With respect to the dirac delta function, what does $\delta [x + 2A, y - A]$ I have come across the following function and I'm trying to figure out what it really is.  I have this function:

$f[x, y] = \delta [x + 2A, y - A] - \delta [x - A, y + A]$.  The $\delta$ is representative of the dirac delta function.  This function is used as input to some finite impulse response filter.  

What does this function really mean?  Is the first part of the function 0 everywhere except $-2A, A$ and the second part 0 everywhere except $A, -A$ ?
A (two-dimensional) finite-impulse-response filter has an impulse response $g(x,y)$ 
that is nonzero only for $(x,y)$ in a region of finite area (continuous parameters) 
of for a finite number of values of $x$ and $y$ (discrete parameter). For example,
$g(x,y)$ might be nonzero only for points inside a circle of radius $r$.  Specifically,
consider
$$g(x,y) = \begin{cases}1, &amp;x^2 + y^2 \leq r^2,\\0, &amp;\text{otherwise}\end{cases}$$
describes an image filter whose response to a point source (impulse function)
at the origin is a disc of radius $r$ in the filtered image.  For input $f(x,y) = \delta (x + 2A, y - A) - \delta (x - A, y + A)$, the filter output would be the sum of a positive
disc centered at $(-2A,A)$ and a negative disc centered at $(A,-A)$ with cancellation
occurring where the discs overlapped. (Disc ovrlap would be determined by the
relationship between $A$ and $r$). More formally,
$$g(x,y)\circledast f(x,y) = \begin{cases}
1, &amp;(x+2A)^2 + (y-A)^2 \leq r^2, (x-A)^2+(y+A)^2 &gt; r^2,\\
-1, &amp;(x+2A)^2 + (y-A)^2 &gt; r^2, (x-A)^2+(y+A)^2 \leq r^2,\\
0, &amp;\text{otherwise.}\end{cases}$$
where we have combined the outer darkness of $0$ with the $0$ produced
by the cancellation of the discs in the region of overlap (if any).

Similar calculations can be done for the discrete case as well.