I know about Fourier Transforms, but I don't know how to apply it here, and I think that is over the top. I gave my ideas of the responses, but I really don't know what I'm looking for...
Supposed that you form a low-pass spatial filter h(x,y) that averages all the eight immediate neighbors of a pixel (x,y) but excludes itself.
a. Find the equivalent frequency domain filter H(u,v):
My answer is to (a):
1/8*H(u-1, v-1) + 1/8*H(u-1, v) + 1/8*H(u-1, v+1) +
1/8*H(u, v-1) + 0 + 1/8*H(u, v+1) +
1/8*H(u+1, v-1) + 1/8*H(u+1, v) + 1/8*H(u-1, v-1)
is this the frequency domain?
b. Show that your result is again a low-pass filter.
does this have to do with the coefficients being positive?