Question on 2-D Convolution This was a question on one of my past year paper questions.


  Question:  Prove
  
  $$f(m,n)*g(m-r,n-s) = f(m-r,n-s) *g(m,n)$$
  
  where $f(m,n)$ and $g(m,n)$ are 2-D discrete functions, $r$ and $s$
  are integers and $*$ is the 2-D convolution operator.


Not sure how to start on this and need some guidance on it.
In addition to the above comment:

Show that the 2D Z-transforms of both sides are equal. 

Step-by-step: If $F(z_1, z_2)$ is the 2D Z-transform of $f(m,n)$, then what is the 2D Z-transform of 


$f(m-r, n)$?
$f(m-r, n-s)$?
$f(m, n) * g(m, n)$?
$f(m-r, n-s) * g(m, n)$?


(Yes, I realize that the 2D Z-transform may not be taught before this exam was presented, but it is a valid solution, nonetheless.)