Before revision: This gives the 2D impulse the sifting property (which is implied in the equation above), which says that when the 2D impulse function, δ(x − u,y − v), is integrated against any other continuous function, , it "sifts out" the value of f at the location of the impulse, i.e., at the point .
After revision: This gives the 2D impulse the shifting property (which is implied in the equation above), which says that when the 2D impulse function, δ(x − u,y − v), is integrated against any other continuous function, , it "sifts out" the value of f at the location of the impulse, i.e., at the point .