Spatial domain to frequency domain

Posted by John Elway on Stack Overflow See other posts from Stack Overflow or by John Elway
Published on 2010-05-26T07:32:56Z Indexed on 2010/05/26 12:11 UTC
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homework

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filter

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spatial

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frequency

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?

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