$ 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.

  • $\begingroup$ Can you show us what you did so far? $\endgroup$ – jojek Feb 28 '15 at 17:56
  • $\begingroup$ 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. $\endgroup$ – user1832413 Feb 28 '15 at 18:02
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    $\begingroup$ 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. $\endgroup$ – lp251 Feb 28 '15 at 18:55
  • $\begingroup$ Try looking at this for the 1D case and see if that helps. $\endgroup$ – Peter K. Feb 28 '15 at 20:06
  • $\begingroup$ Also, this is the answer wolframalpha.com/input/?i=Fourier+transform+[Piecewise[{{1%2Cx%3E0}%2C{0%2C+x%3C%3D0}}]] $\endgroup$ – sav Mar 1 '15 at 5:50

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