# How to convert infinite intergral to sum

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)

• What are $f$, $x$ and $y$? – 5xum May 4 '15 at 13:43
• $f$ ,$x$ and $y$ are shift-invariant functions. Is their definition necessary for conversion? – Arijoon May 4 '15 at 13:50
• 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? – 5xum May 4 '15 at 13:52
• 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 – Arijoon May 4 '15 at 13:55