Translation transform

If we define translation transform by T(Xo,yo)f(x , y) := f ( x — xq, ij — yo), (*0, yo) € Z 2, obviously we have P j T ^ ^ ) = So we arrive at

(T (x0,yo)f)o(x,y) = fo{x - x 0, y - y0) = ^ 47,2 ^ 7 , 2 ^ ~ X^ V ~ Vo) k 1 ,A?2