In digital image processing, first-order derivatives can be approximated by the spatial differences g_x=(f(x, y)_x)=f(x+1,y)-f(x, y) and g_y=(f(x, y)/y)=f(x, y+1)-f(x, y).

a. Find the equivalent filter transfer functions Hx(u, v) and Hy(u, v) in the frequency domain.

b. Show that these are highpass filter transfer functions. (Hint: Study the solution to Problem 4.51 U.)

Transcribed image text