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To be fair you can implement any function over a finite domain using a sufficiently large lookup table.

The OP seems weird - it's clearly a beginner asking, but the answers assume an understanding of spatial frequency and Fourier transforms. I think it would be more intuitive to explain in terms of convolutions with small kernels.

Really? For my money cool would be something like http://www.graficaobscura.com/interp/

That's great, both conceptually and from an ease-of-implementation perspective. Somehow I've never encountered that work, thanks for pointing it out!

You need the if statements and nonlinear math to create the look-up tables.

Not to create the lookup table in the example.

And I love reading about applications of linear algebra like this. Makes me want to write my own image processing algorithms as practice.