Spatial domain to frequency domain

Question

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...

1. 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?

Answer 1

This is not a programming question but a math / signal processing question. Try to represent your space functions with dirac function.

Then you have to recognise some well known Fourier transform.