9/14/2001
CS 461, Copyright G.D. Hager
Understanding Convolution
•Another way to think about convolution is in terms of how it changes the frequency distribution in the image.
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•Recall the fourier representation of a function
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–F(u) = s f(x) e-2p i u x dx
–recall that e-2p i u x = cos(2p u x) – i sin (2 p u x)
–Also we have f(x) = s F(u) e-2p i u x du
–F(u) = |F(u)| ei F(u)
•a decomposition into magnitude and phase
–|F(u)|^2 is the power spectrum
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•Questions: what function takes many many many terms in the Fourier expansion?