Consider a linear filter whose impulse response is the

Question

Consider a linear filter whose impulse response is the second derivative of the Gaussian kernel exp( -x 2/2a 2). Show that, regardless of the value of a, the response of this filter to an edge modeled by a step function, is a signal whose zero-crossing is at the location of the edge. Generalize this result in two dimensions by considering the Laplacian of the Gaussian kernel exp[ - (x² + y²)2σ²