(a) [6 points] Let f(x,y) be an image. Let h(x,y) be the image obtained by applying the a 3 by 3 spatial low pass mask (averaging filter) to f(x,y). Similarly let g(x,y) be the image obtained by applying a 3 by 3 spatial high pass mask to f(x,y). Prove that

g(x,y) = f(x,y) - h(x,y)

Note: one or more examples do not constitute a proof.

(b) [5 points] Is the high pass mask separable? What is the implication of separability on computations?