The two-dimensional Fourier transform of a function $f(t, s)$ is given by
\[
F(\omega, \theta)=\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} f(t, s) \exp (-j \omega t) \exp (-j \theta s) d t d s .
\]
Let $\delta(t)$ be the delta function and let $u(t)=0$ for $t<0$ and $u(t)=1$ for $t \geq 0$. If the Fourier transform is $F(\omega, \theta)=\delta(\omega-\theta) /(j \omega+1)$, then $f(t, s)$ equals a constant multiple of
- $\exp (-(t-s)) u(t-s)$
- $\exp (-(t+s)) u(t+s)$
- $\exp (-t) u(t) \delta(s)$
- $\exp (-t) \delta(t+s)$
- None of the above