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How to convert Wiener filter formulas from integral to sum? They are for images therefore it must be possible to convert them to sums. Any help will be appreciated:

I could not find much info on this online as my integral is from $\infty$ to $-\infty$. For example how would you convert the following?

$\int\limits_{-\infty}^{\infty}f(r)[x(t-r)+ y(t - r)]\;dr$

And is it basically changing all the occurrences of $r$ or each conversion requires extensive computation?

How would you go about double integrals? Is it just another summation added? (with it's limit)

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  • $\begingroup$ What are $f$, $x$ and $y$? $\endgroup$ – 5xum May 4 '15 at 13:43
  • $\begingroup$ $f$ ,$x$ and $y$ are shift-invariant functions. Is their definition necessary for conversion? $\endgroup$ – Arijoon May 4 '15 at 13:50
  • $\begingroup$ their definition is important to understand what you are trying to do. I still don't, for example. What does the sentence "They are for images therefore it must be possible to convert them to sums" even mean? $\endgroup$ – 5xum May 4 '15 at 13:52
  • $\begingroup$ The integral operates on an image, (Wiener filter for image deblurring), and images have a finite set of pixels. Therefore it should be possible to use $\sum$ instead of integral $\endgroup$ – Arijoon May 4 '15 at 13:55

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