56
• So far, I applied the standard formula for 2D Fourier Transform with the bounds on integrals for dy going from negative infinity to positive infinity and for dx going from 0 to positive infinity. However, when I evaluated the integrals, the answer I got was infinity. – user1832413 Feb 28 '15 at 18:02
• Can you write f(x,y) as g(x)h(y), for simple functions g & h? Then you just need to compute two simple 1D Fourier transforms that should be in any table of transforms. – lp251 Feb 28 '15 at 18:55
• Try looking at this for the 1D case and see if that helps. – Peter K. Feb 28 '15 at 20:06
• Also, this is the answer wolframalpha.com/input/?i=Fourier+transform+[Piecewise[{{1%2Cx%3E0}%2C{0%2C+x%3C%3D0}}]] – sav Mar 1 '15 at 5:50